<?xml version="1.0" encoding="UTF-8"?>
  <?xml-stylesheet type="text/xsl" href="rfc2629.xslt" ?>
  <!-- generated by https://github.com/cabo/kramdown-rfc2629 version 1.5.24 -->

<!DOCTYPE rfc SYSTEM "rfc2629.dtd" [
]>


<rfc ipr="trust200902" docName="draft-ietf-openpgp-crypto-refresh-05" category="std" consensus="true" obsoletes="4880, 5581, 6637" tocDepth="4" tocInclude="true" sortRefs="true" symRefs="true">
  <front>
    <title>OpenPGP Message Format</title>

    <author initials="W." surname="Koch" fullname="Werner Koch" role="editor">
      <organization>GnuPG e.V.</organization>
      <address>
        <postal>
          <street>Rochusstr. 44</street>
          <city>Duesseldorf</city>
          <code>40479</code>
          <country>Germany</country>
        </postal>
        <email>wk@gnupg.org</email>
        <uri>https://gnupg.org/verein</uri>
      </address>
    </author>
    <author initials="P." surname="Wouters" fullname="Paul Wouters" role="editor">
      <organization>Aiven</organization>
      <address>
        <email>paul.wouters@aiven.io</email>
      </address>
    </author>

    <date year="2022" month="March" day="07"/>

    <area>sec</area>
    <workgroup>Network Working Group</workgroup>
    <keyword>Internet-Draft</keyword>

    <abstract>


<t>This document specifies the message formats used in OpenPGP.
OpenPGP provides encryption with public-key or symmetric cryptographic algorithms, digital signatures, compression and key management.</t>

<t>This document is maintained in order to publish all necessary information needed to develop interoperable applications based on the OpenPGP format.
It is not a step-by-step cookbook for writing an application.
It describes only the format and methods needed to read, check, generate, and write conforming packets crossing any network.
It does not deal with storage and implementation questions.
It does, however, discuss implementation issues necessary to avoid security flaws.</t>

<t>This document obsoletes: RFC 4880 (OpenPGP), RFC 5581 (Camellia in OpenPGP) and RFC 6637 (Elliptic Curves in OpenPGP).</t>



    </abstract>



  </front>

  <middle>


<section anchor="introduction"><name>Introduction</name>

<t>This document provides information on the message-exchange packet formats used by OpenPGP to provide encryption, decryption, signing, and key management functions.
It is a revision of RFC 4880, "OpenPGP Message Format", which is a revision of RFC 2440, which itself replaces RFC 1991, "PGP Message Exchange Formats" <xref target="RFC1991"/> <xref target="RFC2440"/> <xref target="RFC4880"/>.</t>

<t>This document obsoletes: RFC 4880 (OpenPGP), RFC 5581 (Camellia in OpenPGP) and RFC 6637 (Elliptic Curves in OpenPGP).</t>

<section anchor="terms"><name>Terms</name>

<t><list style="symbols">
  <t>OpenPGP - This is a term for security software that uses PGP 5 as a basis, formalized in this document.</t>
  <t>PGP - Pretty Good Privacy.
PGP is a family of software systems developed by Philip R. Zimmermann from which OpenPGP is based.</t>
  <t>PGP 2 - This version of PGP has many variants; where necessary a more detailed version number is used here.
PGP 2 uses only RSA, MD5, and IDEA for its cryptographic transforms.
An informational RFC, RFC 1991, was written describing this version of PGP.</t>
  <t>PGP 5 - This version of PGP is formerly known as "PGP 3" in the community.
It has new formats and corrects a number of problems in the PGP 2 design.
It is referred to here as PGP 5 because that software was the first release of the "PGP 3" code base.</t>
  <t>GnuPG - GNU Privacy Guard, also called GPG.
GnuPG is an OpenPGP implementation that avoids all encumbered algorithms.
Consequently, early versions of GnuPG did not include RSA public keys.</t>
</list></t>

<t>"PGP", "Pretty Good", and "Pretty Good Privacy" are trademarks of PGP Corporation and are used with permission.
The term "OpenPGP" refers to the protocol described in this and related documents.</t>

<t>The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and only when, they appear in all capitals, as shown here.</t>

<t>The key words "PRIVATE USE", "SPECIFICATION REQUIRED", and "RFC REQUIRED" that appear in this document when used to describe namespace allocation are to be interpreted as described in <xref target="RFC8126"/>.</t>

</section>
</section>
<section anchor="general-functions"><name>General functions</name>

<t>OpenPGP provides data integrity services for messages and data files by using these core technologies:</t>

<t><list style="symbols">
  <t>digital signatures</t>
  <t>encryption</t>
  <t>compression</t>
  <t>Radix-64 conversion</t>
</list></t>

<t>In addition, OpenPGP provides key management and certificate services, but many of these are beyond the scope of this document.</t>

<section anchor="confidentiality-via-encryption"><name>Confidentiality via Encryption</name>

<t>OpenPGP combines symmetric-key encryption and public-key encryption to provide confidentiality.
When made confidential, first the object is encrypted using a symmetric encryption algorithm.
Each symmetric key is used only once, for a single object.
A new "session key" is generated as a random number for each object (sometimes referred to as a session).
Since it is used only once, the session key is bound to the message and transmitted with it.
To protect the key, it is encrypted with the receiver's public key.
The sequence is as follows:</t>

<t><list style="numbers">
  <t>The sender creates a message.</t>
  <t>The sending OpenPGP generates a random number to be used as a session key for this message only.</t>
  <t>The session key is encrypted using each recipient's public key.
These "encrypted session keys" start the message.</t>
  <t>The sending OpenPGP encrypts the message using the session key, which forms the remainder of the message.</t>
  <t>The receiving OpenPGP decrypts the session key using the recipient's private key.</t>
  <t>The receiving OpenPGP decrypts the message using the session key.
If the message was compressed, it will be decompressed.</t>
</list></t>

<t>With symmetric-key encryption, an object may be encrypted with a symmetric key derived from a passphrase (or other shared secret), or a two-stage mechanism similar to the public-key method described above in which a session key is itself encrypted with a symmetric algorithm keyed from a shared secret.</t>

<t>Both digital signature and confidentiality services may be applied to the same message.
First, a signature is generated for the message and attached to the message.
Then the message plus signature is encrypted using a symmetric session key.
Finally, the session key is encrypted using public-key encryption and prefixed to the encrypted block.</t>

</section>
<section anchor="authentication-via-digital-signature"><name>Authentication via Digital Signature</name>

<t>The digital signature uses a hash code or message digest algorithm, and a public-key signature algorithm.
The sequence is as follows:</t>

<t><list style="numbers">
  <t>The sender creates a message.</t>
  <t>The sending software generates a hash code of the message.</t>
  <t>The sending software generates a signature from the hash code using the sender's private key.</t>
  <t>The binary signature is attached to the message.</t>
  <t>The receiving software keeps a copy of the message signature.</t>
  <t>The receiving software generates a new hash code for the received message and verifies it using the message's signature.
If the verification is successful, the message is accepted as authentic.</t>
</list></t>

</section>
<section anchor="compression"><name>Compression</name>

<t>If an implementation does not implement compression, its authors should be aware that most OpenPGP messages in the world are compressed.
Thus, it may even be wise for a space-constrained implementation to implement decompression, but not compression.</t>

</section>
<section anchor="conversion-to-radix-64"><name>Conversion to Radix-64</name>

<t>OpenPGP's underlying native representation for encrypted messages, signature certificates, and keys is a stream of arbitrary octets.
Some systems only permit the use of blocks consisting of seven-bit, printable text.
For transporting OpenPGP's native raw binary octets through channels that are not safe to raw binary data, a printable encoding of these binary octets is needed.
OpenPGP provides the service of converting the raw 8-bit binary octet stream to a stream of printable ASCII characters, called Radix-64 encoding or ASCII Armor.</t>

<t>Implementations SHOULD provide Radix-64 conversions.</t>

</section>
<section anchor="signature-only-applications"><name>Signature-Only Applications</name>

<t>OpenPGP is designed for applications that use both encryption and signatures, but there are a number of problems that are solved by a signature-only implementation.
Although this specification requires both encryption and signatures, it is reasonable for there to be subset implementations that are non-conformant only in that they omit encryption.</t>

</section>
</section>
<section anchor="data-element-formats"><name>Data Element Formats</name>

<t>This section describes the data elements used by OpenPGP.</t>

<section anchor="scalar-numbers"><name>Scalar Numbers</name>

<t>Scalar numbers are unsigned and are always stored in big-endian format.
Using n[k] to refer to the kth octet being interpreted, the value of a two-octet scalar is ((n[0] &lt;&lt; 8) + n[1]).
The value of a four-octet scalar is ((n[0] &lt;&lt; 24) + (n[1] &lt;&lt; 16) + (n[2] &lt;&lt; 8) + n[3]).</t>

</section>
<section anchor="mpi"><name>Multiprecision Integers</name>

<t>Multiprecision integers (also called MPIs) are unsigned integers used to hold large integers such as the ones used in cryptographic calculations.</t>

<t>An MPI consists of two pieces: a two-octet scalar that is the length of the MPI in bits followed by a string of octets that contain the actual integer.</t>

<t>These octets form a big-endian number; a big-endian number can be made into an MPI by prefixing it with the appropriate length.</t>

<t>Examples:</t>

<t>(all numbers are in hexadecimal)</t>

<t>The string of octets [00 01 01] forms an MPI with the value 1.
The string [00 09 01 FF] forms an MPI with the value of 511.</t>

<t>Additional rules:</t>

<t>The size of an MPI is ((MPI.length + 7) / 8) + 2 octets.</t>

<t>The length field of an MPI describes the length starting from its most significant non-zero bit.
Thus, the MPI [00 02 01] is not formed correctly.
It should be [00 01 01].</t>

<t>Unused bits of an MPI MUST be zero.</t>

<t>Also note that when an MPI is encrypted, the length refers to the plaintext MPI.
It may be ill-formed in its ciphertext.</t>

<section anchor="using-mpis-to-encode-other-data"><name>Using MPIs to encode other data</name>

<t>Note that MPIs are used in some places used to encode non-integer data, such as an elliptic curve point (see <xref target="ec-point-wire-formats"/>, or an octet string of known, fixed length (see <xref target="ec-scalar-wire-formats"/>).
The wire representation is the same: two octets of length in bits counted from the first non-zero bit, followed by the smallest series of octets that can represent the value while stripping off any leading zero octets.</t>

</section>
</section>
<section anchor="key-ids"><name>Key IDs</name>

<t>A Key ID is an eight-octet scalar that identifies a key.
Implementations SHOULD NOT assume that Key IDs are unique.
<xref target="key-ids-fingerprints"/> describes how Key IDs are formed.</t>

</section>
<section anchor="text"><name>Text</name>

<t>Unless otherwise specified, the character set for text is the UTF-8 <xref target="RFC3629"/> encoding of Unicode <xref target="ISO10646"/>.</t>

</section>
<section anchor="time-fields"><name>Time Fields</name>

<t>A time field is an unsigned four-octet number containing the number of seconds elapsed since midnight, 1 January 1970 UTC.</t>

</section>
<section anchor="keyrings"><name>Keyrings</name>

<t>A keyring is a collection of one or more keys in a file or database.
Traditionally, a keyring is simply a sequential list of keys, but may be any suitable database.
It is beyond the scope of this standard to discuss the details of keyrings or other databases.</t>

</section>
<section anchor="string-to-key-s2k-specifiers"><name>String-to-Key (S2K) Specifiers</name>

<t>A string-to-key (S2K) specifier is used to convert a passphrase string into a symmetric-key encryption/decryption key.
They are used in two places, currently: to encrypt the secret part of private keys in the private keyring, and to convert passphrases to encryption keys for symmetrically encrypted messages.</t>

<section anchor="s2k-types"><name>String-to-Key (S2K) Specifier Types</name>

<t>There are four types of S2K specifiers currently supported, and some reserved values:</t>

<texttable title="S2K type registry">
      <ttcol align='right'>ID</ttcol>
      <ttcol align='left'>S2K Type</ttcol>
      <ttcol align='left'>Generate?</ttcol>
      <ttcol align='left'>S2K field size (octets)</ttcol>
      <ttcol align='left'>Reference</ttcol>
      <c>0</c>
      <c>Simple S2K</c>
      <c>N</c>
      <c>2</c>
      <c><xref target="s2k-simple"/></c>
      <c>1</c>
      <c>Salted S2K</c>
      <c>Only when string is high entropy</c>
      <c>10</c>
      <c><xref target="s2k-salted"/></c>
      <c>2</c>
      <c>Reserved value</c>
      <c>N</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>3</c>
      <c>Iterated and Salted S2K</c>
      <c>Y</c>
      <c>11</c>
      <c><xref target="s2k-iter-salted"/></c>
      <c>4</c>
      <c>Argon2</c>
      <c>Y</c>
      <c>20</c>
      <c><xref target="s2k-argon2"/></c>
      <c>100 to 110</c>
      <c>Private/Experimental S2K</c>
      <c>As appropriate</c>
      <c>&#160;</c>
      <c>&#160;</c>
</texttable>

<t>These are described in the subsections below.</t>

<section anchor="s2k-simple"><name>Simple S2K</name>

<t>This directly hashes the string to produce the key data.
See below for how this hashing is done.</t>

<figure><artwork><![CDATA[
  Octet 0:        0x00
  Octet 1:        hash algorithm
]]></artwork></figure>

<t>Simple S2K hashes the passphrase to produce the session key.
The manner in which this is done depends on the size of the session key (which will depend on the cipher used) and the size of the hash algorithm's output.
If the hash size is greater than the session key size, the high-order (leftmost) octets of the hash are used as the key.</t>

<t>If the hash size is less than the key size, multiple instances of the hash context are created --- enough to produce the required key data.
These instances are preloaded with 0, 1, 2, ...
octets of zeros (that is to say, the first instance has no preloading, the second gets preloaded with 1 octet of zero, the third is preloaded with two octets of zeros, and so forth).</t>

<t>As the data is hashed, it is given independently to each hash context.
Since the contexts have been initialized differently, they will each produce different hash output.
Once the passphrase is hashed, the output data from the multiple hashes is concatenated, first hash leftmost, to produce the key data, with any excess octets on the right discarded.</t>

</section>
<section anchor="s2k-salted"><name>Salted S2K</name>

<t>This includes a "salt" value in the S2K specifier --- some arbitrary data --- that gets hashed along with the passphrase string, to help prevent dictionary attacks.</t>

<figure><artwork><![CDATA[
  Octet 0:        0x01
  Octet 1:        hash algorithm
  Octets 2-9:     8-octet salt value
]]></artwork></figure>

<t>Salted S2K is exactly like Simple S2K, except that the input to the hash function(s) consists of the 8 octets of salt from the S2K specifier, followed by the passphrase.</t>

</section>
<section anchor="s2k-iter-salted"><name>Iterated and Salted S2K</name>

<t>This includes both a salt and an octet count.
The salt is combined with the passphrase and the resulting value is hashed repeatedly.
This further increases the amount of work an attacker must do to try dictionary attacks.</t>

<figure><artwork><![CDATA[
  Octet  0:        0x03
  Octet  1:        hash algorithm
  Octets 2-9:      8-octet salt value
  Octet  10:       count, a one-octet, coded value
]]></artwork></figure>

<t>The count is coded into a one-octet number using the following formula:</t>

<figure><artwork><![CDATA[
  #define EXPBIAS 6
      count = ((Int32)16 + (c & 15)) << ((c >> 4) + EXPBIAS);
]]></artwork></figure>

<t>The above formula is in C, where "Int32" is a type for a 32-bit integer, and the variable "c" is the coded count, Octet 10.</t>

<t>Iterated-Salted S2K hashes the passphrase and salt data multiple times.
The total number of octets to be hashed is specified in the encoded count in the S2K specifier.
Note that the resulting count value is an octet count of how many octets will be hashed, not an iteration count.</t>

<t>Initially, one or more hash contexts are set up as with the other S2K algorithms, depending on how many octets of key data are needed.
Then the salt, followed by the passphrase data, is repeatedly hashed until the number of octets specified by the octet count has been hashed.
The one exception is that if the octet count is less than the size of the salt plus passphrase, the full salt plus passphrase will be hashed even though that is greater than the octet count.
After the hashing is done, the data is unloaded from the hash context(s) as with the other S2K algorithms.</t>

</section>
<section anchor="s2k-argon2"><name>Argon2</name>

<t>This S2K method hashes the passphrase using Argon2, specified in <xref target="RFC9106"/>.
This provides memory-hardness, further protecting the passphrase against brute-force attacks.</t>

<figure><artwork><![CDATA[
  Octet  0:        0x04
  Octets 1-16:     16-octet salt value
  Octet  17:       one-octet number of passes t
  Octet  18:       one-octet degree of parallelism p
  Octet  19:       one-octet exponent indicating the memory size m
]]></artwork></figure>

<t>The salt SHOULD be unique for each password.</t>

<t>The number of passes t and the degree of parallelism p MUST be non-zero.</t>

<t>The memory size m is 2**encoded_m kibibytes of RAM, where "encoded_m" is the encoded memory size in Octet 19.
The encoded memory size MUST be a value from 3+ceil(log_2(p)) to 31, such that the decoded memory size m is a value from 8*p to 2**31.
Note that memory-hardness size is indicated in kibibytes (KiB), not octets.</t>

<t>Argon2 is invoked with the passphrase as P, the salt as S, the values of t, p and m as described above, the required key size as the tag length T, 0x13 as the version v, and Argon2id as the type.</t>

<t>For the recommended values of t, p and m, see Section 4 of <xref target="RFC9106"/>.
If the recommended value of m for a given application is not a power of 2, it is RECOMMENDED to round up to the next power of 2 if the resulting performance would be acceptable, and round down otherwise (keeping in mind that m must be at least 8*p).</t>

<t>As an example, with the first recommended option (t=1, p=4, m=2**21), the full S2K specifier would be:</t>

<figure><artwork><![CDATA[
  04 XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX
  XX 01 04 15
]]></artwork></figure>

<t>(where XX represents a random octet of salt).</t>

</section>
</section>
<section anchor="string-to-key-usage"><name>String-to-Key Usage</name>

<t>Simple S2K and Salted S2K specifiers can be brute-forced when used with a low-entropy string, such as those typically provided by users.
In addition, the usage of Simple S2K can lead to key and IV reuse (see <xref target="skesk"/>).
Therefore, when generating S2K specifiers, implementations MUST NOT use Simple S2K, and SHOULD NOT use Salted S2K unless the implementation knows that the string is high-entropy (for example, it generated the string itself using a known-good source of randomness).
It is RECOMMENDED that implementations use Argon2.</t>

<section anchor="secret-key-encryption"><name>Secret-Key Encryption</name>

<t>An S2K specifier can be stored in the secret keyring to specify how to convert the passphrase to a key that unlocks the secret data.
Older versions of PGP just stored a symmetric cipher algorithm octet preceding the secret data or a zero to indicate that the secret data was unencrypted.
The MD5 hash function was always used to convert the passphrase to a key for the specified cipher algorithm.</t>

<t>For compatibility, when an S2K specifier is used, the special value 253, 254, or 255 is stored in the position where the cipher algorithm octet would have been in the old data structure.
This is then followed immediately by a one-octet algorithm identifier, and other fields relevant to the type of encryption used.</t>

<t>Therefore, the first octet of the secret key material describes how the secret key data is presented.</t>

<t>In the table below, <spanx style="verb">check(x)</spanx> means the "2-octet checksum" meaning the sum of all octets in x mod 65536.</t>

<texttable title="Secret Key protection details" anchor="secret-key-protection-details">
      <ttcol align='left'>First octet</ttcol>
      <ttcol align='left'>Next fields</ttcol>
      <ttcol align='left'>Encryption</ttcol>
      <ttcol align='left'>Generate?</ttcol>
      <c>0</c>
      <c>-</c>
      <c>cleartext secrets || check(secrets)</c>
      <c>Yes</c>
      <c>Known symmetric cipher algo ID (see <xref target="symmetric-algos"/>)</c>
      <c>IV</c>
      <c>CFB(MD5(password), secrets || check(secrets))</c>
      <c>No</c>
      <c>253</c>
      <c>cipher-algo, AEAD-mode, S2K-specifier, nonce</c>
      <c>AEAD(S2K(password), secrets, pubkey)</c>
      <c>Yes</c>
      <c>254</c>
      <c>cipher-algo, S2K-specifier, IV</c>
      <c>CFB(S2K(password), secrets || SHA1(secrets))</c>
      <c>Yes</c>
      <c>255</c>
      <c>cipher-algo, S2K-specifier, IV</c>
      <c>CFB(S2K(password), secrets || check(secrets))</c>
      <c>No</c>
</texttable>

<t>Each row with "Generate?" marked as "No" is described for backward compatibility, and MUST NOT be generated.</t>

<t>An implementation MUST NOT create and MUST reject as malformed a secret key packet where the S2K usage octet is anything but 253 and the S2K specifier type is Argon2.</t>

</section>
<section anchor="symmetric-key-message-encryption"><name>Symmetric-Key Message Encryption</name>

<t>OpenPGP can create a Symmetric-key Encrypted Session Key (ESK) packet at the front of a message.
This is used to allow S2K specifiers to be used for the passphrase conversion or to create messages with a mix of symmetric-key ESKs and public-key ESKs.
This allows a message to be decrypted either with a passphrase or a public-key pair.</t>

<t>PGP 2 always used IDEA with Simple string-to-key conversion when encrypting a message with a symmetric algorithm.
See <xref target="sed"/>.
This MUST NOT be generated, but MAY be consumed for backward-compatibility.</t>

</section>
</section>
</section>
</section>
<section anchor="packet-syntax"><name>Packet Syntax</name>

<t>This section describes the packets used by OpenPGP.</t>

<section anchor="overview"><name>Overview</name>

<t>An OpenPGP message is constructed from a number of records that are traditionally called packets.
A packet is a chunk of data that has a tag specifying its meaning.
An OpenPGP message, keyring, certificate, and so forth consists of a number of packets.
Some of those packets may contain other OpenPGP packets (for example, a compressed data packet, when uncompressed, contains OpenPGP packets).</t>

<t>Each packet consists of a packet header, followed by the packet body.
The packet header is of variable length.</t>

<t>When handling a stream of packets, the length information in each packet header is the canonical source of packet boundaries.
An implementation handling a packet stream that wants to find the next packet MUST look for it at the precise offset indicated in the previous packet header.</t>

<t>Additionally, some packets contain internal length indicators (for example, a subfield within the packet).
In the event that a subfield length indicator within a packet implies inclusion of octets outside the range indicated in the packet header, a parser MUST truncate the subfield at the octet boundary indicated in the packet header.
Such a truncation renders the packet malformed and unusable.
An implementation MUST NOT interpret octets outside the range indicated in the packet header as part of the contents of the packet.</t>

</section>
<section anchor="packet-headers"><name>Packet Headers</name>

<t>The first octet of the packet header is called the "Packet Tag".
It determines the format of the header and denotes the packet contents.
The remainder of the packet header is the length of the packet.</t>

<t>There are two packet formats, the (current) OpenPGP packet format specified by this document and its predecessors and the Legacy packet format as used by PGP 2.x implementations.</t>

<t>Note that the most significant bit is the leftmost bit, called bit 7.
A mask for this bit is 0x80 in hexadecimal.</t>

<figure><artwork><![CDATA[
       ┌───────────────┐
  PTag │7 6 5 4 3 2 1 0│
       └───────────────┘
  Bit 7 -- Always one
  Bit 6 -- Always one (except for Legacy packet format)
]]></artwork></figure>

<t>The Legacy packet format MAY be used when consuming packets to facilitate interoperability with legacy implementations and accessing archived data.
The Legacy packet format SHOULD NOT be used to generate new data, unless the recipient is known to only support the Legacy packet format.</t>

<t>An implementation that consumes and re-distributes pre-existing OpenPGP data (such as Transferable Public Keys) may encounter packets framed with the Legacy packet format.
Such an implementation MAY either re-distribute these packets in their Legacy format, or transform them to the current OpenPGP packet format before re-distribution.</t>

<t>The current OpenPGP packet format packets contain:</t>

<figure><artwork><![CDATA[
  Bits 5 to 0 -- packet tag
]]></artwork></figure>

<t>Legacy packet format packets contain:</t>

<figure><artwork><![CDATA[
  Bits 5 to 2 -- packet tag
  Bits 1 to 0 -- length-type
]]></artwork></figure>

<section anchor="openpgp-packet-format"><name>OpenPGP Format Packet Lengths</name>

<t>OpenPGP format packets have four possible ways of encoding length:</t>

<t><list style="numbers">
  <t>A one-octet Body Length header encodes packet lengths of up to 191 octets.</t>
  <t>A two-octet Body Length header encodes packet lengths of 192 to 8383 octets.</t>
  <t>A five-octet Body Length header encodes packet lengths of up to 4,294,967,295 (0xFFFFFFFF) octets in length.
(This actually encodes a four-octet scalar number.)</t>
  <t>When the length of the packet body is not known in advance by the issuer, Partial Body Length headers encode a packet of indeterminate length, effectively making it a stream.</t>
</list></t>

<section anchor="one-octet-lengths"><name>One-Octet Lengths</name>

<t>A one-octet Body Length header encodes a length of 0 to 191 octets.
This type of length header is recognized because the one octet value is less than 192.
The body length is equal to:</t>

<figure><artwork><![CDATA[
  bodyLen = 1st_octet;
]]></artwork></figure>

</section>
<section anchor="two-octet-lengths"><name>Two-Octet Lengths</name>

<t>A two-octet Body Length header encodes a length of 192 to 8383 octets.
It is recognized because its first octet is in the range 192 to 223.
The body length is equal to:</t>

<figure><artwork><![CDATA[
  bodyLen = ((1st_octet - 192) << 8) + (2nd_octet) + 192
]]></artwork></figure>

</section>
<section anchor="five-octet-lengths"><name>Five-Octet Lengths</name>

<t>A five-octet Body Length header consists of a single octet holding the value 255, followed by a four-octet scalar.
The body length is equal to:</t>

<figure><artwork><![CDATA[
  bodyLen = (2nd_octet << 24) | (3rd_octet << 16) |
            (4th_octet << 8)  | 5th_octet
]]></artwork></figure>

<t>This basic set of one, two, and five-octet lengths is also used internally to some packets.</t>

</section>
<section anchor="partial-body-lengths"><name>Partial Body Lengths</name>

<t>A Partial Body Length header is one octet long and encodes the length of only part of the data packet.
This length is a power of 2, from 1 to 1,073,741,824 (2 to the 30th power).
It is recognized by its one octet value that is greater than or equal to 224, and less than 255.
The Partial Body Length is equal to:</t>

<figure><artwork><![CDATA[
  partialBodyLen = 1 << (1st_octet & 0x1F);
]]></artwork></figure>

<t>Each Partial Body Length header is followed by a portion of the packet body data.
The Partial Body Length header specifies this portion's length.
Another length header (one octet, two-octet, five-octet, or partial) follows that portion.
The last length header in the packet MUST NOT be a Partial Body Length header.
Partial Body Length headers may only be used for the non-final parts of the packet.</t>

<t>Note also that the last Body Length header can be a zero-length header.</t>

<t>An implementation MAY use Partial Body Lengths for data packets, be they literal, compressed, or encrypted.
The first partial length MUST be at least 512 octets long.
Partial Body Lengths MUST NOT be used for any other packet types.</t>

</section>
</section>
<section anchor="legacy-packet-format"><name>Legacy Format Packet Lengths</name>

<t>The meaning of the length-type in Legacy format packets is:</t>

<dl>
  <dt>
0  </dt>
  <dd>
    <t>The packet has a one-octet length.
The header is 2 octets long.</t>
  </dd>
  <dt>
1  </dt>
  <dd>
    <t>The packet has a two-octet length.
The header is 3 octets long.</t>
  </dd>
  <dt>
2  </dt>
  <dd>
    <t>The packet has a four-octet length.
The header is 5 octets long.</t>
  </dd>
  <dt>
3  </dt>
  <dd>
    <t>The packet is of indeterminate length.
The header is 1 octet long, and the implementation must determine how long the packet is.
If the packet is in a file, this means that the packet extends until the end of the file.
The OpenPGP format headers have a mechanism for precisely encoding data of indeterminate length.
An implementation MUST NOT generate a Legacy format packet with indeterminate length.
An implementation MAY interpret an indeterminate length Legacy format packet in order to deal with historic data, or data generated by a legacy system.</t>
  </dd>
</dl>

</section>
<section anchor="packet-length-examples"><name>Packet Length Examples</name>

<t>These examples show ways that OpenPGP format packets might encode the packet lengths.</t>

<t>A packet with length 100 may have its length encoded in one octet: 0x64.
This is followed by 100 octets of data.</t>

<t>A packet with length 1723 may have its length encoded in two octets: 0xC5, 0xFB.
This header is followed by the 1723 octets of data.</t>

<t>A packet with length 100000 may have its length encoded in five octets: 0xFF, 0x00, 0x01, 0x86, 0xA0.</t>

<t>It might also be encoded in the following octet stream: 0xEF, first 32768 octets of data; 0xE1, next two octets of data; 0xE0, next one octet of data; 0xF0, next 65536 octets of data; 0xC5, 0xDD, last 1693 octets of data.
This is just one possible encoding, and many variations are possible on the size of the Partial Body Length headers, as long as a regular Body Length header encodes the last portion of the data.</t>

<t>Please note that in all of these explanations, the total length of the packet is the length of the header(s) plus the length of the body.</t>

</section>
</section>
<section anchor="packet-tags"><name>Packet Tags</name>

<t>The packet tag denotes what type of packet the body holds.
Note that Legacy format headers can only have tags less than 16, whereas OpenPGP format headers can have tags as great as 63.
The defined tags (in decimal) are as follows:</t>

<texttable title="Packet type registry">
      <ttcol align='right'>Tag</ttcol>
      <ttcol align='left'>Packet Type</ttcol>
      <c>0</c>
      <c>Reserved - a packet tag MUST NOT have this value</c>
      <c>1</c>
      <c>Public-Key Encrypted Session Key Packet</c>
      <c>2</c>
      <c>Signature Packet</c>
      <c>3</c>
      <c>Symmetric-Key Encrypted Session Key Packet</c>
      <c>4</c>
      <c>One-Pass Signature Packet</c>
      <c>5</c>
      <c>Secret-Key Packet</c>
      <c>6</c>
      <c>Public-Key Packet</c>
      <c>7</c>
      <c>Secret-Subkey Packet</c>
      <c>8</c>
      <c>Compressed Data Packet</c>
      <c>9</c>
      <c>Symmetrically Encrypted Data Packet</c>
      <c>10</c>
      <c>Marker Packet</c>
      <c>11</c>
      <c>Literal Data Packet</c>
      <c>12</c>
      <c>Trust Packet</c>
      <c>13</c>
      <c>User ID Packet</c>
      <c>14</c>
      <c>Public-Subkey Packet</c>
      <c>17</c>
      <c>User Attribute Packet</c>
      <c>18</c>
      <c>Sym. Encrypted and Integrity Protected Data Packet</c>
      <c>19</c>
      <c>Reserved (formerly Modification Detection Code Packet)</c>
      <c>20</c>
      <c>Reserved (formerly AEAD Encrypted Data Packet)</c>
      <c>21</c>
      <c>Padding Packet</c>
      <c>60 to 63</c>
      <c>Private or Experimental Values</c>
</texttable>

</section>
</section>
<section anchor="packet-types"><name>Packet Types</name>

<section anchor="pkesk"><name>Public-Key Encrypted Session Key Packets (Tag 1)</name>

<t>Zero or more Public-Key Encrypted Session Key (PKESK) packets and/or Symmetric-Key Encrypted Session Key packets (<xref target="skesk"/>) may precede an encryption container (that is, a Symmetrically Encrypted Integrity Protected Data packet or --- for historic data --- a Symmetrically Encrypted Data packet), which holds an encrypted message.
The message is encrypted with the session key, and the session key is itself encrypted and stored in the Encrypted Session Key packet(s).
The encryption container is preceded by one Public-Key Encrypted Session Key packet for each OpenPGP key to which the message is encrypted.
The recipient of the message finds a session key that is encrypted to their public key, decrypts the session key, and then uses the session key to decrypt the message.</t>

<t>The body of this packet starts with a one-octet number giving the version number of the packet type.
The currently defined versions are 3 and 5.
The remainder of the packet depends on the version.</t>

<t>The versions differ in how they identify the recipient key, and in what they encode.
The version of the PKESK packet must align with the version of the SEIPD packet (see <xref target="encrypted-message-versions"/>).</t>

<section anchor="v3-pkesk"><name>v3 PKESK</name>

<t>A version 3 Public-Key Encrypted Session Key (PKESK) packet precedes a version 1 Symmetrically Encrypted Integrity Protected Data (v1 SEIPD, see <xref target="version-one-seipd"/>) packet.
In historic data, it is sometimes found preceding a deprecated Symmetrically Encrypted Data packet (SED, see <xref target="sed"/>).
A v3 PKESK packet MUST NOT precede a v2 SEIPD packet (see <xref target="encrypted-message-versions"/>).</t>

<t>The v3 PKESK packet consists of:</t>

<t><list style="symbols">
  <t>A one-octet version number with value 3.</t>
  <t>An eight-octet number that gives the Key ID of the public key to which the session key is encrypted.
If the session key is encrypted to a subkey, then the Key ID of this subkey is used here instead of the Key ID of the primary key.
The Key ID may also be all zeros, for an "anonymous recipient" (see <xref target="pkesk-notes"/>).</t>
  <t>A one-octet number giving the public-key algorithm used.</t>
  <t>A series of values comprising the encrypted session key.
This is algorithm-specific and described below.</t>
</list></t>

<t>When creating a v3 PKESK packet, the session key is first prefixed with a one-octet algorithm identifier that specifies the symmetric encryption algorithm used to encrypt the following encryption container.
Then a two-octet checksum is appended, which is equal to the sum of the preceding session key octets, not including the algorithm identifier, modulo 65536.</t>

<t>The resulting octet string (algorithm identifier, session key, and checksum) is encrypted according to the public-key algorithm used, as described below.</t>

</section>
<section anchor="v5-pkesk"><name>v5 PKESK</name>

<t>A version 5 Public-Key Encrypted Session Key (PKESK) packet precedes a version 2 Symmetrically Encrypted Integrity Protected Data (v2 SEIPD, see <xref target="version-two-seipd"/>) packet.
A v5 PKESK packet MUST NOT precede a v1 SEIPD packet or a deprecated Symmetrically Encrypted Data packet (see <xref target="encrypted-message-versions"/>).</t>

<t>The v5 PKESK packet consists of:</t>

<t><list style="symbols">
  <t>A one-octet version number with value 5.</t>
  <t>A one octet key version number and N octets of the fingerprint of the public key or subkey to which the session key is encrypted.
Note that the length N of the fingerprint for a version 4 key is 20 octets; for a version 5 key N is 32.
The key version number may also be zero, and the fingerprint omitted (that is, the length N is zero in this case), for an "anonymous recipient" (see <xref target="pkesk-notes"/>).</t>
  <t>A one-octet number giving the public-key algorithm used.</t>
  <t>A series of values comprising the encrypted session key.
This is algorithm-specific and described below.</t>
</list></t>

<t>When creating a V5 PKESK packet, the symmetric encryption algorithm identifier is not included.
Before encrypting, a two-octet checksum is appended, which is equal to the sum of the preceding session key octets, modulo 65536.</t>

<t>The resulting octet string (session key and checksum) is encrypted according to the public-key algorithm used, as described below.</t>

</section>
<section anchor="pkesk-rsa"><name>Algorithm Specific Fields for RSA encryption</name>

<t><list style="symbols">
  <t>Multiprecision integer (MPI) of RSA-encrypted value m**e mod n.</t>
</list></t>

<t>The value "m" in the above formula is the plaintext value described above, encoded in the PKCS#1 block encoding EME-PKCS1-v1_5 described in Section 7.2.1 of <xref target="RFC8017"/> (see also <xref target="pkcs-encoding"/>).
Note that when an implementation forms several PKESKs with one session key, forming a message that can be decrypted by several keys, the implementation MUST make a new PKCS#1 encoding for each key.</t>

</section>
<section anchor="pkesk-elgamal"><name>Algorithm Specific Fields for Elgamal encryption</name>

<t><list style="symbols">
  <t>MPI of Elgamal (Diffie-Hellman) value g**k mod p.</t>
  <t>MPI of Elgamal (Diffie-Hellman) value m * y**k mod p.</t>
</list></t>

<t>The value "m" in the above formula is the plaintext value described above, encoded in the PKCS#1 block encoding EME-PKCS1-v1_5 described in Section 7.2.1 of <xref target="RFC8017"/> (see also <xref target="pkcs-encoding"/>).
Note that when an implementation forms several PKESKs with one session key, forming a message that can be decrypted by several keys, the implementation MUST make a new PKCS#1 encoding for each key.</t>

</section>
<section anchor="pkesk-ecdh"><name>Algorithm-Specific Fields for ECDH encryption</name>

<t><list style="symbols">
  <t>MPI of an EC point representing an ephemeral public key, in the point format associated with the curve as specified in <xref target="ec-curves"/>.</t>
  <t>A one-octet size, followed by a symmetric key encoded using the method described in <xref target="ec-dh-algorithm-ecdh"/>.</t>
</list></t>

</section>
<section anchor="pkesk-notes"><name>Notes on PKESK</name>

<t>An implementation MAY accept or use a Key ID of all zeros, or a key version of zero and no key fingerprint, to hide the intended decryption key.
In this case, the receiving implementation would try all available private keys, checking for a valid decrypted session key.
This format helps reduce traffic analysis of messages.</t>

</section>
</section>
<section anchor="signature-packet"><name>Signature Packet (Tag 2)</name>

<t>A Signature packet describes a binding between some public key and some data.
The most common signatures are a signature of a file or a block of text, and a signature that is a certification of a User ID.</t>

<t>Three versions of Signature packets are defined.
Version 3 provides basic signature information, while versions 4 and 5 provide an expandable format with subpackets that can specify more information about the signature.</t>

<t>An implementation MUST generate a version 5 signature when signing with a version 5 key.
An implementation MUST generate a version 4 signature when signing with a version 4 key.
Implementations MUST NOT create version 3 signatures; they MAY accept version 3 signatures.</t>

<section anchor="signature-types"><name>Signature Types</name>

<t>There are a number of possible meanings for a signature, which are indicated in a signature type octet in any given signature.
Please note that the vagueness of these meanings is not a flaw, but a feature of the system.
Because OpenPGP places final authority for validity upon the receiver of a signature, it may be that one signer's casual act might be more rigorous than some other authority's positive act.
See <xref target="computing-signatures"/> for detailed information on how to compute and verify signatures of each type.</t>

<t>These meanings are as follows:</t>

<dl newline="true">
  <dt>
0x00: Signature of a binary document.  </dt>
  <dd>
    <t>This means the signer owns it, created it, or certifies that it has not been modified.</t>
  </dd>
  <dt>
0x01: Signature of a canonical text document.  </dt>
  <dd>
    <t>This means the signer owns it, created it, or certifies that it has not been modified.
The signature is calculated over the text data with its line endings converted to &lt;CR&gt;&lt;LF&gt;.</t>
  </dd>
  <dt>
0x02: Standalone signature.  </dt>
  <dd>
    <t>This signature is a signature of only its own subpacket contents.
It is calculated identically to a signature over a zero-length binary document.
V3 standalone signatures MUST NOT be generated and MUST be ignored.</t>
  </dd>
  <dt>
0x10: Generic certification of a User ID and Public-Key packet.  </dt>
  <dd>
    <t>The issuer of this certification does not make any particular assertion as to how well the certifier has checked that the owner of the key is in fact the person described by the User ID.</t>
  </dd>
  <dt>
0x11: Persona certification of a User ID and Public-Key packet.  </dt>
  <dd>
    <t>The issuer of this certification has not done any verification of the claim that the owner of this key is the User ID specified.</t>
  </dd>
  <dt>
0x12: Casual certification of a User ID and Public-Key packet.  </dt>
  <dd>
    <t>The issuer of this certification has done some casual verification of the claim of identity.</t>
  </dd>
  <dt>
0x13: Positive certification of a User ID and Public-Key packet.  </dt>
  <dd>
    <t>The issuer of this certification has done substantial verification of the claim of identity.
</t>

    <t>Most OpenPGP implementations make their "key signatures" as 0x10 certifications.
Some implementations can issue 0x11-0x13 certifications, but few differentiate between the types.</t>
  </dd>
  <dt>
0x18: Subkey Binding Signature.  </dt>
  <dd>
    <t>This signature is a statement by the top-level signing key that indicates that it owns the subkey.
This signature is calculated directly on the primary key and subkey, and not on any User ID or other packets.
A signature that binds a signing subkey MUST have an Embedded Signature subpacket in this binding signature that contains a 0x19 signature made by the signing subkey on the primary key and subkey.</t>
  </dd>
  <dt>
0x19: Primary Key Binding Signature.  </dt>
  <dd>
    <t>This signature is a statement by a signing subkey, indicating that it is owned by the primary key and subkey.
This signature is calculated the same way as a 0x18 signature: directly on the primary key and subkey, and not on any User ID or other packets.</t>
  </dd>
  <dt>
0x1F: Signature directly on a key.  </dt>
  <dd>
    <t>This signature is calculated directly on a key.
It binds the information in the Signature subpackets to the key, and is appropriate to be used for subpackets that provide information about the key, such as the Key Flags subpacket or (deprecated) Revocation Key.
It is also appropriate for statements that non-self certifiers want to make about the key itself, rather than the binding between a key and a name.</t>
  </dd>
  <dt>
0x20: Key revocation signature.  </dt>
  <dd>
    <t>The signature is calculated directly on the key being revoked.
A revoked key is not to be used.
Only revocation signatures by the key being revoked, or by a (deprecated) Revocation Key, should be considered valid revocation signatures.</t>
  </dd>
  <dt>
0x28: Subkey revocation signature.  </dt>
  <dd>
    <t>The signature is calculated directly on the subkey being revoked.
A revoked subkey is not to be used.
Only revocation signatures by the top-level signature key that is bound to this subkey, or by a (deprecated) Revocation Key, should be considered valid revocation signatures.</t>
  </dd>
  <dt>
0x30: Certification revocation signature.  </dt>
  <dd>
    <t>This signature revokes an earlier User ID certification signature (signature class 0x10 through 0x13) or direct-key signature (0x1F).
It should be issued by the same key that issued the revoked signature or by a (deprecated) Revocation Key.
The signature is computed over the same data as the certificate that it revokes, and should have a later creation date than that certificate.</t>
  </dd>
  <dt>
0x40: Timestamp signature.  </dt>
  <dd>
    <t>This signature is only meaningful for the timestamp contained in it.</t>
  </dd>
  <dt>
0x50: Third-Party Confirmation signature.  </dt>
  <dd>
    <t>This signature is a signature over some other OpenPGP Signature packet(s).
It is analogous to a notary seal on the signed data.
A third-party signature SHOULD include Signature Target subpacket(s) to give easy identification.
Note that we really do mean SHOULD.
There are plausible uses for this (such as a blind party that only sees the signature, not the key or source document) that cannot include a target subpacket.</t>
  </dd>
</dl>

</section>
<section anchor="version-three-sig"><name>Version 3 Signature Packet Format</name>

<t>The body of a version 3 Signature Packet contains:</t>

<t><list style="symbols">
  <t>One-octet version number (3).</t>
  <t>One-octet length of following hashed material.
MUST be 5.  <list style="symbols">
      <t>One-octet signature type.</t>
      <t>Four-octet creation time.</t>
    </list></t>
  <t>Eight-octet Key ID of signer.</t>
  <t>One-octet public-key algorithm.</t>
  <t>One-octet hash algorithm.</t>
  <t>Two-octet field holding left 16 bits of signed hash value.</t>
  <t>One or more multiprecision integers comprising the signature.
This portion is algorithm specific, as described below.</t>
</list></t>

<t>The concatenation of the data to be signed, the signature type, and creation time from the Signature packet (5 additional octets) is hashed.
The resulting hash value is used in the signature algorithm.
The high 16 bits (first two octets) of the hash are included in the Signature packet to provide a way to reject some invalid signatures without performing a signature verification.</t>

<t>Algorithm-Specific Fields for RSA signatures:</t>

<t><list style="symbols">
  <t>Multiprecision integer (MPI) of RSA signature value m**d mod n.</t>
</list></t>

<t>Algorithm-Specific Fields for DSA signatures:</t>

<t><list style="symbols">
  <t>MPI of DSA value r.</t>
  <t>MPI of DSA value s.</t>
</list></t>

<t>The signature calculation is based on a hash of the signed data, as described above.
The details of the calculation are different for DSA signatures than for RSA signatures.</t>

<t>With RSA signatures, the hash value is encoded using PKCS#1 encoding type EMSA-PKCS1-v1_5 as described in Section 9.2 of <xref target="RFC8017"/>.
This requires inserting the hash value as an octet string into an ASN.1 structure.
The object identifier for the type of hash being used is included in the structure.
The hexadecimal representations for the currently defined hash algorithms are as follows:</t>

<texttable title="Hash hexadecimal representations">
      <ttcol align='left'>algorithm</ttcol>
      <ttcol align='left'>hexadecimal representation</ttcol>
      <c>MD5</c>
      <c>0x2A, 0x86, 0x48, 0x86, 0xF7, 0x0D, 0x02, 0x05</c>
      <c>RIPEMD-160</c>
      <c>0x2B, 0x24, 0x03, 0x02, 0x01</c>
      <c>SHA-1</c>
      <c>0x2B, 0x0E, 0x03, 0x02, 0x1A</c>
      <c>SHA224</c>
      <c>0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x04</c>
      <c>SHA256</c>
      <c>0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01</c>
      <c>SHA384</c>
      <c>0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02</c>
      <c>SHA512</c>
      <c>0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03</c>
</texttable>

<t>The ASN.1 Object Identifiers (OIDs) are as follows:</t>

<texttable title="Hash OIDs">
      <ttcol align='left'>algorithm</ttcol>
      <ttcol align='left'>OID</ttcol>
      <c>MD5</c>
      <c>1.2.840.113549.2.5</c>
      <c>RIPEMD-160</c>
      <c>1.3.36.3.2.1</c>
      <c>SHA-1</c>
      <c>1.3.14.3.2.26</c>
      <c>SHA224</c>
      <c>2.16.840.1.101.3.4.2.4</c>
      <c>SHA256</c>
      <c>2.16.840.1.101.3.4.2.1</c>
      <c>SHA384</c>
      <c>2.16.840.1.101.3.4.2.2</c>
      <c>SHA512</c>
      <c>2.16.840.1.101.3.4.2.3</c>
</texttable>

<t>The full hash prefixes for these are as follows:</t>

<texttable title="Hash hexadecimal prefixes">
      <ttcol align='left'>algorithm</ttcol>
      <ttcol align='left'>full hash prefix</ttcol>
      <c>MD5</c>
      <c>0x30, 0x20, 0x30, 0x0C, 0x06, 0x08, 0x2A, 0x86, 0x48, 0x86, 0xF7, 0x0D, 0x02, 0x05, 0x05, 0x00, 0x04, 0x10</c>
      <c>RIPEMD-160</c>
      <c>0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2B, 0x24, 0x03, 0x02, 0x01, 0x05, 0x00, 0x04, 0x14</c>
      <c>SHA-1</c>
      <c>0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2B, 0x0E, 0x03, 0x02, 0x1A, 0x05, 0x00, 0x04, 0x14</c>
      <c>SHA224</c>
      <c>0x30, 0x2D, 0x30, 0x0D, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x04, 0x05, 0x00, 0x04, 0x1C</c>
      <c>SHA256</c>
      <c>0x30, 0x31, 0x30, 0x0D, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20</c>
      <c>SHA384</c>
      <c>0x30, 0x41, 0x30, 0x0D, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02, 0x05, 0x00, 0x04, 0x30</c>
      <c>SHA512</c>
      <c>0x30, 0x51, 0x30, 0x0D, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03, 0x05, 0x00, 0x04, 0x40</c>
</texttable>

<t>DSA signatures MUST use hashes that are equal in size to the number of bits of q, the group generated by the DSA key's generator value.</t>

<t>If the output size of the chosen hash is larger than the number of bits of q, the hash result is truncated to fit by taking the number of leftmost bits equal to the number of bits of q.
This (possibly truncated) hash function result is treated as a number and used directly in the DSA signature algorithm.</t>

</section>
<section anchor="version-4-and-5-signature-packet-formats"><name>Version 4 and 5 Signature Packet Formats</name>

<t>The body of a V4 or V5 Signature packet contains:</t>

<t><list style="symbols">
  <t>One-octet version number.
This is 4 for V4 signatures and 5 for V5 signatures.</t>
  <t>One-octet signature type.</t>
  <t>One-octet public-key algorithm.</t>
  <t>One-octet hash algorithm.</t>
  <t>A scalar octet count for following hashed subpacket data.
For a V4 signature, this is a two-octet field.
For a V5 signature, this is a four-octet field.
Note that this is the length in octets of all of the hashed subpackets; a pointer incremented by this number will skip over the hashed subpackets.</t>
  <t>Hashed subpacket data set (zero or more subpackets).</t>
  <t>A scalar octet count for the following unhashed subpacket data.
For a V4 signature, this is a two-octet field.
For a V5 signature, this is a four-octet field.
Note that this is the length in octets of all of the unhashed subpackets; a pointer incremented by this number will skip over the unhashed subpackets.</t>
  <t>Unhashed subpacket data set (zero or more subpackets).</t>
  <t>Two-octet field holding the left 16 bits of the signed hash value.</t>
  <t>Only for V5 signatures, a 16 octet field containing random values used as salt.</t>
  <t>One or more multiprecision integers comprising the signature.
This portion is algorithm specific:</t>
</list></t>

<section anchor="sig-rsa"><name>Algorithm-Specific Fields for RSA signatures</name>

<t><list style="symbols">
  <t>Multiprecision integer (MPI) of RSA signature value m**d mod n.</t>
</list></t>

</section>
<section anchor="sig-dsa"><name>Algorithm-Specific Fields for DSA or ECDSA signatures</name>

<t><list style="symbols">
  <t>MPI of DSA or ECDSA value r.</t>
  <t>MPI of DSA or ECDSA value s.</t>
</list></t>

<t>A version 3 signature MUST NOT be created and MUST NOT be used with ECDSA.</t>

</section>
<section anchor="sig-eddsa"><name>Algorithm-Specific Fields for EdDSA signatures</name>

<t><list style="symbols">
  <t>Two MPI-encoded values, whose contents and formatting depend on the choice of curve used (see <xref target="curve-specific-formats"/>).</t>
</list></t>

<t>A version 3 signature MUST NOT be created and MUST NOT be used with EdDSA.</t>

<section anchor="algorithm-specific-fields-for-ed25519-signatures"><name>Algorithm-Specific Fields for Ed25519 signatures</name>

<t>The two MPIs for Ed25519 use octet strings R and S as described in <xref target="RFC8032"/>.</t>

<t><list style="symbols">
  <t>MPI of an EC point R, represented as a (non-prefixed) native (little-endian) octet string up to 32 octets.</t>
  <t>MPI of EdDSA value S, also in (non-prefixed) native little-endian format with a length up to 32 octets.</t>
</list></t>

</section>
<section anchor="algorithm-specific-fields-for-ed448-signatures"><name>Algorithm-Specific Fields for Ed448 signatures</name>

<t>For Ed448 signatures, the native signature format is used as described in <xref target="RFC8032"/>.
The two MPIs are composed as follows:</t>

<t><list style="symbols">
  <t>The first MPI has a body of 58 octets: a prefix 0x40 octet, followed by 57 octets of the native signature.</t>
  <t>The second MPI is set to 0 (this is a placeholder, and is unused).
Note that an MPI with a value of 0 is encoded on the wire as a pair of zero octets: <spanx style="verb">00 00</spanx>.</t>
</list></t>

</section>
</section>
<section anchor="notes-on-signatures"><name>Notes on Signatures</name>

<t>The concatenation of the data being signed and the signature data from the version number through the hashed subpacket data (inclusive) is hashed.
The resulting hash value is what is signed.
The high 16 bits (first two octets) of the hash are included in the Signature packet to provide a way to reject some invalid signatures without performing a signature verification.</t>

<t>There are two fields consisting of Signature subpackets.
The first field is hashed with the rest of the signature data, while the second is unhashed.
The second set of subpackets is not cryptographically protected by the signature and should include only advisory information.</t>

<t>The differences between a V4 and V5 signature are two-fold: first, a V5 signature increases the width of the size indicators for the signed data, making it more capable when signing large keys or messages.
Second, the hash is salted with 128 bit of random data.</t>

<t>The algorithms for converting the hash function result to a signature are described in <xref target="computing-signatures"/>.</t>

</section>
<section anchor="signature-subpacket"><name>Signature Subpacket Specification</name>

<t>A subpacket data set consists of zero or more Signature subpackets.
In Signature packets, the subpacket data set is preceded by a two-octet (for V4 signatures) or four-octet (for V5 signatures) scalar count of the length in octets of all the subpackets.
A pointer incremented by this number will skip over the subpacket data set.</t>

<t>Each subpacket consists of a subpacket header and a body.
The header consists of:</t>

<t><list style="symbols">
  <t>the subpacket length (1, 2, or 5 octets),</t>
  <t>the subpacket type (1 octet),</t>
</list></t>

<t>and is followed by the subpacket-specific data.</t>

<t>The length includes the type octet but not this length.
Its format is similar to the "new" format packet header lengths, but cannot have Partial Body Lengths.
That is:</t>

<figure><artwork><![CDATA[
if the 1st octet <  192, then
    lengthOfLength = 1
    subpacketLen = 1st_octet

if the 1st octet >= 192 and < 255, then
    lengthOfLength = 2
    subpacketLen = ((1st_octet - 192) << 8) + (2nd_octet) + 192

if the 1st octet = 255, then
    lengthOfLength = 5
    subpacket length = [four-octet scalar starting at 2nd_octet]
]]></artwork></figure>

<t>The value of the subpacket type octet may be:</t>

<texttable title="Subpacket type registry">
      <ttcol align='right'>Type</ttcol>
      <ttcol align='left'>Description</ttcol>
      <c>0</c>
      <c>Reserved</c>
      <c>1</c>
      <c>Reserved</c>
      <c>2</c>
      <c>Signature Creation Time</c>
      <c>3</c>
      <c>Signature Expiration Time</c>
      <c>4</c>
      <c>Exportable Certification</c>
      <c>5</c>
      <c>Trust Signature</c>
      <c>6</c>
      <c>Regular Expression</c>
      <c>7</c>
      <c>Revocable</c>
      <c>8</c>
      <c>Reserved</c>
      <c>9</c>
      <c>Key Expiration Time</c>
      <c>10</c>
      <c>Placeholder for backward compatibility</c>
      <c>11</c>
      <c>Preferred Symmetric Ciphers for v1 SEIPD</c>
      <c>12</c>
      <c>Revocation Key (deprecated)</c>
      <c>13 to 15</c>
      <c>Reserved</c>
      <c>16</c>
      <c>Issuer</c>
      <c>17 to 19</c>
      <c>Reserved</c>
      <c>20</c>
      <c>Notation Data</c>
      <c>21</c>
      <c>Preferred Hash Algorithms</c>
      <c>22</c>
      <c>Preferred Compression Algorithms</c>
      <c>23</c>
      <c>Key Server Preferences</c>
      <c>24</c>
      <c>Preferred Key Server</c>
      <c>25</c>
      <c>Primary User ID</c>
      <c>26</c>
      <c>Policy URI</c>
      <c>27</c>
      <c>Key Flags</c>
      <c>28</c>
      <c>Signer's User ID</c>
      <c>29</c>
      <c>Reason for Revocation</c>
      <c>30</c>
      <c>Features</c>
      <c>31</c>
      <c>Signature Target</c>
      <c>32</c>
      <c>Embedded Signature</c>
      <c>33</c>
      <c>Issuer Fingerprint</c>
      <c>34</c>
      <c>Reserved</c>
      <c>35</c>
      <c>Intended Recipient Fingerprint</c>
      <c>37</c>
      <c>Reserved (Attested Certifications)</c>
      <c>38</c>
      <c>Reserved (Key Block)</c>
      <c>39</c>
      <c>Preferred AEAD Ciphersuites</c>
      <c>100 to 110</c>
      <c>Private or experimental</c>
</texttable>

<t>An implementation SHOULD ignore any subpacket of a type that it does not recognize.</t>

<t>Bit 7 of the subpacket type is the "critical" bit.
If set, it denotes that the subpacket is one that is critical for the evaluator of the signature to recognize.
If a subpacket is encountered that is marked critical but is unknown to the evaluating software, the evaluator SHOULD consider the signature to be in error.</t>

<t>An evaluator may "recognize" a subpacket, but not implement it.
The purpose of the critical bit is to allow the signer to tell an evaluator that it would prefer a new, unknown feature to generate an error than be ignored.</t>

<t>Implementations SHOULD implement the four preferred algorithm subpackets (11, 21, 22, and 34), as well as the "Reason for Revocation" subpacket.
Note, however, that if an implementation chooses not to implement some of the preferences, it is required to behave in a polite manner to respect the wishes of those users who do implement these preferences.</t>

</section>
<section anchor="signature-subpacket-types"><name>Signature Subpacket Types</name>

<t>A number of subpackets are currently defined.
Some subpackets apply to the signature itself and some are attributes of the key.
Subpackets that are found on a self-signature are placed on a certification made by the key itself.
Note that a key may have more than one User ID, and thus may have more than one self-signature, and differing subpackets.</t>

<t>A subpacket may be found either in the hashed or unhashed subpacket sections of a signature.
If a subpacket is not hashed, then the information in it cannot be considered definitive because it is not part of the signature proper.</t>

</section>
<section anchor="self-sigs"><name>Notes on Self-Signatures</name>

<t>A self-signature is a binding signature made by the key to which the signature refers.
There are three types of self-signatures, the certification signatures (types 0x10-0x13), the direct-key signature (type 0x1F), and the subkey binding signature (type 0x18).
A cryptographically-valid self-signature should be accepted from any primary key, regardless of what Key Flags (<xref target="key-flags"/>) apply to the primary key.
In particular, a primary key does not need to have 0x01 set in the first octet of Key Flags order to make a valid self-signature.</t>

<t>For certification self-signatures, each User ID may have a self-signature, and thus different subpackets in those self-signatures.
For subkey binding signatures, each subkey in fact has a self-signature.
Subpackets that appear in a certification self-signature apply to the user name, and subpackets that appear in the subkey self-signature apply to the subkey.
Lastly, subpackets on the direct-key signature apply to the entire key.</t>

<t>Implementing software should interpret a self-signature's preference subpackets as narrowly as possible.
For example, suppose a key has two user names, Alice and Bob.
Suppose that Alice prefers the AEAD ciphersuite AES-256 with OCB, and Bob prefers Camellia-256 with GCM.
If the software locates this key via Alice's name, then the preferred AEAD ciphersuite is AES-256 with OCB; if software locates the key via Bob's name, then the preferred algorithm is Camellia-256 with GCM.
If the key is located by Key ID, the algorithm of the primary User ID of the key provides the preferred AEAD ciphersuite.</t>

<t>Revoking a self-signature or allowing it to expire has a semantic meaning that varies with the signature type.
Revoking the self-signature on a User ID effectively retires that user name.
The self-signature is a statement, "My name X is tied to my signing key K" and is corroborated by other users' certifications.
If another user revokes their certification, they are effectively saying that they no longer believe that name and that key are tied together.
Similarly, if the users themselves revoke their self-signature, then the users no longer go by that name, no longer have that email address, etc.
Revoking a binding signature effectively retires that subkey.
Revoking a direct-key signature cancels that signature.
Please see <xref target="reason-for-revocation"/> for more relevant detail.</t>

<t>Since a self-signature contains important information about the key's use, an implementation SHOULD allow the user to rewrite the self-signature, and important information in it, such as preferences and key expiration.</t>

<t>It is good practice to verify that a self-signature imported into an implementation doesn't advertise features that the implementation doesn't support, rewriting the signature as appropriate.</t>

<t>An implementation that encounters multiple self-signatures on the same object may resolve the ambiguity in any way it sees fit, but it is RECOMMENDED that priority be given to the most recent self-signature.</t>

</section>
<section anchor="signature-creation-time"><name>Signature Creation Time</name>

<t>(4-octet time field)</t>

<t>The time the signature was made.</t>

<t>MUST be present in the hashed area.</t>

</section>
<section anchor="issuer"><name>Issuer</name>

<t>(8-octet Key ID)</t>

<t>The OpenPGP Key ID of the key issuing the signature.
If the version of that key is greater than 4, this subpacket MUST NOT be included in the signature.</t>

</section>
<section anchor="key-expiration-time"><name>Key Expiration Time</name>

<t>(4-octet time field)</t>

<t>The validity period of the key.
This is the number of seconds after the key creation time that the key expires.
For a direct or certification self-signature, the key creation time is that of the primary key.
For a subkey binding signature, the key creation time is that of the subkey.
If this is not present or has a value of zero, the key never expires.
This is found only on a self-signature.</t>

</section>
<section anchor="preferred-v1-seipd"><name>Preferred Symmetric Ciphers for v1 SEIPD</name>

<t>(array of one-octet values)</t>

<t>A series of symmetric cipher algorithm identifiers indicating how the keyholder prefers to receive version 1 Symmetrically Encrypted Integrity Protected Data (<xref target="version-one-seipd"/>).
The subpacket body is an ordered list of octets with the most preferred listed first.
It is assumed that only algorithms listed are supported by the recipient's software.
Algorithm numbers are in <xref target="symmetric-algos"/>.
This is only found on a self-signature.</t>

<t>When generating a v2 SEIPD packet, this preference list is not relevant.
See <xref target="preferred-v2-seipd"/> instead.</t>

</section>
<section anchor="preferred-v2-seipd"><name>Preferred AEAD Ciphersuites</name>

<t>(array of pairs of octets indicating Symmetric Cipher and AEAD algorithms)</t>

<t>A series of paired algorithm identifiers indicating how the keyholder prefers to receive version 2 Symmetrically Encrypted Integrity Protected Data (<xref target="version-two-seipd"/>).
Each pair of octets indicates a combination of a symmetric cipher and an AEAD mode that the key holder prefers to use.
The symmetric cipher identifier precedes the AEAD identifier in each pair.
The subpacket body is an ordered list of pairs of octets with the most preferred algorithm combination listed first.</t>

<t>It is assumed that only the combinations of algorithms listed are supported by the recipient's software, with the exception of the mandatory-to-implement combination of AES-128 and OCB.
If AES-128 and OCB are not found in the subpacket, it is implicitly listed at the end.</t>

<t>AEAD algorithm numbers are listed in <xref target="aead-algorithms"/>.
Symmetric cipher algorithm numbers are listed in <xref target="symmetric-algos"/>.</t>

<t>For example, a subpacket with content of these six octets:</t>

<figure><artwork><![CDATA[
09 02 09 03 13 02
]]></artwork></figure>

<t>Indicates that the keyholder prefers to receive v2 SEIPD using AES-256 with OCB, then AES-256 with GCM, then Camellia-256 with OCB, and finally the implicit AES-128 with OCB.</t>

<t>Note that support for version 2 of the Symmetrically Encrypted Integrity Protected Data packet (<xref target="version-two-seipd"/>) in general is indicated by a Feature Flag (<xref target="features-subpacket"/>).</t>

<t>This subpacket is only found on a self-signature.</t>

<t>When generating a v1 SEIPD packet, this preference list is not relevant.
See <xref target="preferred-v1-seipd"/> instead.</t>

</section>
<section anchor="preferred-hash-algorithms"><name>Preferred Hash Algorithms</name>

<t>(array of one-octet values)</t>

<t>Message digest algorithm numbers that indicate which algorithms the key holder prefers to receive.
Like the preferred AEAD ciphersuites, the list is ordered.
Algorithm numbers are in <xref target="hash-algos"/>.
This is only found on a self-signature.</t>

</section>
<section anchor="preferred-compression-algorithms"><name>Preferred Compression Algorithms</name>

<t>(array of one-octet values)</t>

<t>Compression algorithm numbers that indicate which algorithms the key holder prefers to use.
Like the preferred AEAD ciphersuites, the list is ordered.
Algorithm numbers are in <xref target="compression-algos"/>.
A zero, or the absence of this subpacket, denotes that uncompressed data is preferred; the key holder's software might have no compression software in that implementation.
This is only found on a self-signature.</t>

</section>
<section anchor="signature-expiration-time"><name>Signature Expiration Time</name>

<t>(4-octet time field)</t>

<t>The validity period of the signature.
This is the number of seconds after the signature creation time that the signature expires.
If this is not present or has a value of zero, it never expires.</t>

</section>
<section anchor="exportable-certification"><name>Exportable Certification</name>

<t>(1 octet of exportability, 0 for not, 1 for exportable)</t>

<t>This subpacket denotes whether a certification signature is "exportable", to be used by other users than the signature's issuer.
The packet body contains a Boolean flag indicating whether the signature is exportable.
If this packet is not present, the certification is exportable; it is equivalent to a flag containing a 1.</t>

<t>Non-exportable, or "local", certifications are signatures made by a user to mark a key as valid within that user's implementation only.</t>

<t>Thus, when an implementation prepares a user's copy of a key for transport to another user (this is the process of "exporting" the key), any local certification signatures are deleted from the key.</t>

<t>The receiver of a transported key "imports" it, and likewise trims any local certifications.
In normal operation, there won't be any, assuming the import is performed on an exported key.
However, there are instances where this can reasonably happen.
For example, if an implementation allows keys to be imported from a key database in addition to an exported key, then this situation can arise.</t>

<t>Some implementations do not represent the interest of a single user (for example, a key server).
Such implementations always trim local certifications from any key they handle.</t>

</section>
<section anchor="revocable"><name>Revocable</name>

<t>(1 octet of revocability, 0 for not, 1 for revocable)</t>

<t>Signature's revocability status.
The packet body contains a Boolean flag indicating whether the signature is revocable.
Signatures that are not revocable have any later revocation signatures ignored.
They represent a commitment by the signer that he cannot revoke his signature for the life of his key.
If this packet is not present, the signature is revocable.</t>

</section>
<section anchor="trust-signature"><name>Trust Signature</name>

<t>(1 octet "level" (depth), 1 octet of trust amount)</t>

<t>Signer asserts that the key is not only valid but also trustworthy at the specified level.
Level 0 has the same meaning as an ordinary validity signature.
Level 1 means that the signed key is asserted to be a valid trusted introducer, with the 2nd octet of the body specifying the degree of trust.
Level 2 means that the signed key is asserted to be trusted to issue level 1 trust signatures; that is, the signed key is a "meta introducer".
Generally, a level n trust signature asserts that a key is trusted to issue level n-1 trust signatures.
The trust amount is in a range from 0-255, interpreted such that values less than 120 indicate partial trust and values of 120 or greater indicate complete trust.
Implementations SHOULD emit values of 60 for partial trust and 120 for complete trust.</t>

</section>
<section anchor="regular-expression"><name>Regular Expression</name>

<t>(null-terminated regular expression)</t>

<t>Used in conjunction with trust Signature packets (of level &gt; 0) to limit the scope of trust that is extended.
Only signatures by the target key on User IDs that match the regular expression in the body of this packet have trust extended by the trust Signature subpacket.
The regular expression uses the same syntax as the Henry Spencer's "almost public domain" regular expression <xref target="REGEX"/> package.
A description of the syntax is found in <xref target="regular-expressions"/>.</t>

</section>
<section anchor="revocation-key"><name>Revocation Key</name>

<t>(1 octet of class, 1 octet of public-key algorithm ID, 20 octets of V4 fingerprint)</t>

<t>This mechanism is deprecated.
Applications MUST NOT generate such a subpacket.</t>

<t>An application that wants the functionality of delegating revocation SHOULD instead use an escrowed Revocation Signature.
See <xref target="escrowed-revocations"/> for more details.</t>

<t>The remainder of this section describes how some implementations attempt to interpret this deprecated subpacket.</t>

<t>This packet was intended to authorize the specified key to issue revocation signatures for this key.
Class octet must have bit 0x80 set.
If the bit 0x40 is set, then this means that the revocation information is sensitive.
Other bits are for future expansion to other kinds of authorizations.
This is only found on a direct-key self-signature (type 0x1f).
The use on other types of self-signatures is unspecified.</t>

<t>If the "sensitive" flag is set, the keyholder feels this subpacket contains private trust information that describes a real-world sensitive relationship.
If this flag is set, implementations SHOULD NOT export this signature to other users except in cases where the data needs to be available: when the signature is being sent to the designated revoker, or when it is accompanied by a revocation signature from that revoker.
Note that it may be appropriate to isolate this subpacket within a separate signature so that it is not combined with other subpackets that need to be exported.</t>

</section>
<section anchor="notation-data"><name>Notation Data</name>

<t>(4 octets of flags, 2 octets of name length (M), 2 octets of value length (N), M octets of name data, N octets of value data)</t>

<t>This subpacket describes a "notation" on the signature that the issuer wishes to make.
The notation has a name and a value, each of which are strings of octets.
There may be more than one notation in a signature.
Notations can be used for any extension the issuer of the signature cares to make.
The "flags" field holds four octets of flags.</t>

<t>All undefined flags MUST be zero.
Defined flags are as follows:</t>

<t>First octet:</t>

<texttable title="Notation flag registry (first octet)">
      <ttcol align='left'>flag</ttcol>
      <ttcol align='left'>shorthand</ttcol>
      <ttcol align='left'>definition</ttcol>
      <c>0x80</c>
      <c>human-readable</c>
      <c>This note value is text.</c>
</texttable>

<t>Other octets: none.</t>

<t>Notation names are arbitrary strings encoded in UTF-8.
They reside in two namespaces: The IETF namespace and the user namespace.</t>

<t>The IETF namespace is registered with IANA.
These names MUST NOT contain the "@" character (0x40).
This is a tag for the user namespace.</t>

<t>Names in the user namespace consist of a UTF-8 string tag followed by "@" followed by a DNS domain name.
Note that the tag MUST NOT contain an "@" character.
For example, the "sample" tag used by Example Corporation could be "sample@example.com".</t>

<t>Names in a user space are owned and controlled by the owners of that domain.
Obviously, it's bad form to create a new name in a DNS space that you don't own.</t>

<t>Since the user namespace is in the form of an email address, implementers MAY wish to arrange for that address to reach a person who can be consulted about the use of the named tag.
Note that due to UTF-8 encoding, not all valid user space name tags are valid email addresses.</t>

<t>If there is a critical notation, the criticality applies to that specific notation and not to notations in general.</t>

</section>
<section anchor="key-server-preferences"><name>Key Server Preferences</name>

<t>(N octets of flags)</t>

<t>This is a list of one-bit flags that indicate preferences that the key holder has about how the key is handled on a key server.
All undefined flags MUST be zero.</t>

<t>First octet:</t>

<texttable title="Key server preferences flag registry (first octet)">
      <ttcol align='left'>flag</ttcol>
      <ttcol align='left'>shorthand</ttcol>
      <ttcol align='left'>definition</ttcol>
      <c>0x80</c>
      <c>No-modify</c>
      <c>The key holder requests that this key only be modified or updated by the key holder or an administrator of the key server.</c>
</texttable>

<t>This is found only on a self-signature.</t>

</section>
<section anchor="preferred-key-server"><name>Preferred Key Server</name>

<t>(String)</t>

<t>This is a URI of a key server that the key holder prefers be used for updates.
Note that keys with multiple User IDs can have a preferred key server for each User ID.
Note also that since this is a URI, the key server can actually be a copy of the key retrieved by ftp, http, finger, etc.</t>

</section>
<section anchor="primary-user-id"><name>Primary User ID</name>

<t>(1 octet, Boolean)</t>

<t>This is a flag in a User ID's self-signature that states whether this User ID is the main User ID for this key.
It is reasonable for an implementation to resolve ambiguities in preferences, etc.
by referring to the primary User ID.
If this flag is absent, its value is zero.
If more than one User ID in a key is marked as primary, the implementation may resolve the ambiguity in any way it sees fit, but it is RECOMMENDED that priority be given to the User ID with the most recent self-signature.</t>

<t>When appearing on a self-signature on a User ID packet, this subpacket applies only to User ID packets.
When appearing on a self-signature on a User Attribute packet, this subpacket applies only to User Attribute packets.
That is to say, there are two different and independent "primaries" --- one for User IDs, and one for User Attributes.</t>

</section>
<section anchor="policy-uri"><name>Policy URI</name>

<t>(String)</t>

<t>This subpacket contains a URI of a document that describes the policy under which the signature was issued.</t>

</section>
<section anchor="key-flags"><name>Key Flags</name>

<t>(N octets of flags)</t>

<t>This subpacket contains a list of binary flags that hold information about a key.
It is a string of octets, and an implementation MUST NOT assume a fixed size.
This is so it can grow over time.
If a list is shorter than an implementation expects, the unstated flags are considered to be zero.
The defined flags are as follows:</t>

<t>First octet:</t>

<texttable title="Key flags registry (first octet)">
      <ttcol align='left'>flag</ttcol>
      <ttcol align='left'>definition</ttcol>
      <c>0x01</c>
      <c>This key may be used to make User ID certifications (signature types 0x10-0x13) or direct key signatures (signature type 0x1F) over other keys.</c>
      <c>0x02</c>
      <c>This key may be used to sign data.</c>
      <c>0x04</c>
      <c>This key may be used to encrypt communications.</c>
      <c>0x08</c>
      <c>This key may be used to encrypt storage.</c>
      <c>0x10</c>
      <c>The private component of this key may have been split by a secret-sharing mechanism.</c>
      <c>0x20</c>
      <c>This key may be used for authentication.</c>
      <c>0x80</c>
      <c>The private component of this key may be in the possession of more than one person.</c>
</texttable>

<t>Second octet:</t>

<texttable title="Key flags registry (second octet)">
      <ttcol align='left'>flag</ttcol>
      <ttcol align='left'>definition</ttcol>
      <c>0x04</c>
      <c>Reserved (ADSK).</c>
      <c>0x08</c>
      <c>Reserved (timestamping).</c>
</texttable>

<t>Usage notes:</t>

<t>The flags in this packet may appear in self-signatures or in certification signatures.
They mean different things depending on who is making the statement --- for example, a certification signature that has the "sign data" flag is stating that the certification is for that use.
On the other hand, the "communications encryption" flag in a self-signature is stating a preference that a given key be used for communications.
Note however, that it is a thorny issue to determine what is "communications" and what is "storage".
This decision is left wholly up to the implementation; the authors of this document do not claim any special wisdom on the issue and realize that accepted opinion may change.</t>

<t>The "split key" (0x10) and "group key" (0x80) flags are placed on a self-signature only; they are meaningless on a certification signature.
They SHOULD be placed only on a direct-key signature (type 0x1F) or a subkey signature (type 0x18), one that refers to the key the flag applies to.</t>

</section>
<section anchor="signers-user-id"><name>Signer's User ID</name>

<t>(String)</t>

<t>This subpacket allows a keyholder to state which User ID is responsible for the signing.
Many keyholders use a single key for different purposes, such as business communications as well as personal communications.
This subpacket allows such a keyholder to state which of their roles is making a signature.</t>

<t>This subpacket is not appropriate to use to refer to a User Attribute packet.</t>

</section>
<section anchor="reason-for-revocation"><name>Reason for Revocation</name>

<t>(1 octet of revocation code, N octets of reason string)</t>

<t>This subpacket is used only in key revocation and certification revocation signatures.
It describes the reason why the key or certificate was revoked.</t>

<t>The first octet contains a machine-readable code that denotes the reason for the revocation:</t>

<texttable title="Reasons for revocation">
      <ttcol align='right'>Code</ttcol>
      <ttcol align='left'>Reason</ttcol>
      <c>0</c>
      <c>No reason specified (key revocations or cert revocations)</c>
      <c>1</c>
      <c>Key is superseded (key revocations)</c>
      <c>2</c>
      <c>Key material has been compromised (key revocations)</c>
      <c>3</c>
      <c>Key is retired and no longer used (key revocations)</c>
      <c>32</c>
      <c>User ID information is no longer valid (cert revocations)</c>
      <c>100-110</c>
      <c>Private Use</c>
</texttable>

<t>Following the revocation code is a string of octets that gives information about the Reason for Revocation in human-readable form (UTF-8).
The string may be null (of zero length).
The length of the subpacket is the length of the reason string plus one.
An implementation SHOULD implement this subpacket, include it in all revocation signatures, and interpret revocations appropriately.
There are important semantic differences between the reasons, and there are thus important reasons for revoking signatures.</t>

<t>If a key has been revoked because of a compromise, all signatures created by that key are suspect.
However, if it was merely superseded or retired, old signatures are still valid.
If the revoked signature is the self-signature for certifying a User ID, a revocation denotes that that user name is no longer in use.
Such a revocation SHOULD include a 0x20 code.</t>

<t>Note that any signature may be revoked, including a certification on some other person's key.
There are many good reasons for revoking a certification signature, such as the case where the keyholder leaves the employ of a business with an email address.
A revoked certification is no longer a part of validity calculations.</t>

</section>
<section anchor="features-subpacket"><name>Features</name>

<t>(N octets of flags)</t>

<t>The Features subpacket denotes which advanced OpenPGP features a user's implementation supports.
This is so that as features are added to OpenPGP that cannot be backwards-compatible, a user can state that they can use that feature.
The flags are single bits that indicate that a given feature is supported.</t>

<t>This subpacket is similar to a preferences subpacket, and only appears in a self-signature.</t>

<t>An implementation SHOULD NOT use a feature listed when sending to a user who does not state that they can use it.</t>

<t>Defined features are as follows:</t>

<t>First octet:</t>

<texttable title="Features registry">
      <ttcol align='left'>Feature</ttcol>
      <ttcol align='left'>Definition</ttcol>
      <ttcol align='left'>Reference</ttcol>
      <c>0x01</c>
      <c>Symmetrically Encrypted Integrity Protected Data packet version 1</c>
      <c><xref target="version-one-seipd"/></c>
      <c>0x02</c>
      <c>Reserved</c>
      <c>&#160;</c>
      <c>0x04</c>
      <c>Reserved</c>
      <c>&#160;</c>
      <c>0x08</c>
      <c>Symmetrically Encrypted Integrity Protected Data packet version 2</c>
      <c><xref target="version-two-seipd"/></c>
</texttable>

<t>If an implementation implements any of the defined features, it SHOULD implement the Features subpacket, too.</t>

<t>An implementation may freely infer features from other suitable implementation-dependent mechanisms.</t>

<t>See <xref target="ciphertext-malleability"/> for details about how to use the Features subpacket when generating encryption data.</t>

</section>
<section anchor="signature-target"><name>Signature Target</name>

<t>(1 octet public-key algorithm, 1 octet hash algorithm, N octets hash)</t>

<t>This subpacket identifies a specific target signature to which a signature refers.
For revocation signatures, this subpacket provides explicit designation of which signature is being revoked.
For a third-party or timestamp signature, this designates what signature is signed.
All arguments are an identifier of that target signature.</t>

<t>The N octets of hash data MUST be the size of the hash of the signature.
For example, a target signature with a SHA-1 hash MUST have 20 octets of hash data.</t>

</section>
<section anchor="embedded-signature"><name>Embedded Signature</name>

<t>(1 signature packet body)</t>

<t>This subpacket contains a complete Signature packet body as specified in <xref target="signature-packet"/>.
It is useful when one signature needs to refer to, or be incorporated in, another signature.</t>

</section>
<section anchor="issuer-fingerprint"><name>Issuer Fingerprint</name>

<t>(1 octet key version number, N octets of fingerprint)</t>

<t>The OpenPGP Key fingerprint of the key issuing the signature.
This subpacket SHOULD be included in all signatures.
If the version of the issuing key is 4 and an Issuer subpacket is also included in the signature, the key ID of the Issuer subpacket MUST match the low 64 bits of the fingerprint.</t>

<t>Note that the length N of the fingerprint for a version 4 key is 20 octets; for a version 5 key N is 32.</t>

</section>
<section anchor="intended-recipient-fingerprint"><name>Intended Recipient Fingerprint</name>

<t>(1 octet key version number, N octets of fingerprint)</t>

<t>The OpenPGP Key fingerprint of the intended recipient primary key.
If one or more subpackets of this type are included in a signature, it SHOULD be considered valid only in an encrypted context, where the key it was encrypted to is one of the indicated primary keys, or one of their subkeys.
This can be used to prevent forwarding a signature outside of its intended, encrypted context.</t>

<t>Note that the length N of the fingerprint for a version 4 key is 20 octets; for a version 5 key N is 32.</t>

</section>
</section>
<section anchor="computing-signatures"><name>Computing Signatures</name>

<t>All signatures are formed by producing a hash over the signature data, and then using the resulting hash in the signature algorithm.</t>

<t>When a V5 signature is made, the salt is hashed first.</t>

<t>For binary document signatures (type 0x00), the document data is hashed directly.
For text document signatures (type 0x01), the document is canonicalized by converting line endings to &lt;CR&gt;&lt;LF&gt;, and the resulting data is hashed.</t>

<t>When a V4 signature is made over a key, the hash data starts with the octet 0x99, followed by a two-octet length of the key, and then body of the key packet.
When a V5 signature is made over a key, the hash data starts with the octet 0x9a, followed by a four-octet length of the key, and then body of the key packet.</t>

<t>A subkey binding signature (type 0x18) or primary key binding signature (type 0x19) then hashes the subkey using the same format as the main key (also using 0x99 or 0x9a as the first octet).
Primary key revocation signatures (type 0x20) hash only the key being revoked.
Subkey revocation signature (type 0x28) hash first the primary key and then the subkey being revoked.</t>

<t>A certification signature (type 0x10 through 0x13) hashes the User ID being bound to the key into the hash context after the above data.
A V3 certification hashes the contents of the User ID or attribute packet packet, without any header.
A V4 or V5 certification hashes the constant 0xB4 for User ID certifications or the constant 0xD1 for User Attribute certifications, followed by a four-octet number giving the length of the User ID or User Attribute data, and then the User ID or User Attribute data.</t>

<t>When a signature is made over a Signature packet (type 0x50, "Third-Party Confirmation signature"), the hash data starts with the octet 0x88, followed by the four-octet length of the signature, and then the body of the Signature packet.
(Note that this is a Legacy packet header for a Signature packet with the length-of-length field set to zero.) The unhashed subpacket data of the Signature packet being hashed is not included in the hash, and the unhashed subpacket data length value is set to zero.</t>

<t>Once the data body is hashed, then a trailer is hashed.
This trailer depends on the version of the signature.</t>

<t><list style="symbols">
  <t>A V3 signature hashes five octets of the packet body, starting from the signature type field.
This data is the signature type, followed by the four-octet signature time.</t>
  <t>A V4 or V5 signature hashes the packet body starting from its first field, the version number, through the end of the hashed subpacket data and a final extra trailer.
Thus, the hashed fields are:  <list style="symbols">
      <t>An octet indicating the signature version (0x04 for V4, 0x05 for V5),</t>
      <t>the signature type,</t>
      <t>the public-key algorithm,</t>
      <t>the hash algorithm,</t>
      <t>the hashed subpacket length,</t>
      <t>the hashed subpacket body,</t>
      <t>A second version octet (0x04 for V4, 0x05 for V5)</t>
      <t>A single octet 0xFF,</t>
      <t>A number representing the length of the hashed data from the Signature packet stopping right before the second version octet.
For a V4 signature, this is a four-octet big-endian number, considered to be an unsigned integer modulo 2**32.
For a V5 signature, this is an eight-octet big-endian number, considered to be an unsigned integer modulo 2**64.</t>
    </list></t>
</list></t>

<t>After all this has been hashed in a single hash context, the resulting hash field is used in the signature algorithm and placed at the end of the Signature packet.</t>

<section anchor="subpacket-hints"><name>Subpacket Hints</name>

<t>It is certainly possible for a signature to contain conflicting information in subpackets.
For example, a signature may contain multiple copies of a preference or multiple expiration times.
In most cases, an implementation SHOULD use the last subpacket in the signature, but MAY use any conflict resolution scheme that makes more sense.
Please note that we are intentionally leaving conflict resolution to the implementer; most conflicts are simply syntax errors, and the wishy-washy language here allows a receiver to be generous in what they accept, while putting pressure on a creator to be stingy in what they generate.</t>

<t>Some apparent conflicts may actually make sense --- for example, suppose a keyholder has a V3 key and a V4 key that share the same RSA key material.
Either of these keys can verify a signature created by the other, and it may be reasonable for a signature to contain an issuer subpacket for each key, as a way of explicitly tying those keys to the signature.</t>

</section>
</section>
</section>
<section anchor="skesk"><name>Symmetric-Key Encrypted Session Key Packets (Tag 3)</name>

<t>The Symmetric-Key Encrypted Session Key (SKESK) packet holds the symmetric-key encryption of a session key used to encrypt a message.
Zero or more Public-Key Encrypted Session Key packets (<xref target="pkesk"/>) and/or Symmetric-Key Encrypted Session Key packets may precede a an encryption container (that is, a Symmetrically Encrypted Integrity Protected Data packet or --- for historic data --- a Symmetrically Encrypted Data packet) that holds an encrypted message.
The message is encrypted with a session key, and the session key is itself encrypted and stored in the Encrypted Session Key packet(s).</t>

<t>If the encryption container is preceded by one or more Symmetric-Key Encrypted Session Key packets, each specifies a passphrase that may be used to decrypt the message.
This allows a message to be encrypted to a number of public keys, and also to one or more passphrases.</t>

<t>The body of this packet starts with a one-octet number giving the version number of the packet type.
The currently defined versions are 4 and 5.
The remainder of the packet depends on the version.</t>

<t>The versions differ in how they encrypt the session key with the password, and in what they encode.
The version of the SKESK packet must align with the version of the SEIPD packet (see <xref target="encrypted-message-versions"/>).</t>

<section anchor="v4-skesk"><name>v4 SKESK</name>

<t>A version 4 Symmetric-Key Encrypted Session Key (SKESK) packet precedes a version 1 Symmetrically Encrypted Integrity Protected Data (v1 SEIPD, see <xref target="version-one-seipd"/>) packet.
In historic data, it is sometimes found preceding a deprecated Symmetrically Encrypted Data packet (SED, see <xref target="sed"/>).
A v4 SKESK packet MUST NOT precede a v2 SEIPD packet (see <xref target="encrypted-message-versions"/>).</t>

<t>A version 4 Symmetric-Key Encrypted Session Key packet consists of:</t>

<t><list style="symbols">
  <t>A one-octet version number with value 4.</t>
  <t>A one-octet number describing the symmetric algorithm used.</t>
  <t>A string-to-key (S2K) specifier.
The length of the string-to-key specifier depends on its type (see <xref target="s2k-types"/>).</t>
  <t>Optionally, the encrypted session key itself, which is decrypted with the string-to-key object.</t>
</list></t>

<t>If the encrypted session key is not present (which can be detected on the basis of packet length and S2K specifier size), then the S2K algorithm applied to the passphrase produces the session key for decrypting the message, using the symmetric cipher algorithm from the Symmetric-Key Encrypted Session Key packet.</t>

<t>If the encrypted session key is present, the result of applying the S2K algorithm to the passphrase is used to decrypt just that encrypted session key field, using CFB mode with an IV of all zeros.
The decryption result consists of a one-octet algorithm identifier that specifies the symmetric-key encryption algorithm used to encrypt the following encryption container, followed by the session key octets themselves.</t>

<t>Note: because an all-zero IV is used for this decryption, the S2K specifier MUST use a salt value, either a Salted S2K, an Iterated-Salted S2K, or Argon2.
The salt value will ensure that the decryption key is not repeated even if the passphrase is reused.</t>

</section>
<section anchor="v5-skesk"><name>v5 SKESK</name>

<t>A version 5 Symmetric-Key Encrypted Session Key (SKESK) packet precedes a version 2 Symmetrically Encrypted Integrity Protected Data (v2 SEIPD, see <xref target="version-two-seipd"/>) packet.
A v5 SKESK packet MUST NOT precede a v1 SEIPD packet or a deprecated Symmetrically Encrypted Data packet (see <xref target="encrypted-message-versions"/>).</t>

<t>A version 5 Symmetric-Key Encrypted Session Key packet consists of:</t>

<t><list style="symbols">
  <t>A one-octet version number with value 5.</t>
  <t>A one-octet scalar octet count of the following 5 fields.</t>
  <t>A one-octet symmetric cipher algorithm identifier.</t>
  <t>A one-octet AEAD algorithm identifier.</t>
  <t>A one-octet scalar octet count of the following field.</t>
  <t>A string-to-key (S2K) specifier.
The length of the string-to-key specifier depends on its type (see <xref target="s2k-types"/>).</t>
  <t>A starting initialization vector of size specified by the AEAD algorithm.</t>
  <t>The encrypted session key itself.</t>
  <t>An authentication tag for the AEAD mode.</t>
</list></t>

<t>HKDF is used with SHA256 as hash algorithm, the key derived from S2K as Initial Keying Material (IKM), no salt, and the Packet Tag in new format encoding (bits 7 and 6 set, bits 5-0 carry the packet tag), the packet version, and the cipher-algo and AEAD-mode used to encrypt the key material, are used as info parameter.
Then, the session key is encrypted using the resulting key, with the AEAD algorithm specified for version 2 of the Symmetrically Encrypted Integrity Protected Data packet.
Note that no chunks are used and that there is only one authentication tag.
The Packet Tag in OpenPGP format encoding (bits 7 and 6 set, bits 5-0 carry the packet tag), the packet version number, the cipher algorithm octet, and the AEAD algorithm octet are given as additional data.
For example, the additional data used with AES-128 with OCB consists of the octets 0xC3, 0x05, 0x07, and 0x02.</t>

</section>
</section>
<section anchor="one-pass-signature-packets-tag-4"><name>One-Pass Signature Packets (Tag 4)</name>

<t>The One-Pass Signature packet precedes the signed data and contains enough information to allow the receiver to begin calculating any hashes needed to verify the signature.
It allows the Signature packet to be placed at the end of the message, so that the signer can compute the entire signed message in one pass.</t>

<t>The body of this packet consists of:</t>

<t><list style="symbols">
  <t>A one-octet version number.
The currently defined versions are 3 and 5.</t>
  <t>A one-octet signature type.
Signature types are described in <xref target="signature-types"/>.</t>
  <t>A one-octet number describing the hash algorithm used.</t>
  <t>A one-octet number describing the public-key algorithm used.</t>
  <t>Only for V5 packets, a 16 octet field containing random values used as salt.
The value must match the salt field of the corresponding Signature packet.</t>
  <t>Only for V3 packets, an eight-octet number holding the Key ID of the signing key.</t>
  <t>Only for V5 packets, a one octet key version number and N octets of the fingerprint of the signing key.
Note that the length N of the fingerprint for a version 5 key is 32.</t>
  <t>A one-octet number holding a flag showing whether the signature is nested.
A zero value indicates that the next packet is another One-Pass Signature packet that describes another signature to be applied to the same message data.</t>
</list></t>

<t>When generating a one-pass signature, the OPS packet version MUST correspond to the version of the associated signature packet, except for the historical accident that v4 keys use a v3 one-pass signature packet (there is no v4 OPS):</t>

<texttable title="Versions of packets used in a one-pass signature">
      <ttcol align='left'>Signing key version</ttcol>
      <ttcol align='left'>OPS packet version</ttcol>
      <ttcol align='left'>Signature packet version</ttcol>
      <c>4</c>
      <c>3</c>
      <c>4</c>
      <c>5</c>
      <c>5</c>
      <c>5</c>
</texttable>

<t>Note that if a message contains more than one one-pass signature, then the Signature packets bracket the message; that is, the first Signature packet after the message corresponds to the last one-pass packet and the final Signature packet corresponds to the first one-pass packet.</t>

</section>
<section anchor="key-material-packet"><name>Key Material Packet</name>

<t>A key material packet contains all the information about a public or private key.
There are four variants of this packet type, and two major versions.
Consequently, this section is complex.</t>

<section anchor="key-packet-variants"><name>Key Packet Variants</name>

<section anchor="public-key-packet-tag-6"><name>Public-Key Packet (Tag 6)</name>

<t>A Public-Key packet starts a series of packets that forms an OpenPGP key (sometimes called an OpenPGP certificate).</t>

</section>
<section anchor="public-subkey-packet-tag-14"><name>Public-Subkey Packet (Tag 14)</name>

<t>A Public-Subkey packet (tag 14) has exactly the same format as a Public-Key packet, but denotes a subkey.
One or more subkeys may be associated with a top-level key.
By convention, the top-level key provides signature services, and the subkeys provide encryption services.</t>

</section>
<section anchor="secret-key-packet-tag-5"><name>Secret-Key Packet (Tag 5)</name>

<t>A Secret-Key packet contains all the information that is found in a Public-Key packet, including the public-key material, but also includes the secret-key material after all the public-key fields.</t>

</section>
<section anchor="secret-subkey-packet-tag-7"><name>Secret-Subkey Packet (Tag 7)</name>

<t>A Secret-Subkey packet (tag 7) is the subkey analog of the Secret Key packet and has exactly the same format.</t>

</section>
</section>
<section anchor="public-key-packet-formats"><name>Public-Key Packet Formats</name>

<t>There are three versions of key-material packets.</t>

<t>OpenPGP implementations SHOULD create keys with version 5 format.
V4 keys are deprecated; an implementation SHOULD NOT generate a V4 key, but SHOULD accept it.
V3 keys are deprecated; an implementation MUST NOT generate a V3 key, but MAY accept it.
V2 keys are deprecated; an implementation MUST NOT generate a V2 key, but MAY accept it.</t>

<t>A version 3 public key or public-subkey packet contains:</t>

<t><list style="symbols">
  <t>A one-octet version number (3).</t>
  <t>A four-octet number denoting the time that the key was created.</t>
  <t>A two-octet number denoting the time in days that this key is valid.
If this number is zero, then it does not expire.</t>
  <t>A one-octet number denoting the public-key algorithm of this key.</t>
  <t>A series of multiprecision integers comprising the key material:  <list style="symbols">
      <t>a multiprecision integer (MPI) of RSA public modulus n;</t>
      <t>an MPI of RSA public encryption exponent e.</t>
    </list></t>
</list></t>

<t>V3 keys are deprecated.
They contain three weaknesses.
First, it is relatively easy to construct a V3 key that has the same Key ID as any other key because the Key ID is simply the low 64 bits of the public modulus.
Secondly, because the fingerprint of a V3 key hashes the key material, but not its length, there is an increased opportunity for fingerprint collisions.
Third, there are weaknesses in the MD5 hash algorithm that make developers prefer other algorithms.
See <xref target="key-ids-fingerprints"/> for a fuller discussion of Key IDs and fingerprints.</t>

<t>V2 keys are identical to the deprecated V3 keys except for the version number.</t>

<t>The version 4 format is similar to the version 3 format except for the absence of a validity period.
This has been moved to the Signature packet.
In addition, fingerprints of version 4 keys are calculated differently from version 3 keys, as described in <xref target="enhanced-key-formats"/>.</t>

<t>A version 4 packet contains:</t>

<t><list style="symbols">
  <t>A one-octet version number (4).</t>
  <t>A four-octet number denoting the time that the key was created.</t>
  <t>A one-octet number denoting the public-key algorithm of this key.</t>
  <t>A series of values comprising the key material.
This is algorithm-specific and described in <xref target="algorithm-specific-parts-of-keys"/>.</t>
</list></t>

<t>The version 5 format is similar to the version 4 format except for the addition of a count for the key material.
This count helps parsing secret key packets (which are an extension of the public key packet format) in the case of an unknown algorithm.
In addition, fingerprints of version 5 keys are calculated differently from version 4 keys, as described in <xref target="enhanced-key-formats"/>.</t>

<t>A version 5 packet contains:</t>

<t><list style="symbols">
  <t>A one-octet version number (5).</t>
  <t>A four-octet number denoting the time that the key was created.</t>
  <t>A one-octet number denoting the public-key algorithm of this key.</t>
  <t>A four-octet scalar octet count for the following public key material.</t>
  <t>A series of values comprising the public key material.
This is algorithm-specific and described in <xref target="algorithm-specific-parts-of-keys"/>.</t>
</list></t>

</section>
<section anchor="secret-key-packet-formats"><name>Secret-Key Packet Formats</name>

<t>The Secret-Key and Secret-Subkey packets contain all the data of the Public-Key and Public-Subkey packets, with additional algorithm-specific secret-key data appended, usually in encrypted form.</t>

<t>The packet contains:</t>

<t><list style="symbols">
  <t>The fields of a Public-Key or Public-Subkey packet, as described above.</t>
  <t>One octet indicating string-to-key usage conventions.
Zero indicates that the secret-key data is not encrypted.
255, 254, or 253 indicates that a string-to-key specifier is being given.
Any other value is a symmetric-key encryption algorithm identifier.
A version 5 packet MUST NOT use the value 255.</t>
  <t>Only for a version 5 packet, a one-octet scalar octet count of the next 5 optional fields.</t>
  <t>[Optional] If string-to-key usage octet was 255, 254, or 253, a one-octet symmetric encryption algorithm.</t>
  <t>[Optional] If string-to-key usage octet was 253, a one-octet AEAD algorithm.</t>
  <t>[Optional] Only for a version 5 packet, and if string-to-key usage octet was 255, 254, or 253, an one-octet count of the following field.</t>
  <t>[Optional] If string-to-key usage octet was 255, 254, or 253, a string-to-key (S2K) specifier.
The length of the string-to-key specifier depends on its type (see <xref target="s2k-types"/>).</t>
  <t>[Optional] If string-to-key usage octet was 253 (that is, the secret data is AEAD-encrypted), an initialization vector (IV) of size specified by the AEAD algorithm (see <xref target="version-two-seipd"/>), which is used as the nonce for the AEAD algorithm.</t>
  <t>[Optional] If string-to-key usage octet was 255, 254, or a cipher algorithm identifier (that is, the secret data is CFB-encrypted), an initialization vector (IV) of the same length as the cipher's block size.</t>
  <t>Plain or encrypted multiprecision integers comprising the secret key data.
This is algorithm-specific and described in <xref target="algorithm-specific-parts-of-keys"/>.
If the string-to-key usage octet is 253, then an AEAD authentication tag is part of that data.
If the string-to-key usage octet is 254, a 20-octet SHA-1 hash of the plaintext of the algorithm-specific portion is appended to plaintext and encrypted with it.
If the string-to-key usage octet is 255 or another nonzero value (that is, a symmetric-key encryption algorithm identifier), a two-octet checksum of the plaintext of the algorithm-specific portion (sum of all octets, mod 65536) is appended to plaintext and encrypted with it.
(This is deprecated and SHOULD NOT be used, see below.)</t>
  <t>If the string-to-key usage octet is zero, then a two-octet checksum of the algorithm-specific portion (sum of all octets, mod 65536).</t>
</list></t>

<t>The details about storing algorithm-specific secrets above are summarized in <xref target="secret-key-protection-details"/>.</t>

<t>Note that the version 5 packet format adds two count values to help parsing packets with unknown S2K or public key algorithms.</t>

<t>Secret MPI values can be encrypted using a passphrase.
If a string-to-key specifier is given, that describes the algorithm for converting the passphrase to a key, else a simple MD5 hash of the passphrase is used.
Implementations MUST use a string-to-key specifier; the simple hash is for backward compatibility and is deprecated, though implementations MAY continue to use existing private keys in the old format.
The cipher for encrypting the MPIs is specified in the Secret-Key packet.</t>

<t>Encryption/decryption of the secret data is done using the key created from the passphrase and the initialization vector from the packet.
If the string-to-key usage octet is not 253, CFB mode is used.
A different mode is used with V3 keys (which are only RSA) than with other key formats.
With V3 keys, the MPI bit count prefix (that is, the first two octets) is not encrypted.
Only the MPI non-prefix data is encrypted.
Furthermore, the CFB state is resynchronized at the beginning of each new MPI value, so that the CFB block boundary is aligned with the start of the MPI data.</t>

<t>With V4 and V5 keys, a simpler method is used.
All secret MPI values are encrypted, including the MPI bitcount prefix.</t>

<t>If the string-to-key usage octet is 253, the key encryption key is derived using HKDF (see <xref target="RFC5869"/>) to provide key separation.
HKDF is used with SHA256 as hash algorithm, the key derived from S2K as Initial Keying Material (IKM), no salt, and the Packet Tag in OpenPGP format encoding (bits 7 and 6 set, bits 5-0 carry the packet tag), the packet version, and the cipher-algo and AEAD-mode used to encrypt the key material, are used as info parameter.
Then, the encrypted MPI values are encrypted as one combined plaintext using one of the AEAD algorithms specified for version 2 of the Symmetrically Encrypted Integrity Protected Data packet.
Note that no chunks are used and that there is only one authentication tag.
As additional data, the Packet Tag in OpenPGP format encoding (bits 7 and 6 set, bits 5-0 carry the packet tag), followed by the public key packet fields, starting with the packet version number, are passed to the AEAD algorithm.
For example, the additional data used with a Secret-Key Packet of version 4 consists of the octets 0xC5, 0x04, followed by four octets of creation time, one octet denoting the public-key algorithm, and the algorithm-specific public-key parameters.
For a Secret-Subkey Packet, the first octet would be 0xC7.
For a version 5 key packet, the second octet would be 0x05, and the four-octet octet count of the public key material would be included as well (see <xref target="public-key-packet-formats"/>).</t>

<t>The two-octet checksum that follows the algorithm-specific portion is the algebraic sum, mod 65536, of the plaintext of all the algorithm-specific octets (including MPI prefix and data).
With V3 keys, the checksum is stored in the clear.
With V4 keys, the checksum is encrypted like the algorithm-specific data.
This value is used to check that the passphrase was correct.
However, this checksum is deprecated; an implementation SHOULD NOT use it, but should rather use the SHA-1 hash denoted with a usage octet of 254.
The reason for this is that there are some attacks that involve undetectably modifying the secret key.
If the string-to-key usage octet is 253 no checksum or SHA-1 hash is used but the authentication tag of the AEAD algorithm follows.</t>

<t>When decrypting the secret key material using any of these schemes (that is, where the usage octet is non-zero), the resulting cleartext octet stream MUST be well-formed.
In particular, an implementation MUST NOT interpret octets beyond the unwrapped cleartext octet stream as part of any of the unwrapped MPI objects.
Furthermore, an implementation MUST reject as unusable any secret key material whose cleartext length does not align with the lengths of the unwrapped MPI objects.</t>

</section>
</section>
<section anchor="algorithm-specific-parts-of-keys"><name>Algorithm-specific Parts of Keys</name>

<t>The public and secret key format specifies algorithm-specific parts of a key.
The following sections describe them in detail.</t>

<section anchor="key-rsa"><name>Algorithm-Specific Part for RSA Keys</name>

<t>The public key is this series of multiprecision integers:</t>

<t><list style="symbols">
  <t>MPI of RSA public modulus n;</t>
  <t>MPI of RSA public encryption exponent e.</t>
</list></t>

<t>The secret key is this series of multiprecision integers:</t>

<t><list style="symbols">
  <t>MPI of RSA secret exponent d;</t>
  <t>MPI of RSA secret prime value p;</t>
  <t>MPI of RSA secret prime value q (p &lt; q);</t>
  <t>MPI of u, the multiplicative inverse of p, mod q.</t>
</list></t>

</section>
<section anchor="key-dsa"><name>Algorithm-Specific Part for DSA Keys</name>

<t>The public key is this series of multiprecision integers:</t>

<t><list style="symbols">
  <t>MPI of DSA prime p;</t>
  <t>MPI of DSA group order q (q is a prime divisor of p-1);</t>
  <t>MPI of DSA group generator g;</t>
  <t>MPI of DSA public-key value y (= g**x mod p where x is secret).</t>
</list></t>

<t>The secret key is this single multiprecision integer:</t>

<t><list style="symbols">
  <t>MPI of DSA secret exponent x.</t>
</list></t>

</section>
<section anchor="key-elgamal"><name>Algorithm-Specific Part for Elgamal Keys</name>

<t>The public key is this series of multiprecision integers:</t>

<t><list style="symbols">
  <t>MPI of Elgamal prime p;</t>
  <t>MPI of Elgamal group generator g;</t>
  <t>MPI of Elgamal public key value y (= g**x mod p where x is secret).</t>
</list></t>

<t>The secret key is this single multiprecision integer:</t>

<t><list style="symbols">
  <t>MPI of Elgamal secret exponent x.</t>
</list></t>

</section>
<section anchor="key-ecdsa"><name>Algorithm-Specific Part for ECDSA Keys</name>

<t>The public key is this series of values:</t>

<t><list style="symbols">
  <t>A variable-length field containing a curve OID, which is formatted as follows:  <list style="symbols">
      <t>A one-octet size of the following field; values 0 and 0xFF are reserved for future extensions,</t>
      <t>The octets representing a curve OID (defined in <xref target="ec-curves"/>);</t>
    </list></t>
  <t>MPI of an EC point representing a public key.</t>
</list></t>

<t>The secret key is this single multiprecision integer:</t>

<t><list style="symbols">
  <t>MPI of an integer representing the secret key, which is a scalar of the public EC point.</t>
</list></t>

</section>
<section anchor="key-eddsa"><name>Algorithm-Specific Part for EdDSA Keys</name>

<t>The public key is this series of values:</t>

<t><list style="symbols">
  <t>A variable-length field containing a curve OID, formatted as follows:  <list style="symbols">
      <t>A one-octet size of the following field; values 0 and 0xFF are reserved for future extensions,</t>
      <t>The octets representing a curve OID, defined in <xref target="ec-curves"/>;</t>
    </list></t>
  <t>An MPI of an EC point representing a public key Q in prefixed native form (see <xref target="ec-point-prefixed-native"/>).</t>
</list></t>

<t>The secret key is this single multiprecision integer:</t>

<t><list style="symbols">
  <t>An MPI-encoded octet string representing the native form of the secret key, in the curve-specific format described in <xref target="curve-specific-formats"/>.</t>
</list></t>

<t>See <xref target="RFC8032"/> for more details about the native octet strings.</t>

</section>
<section anchor="key-ecdh"><name>Algorithm-Specific Part for ECDH Keys</name>

<t>The public key is this series of values:</t>

<t><list style="symbols">
  <t>A variable-length field containing a curve OID, which is formatted as follows:  <list style="symbols">
      <t>A one-octet size of the following field; values 0 and 0xFF are reserved for future extensions,</t>
      <t>Octets representing a curve OID, defined in <xref target="ec-curves"/>;</t>
    </list></t>
  <t>MPI of an EC point representing a public key, in the point format associated with the curve as specified in <xref target="curve-specific-formats"/></t>
  <t>A variable-length field containing KDF parameters, which is formatted as follows:  <list style="symbols">
      <t>A one-octet size of the following fields; values 0 and 0xFF are reserved for future extensions,</t>
      <t>A one-octet value 1, reserved for future extensions,</t>
      <t>A one-octet hash function ID used with a KDF,</t>
      <t>A one-octet algorithm ID for the symmetric algorithm used to wrap the symmetric key used for the message encryption; see <xref target="ec-dh-algorithm-ecdh"/> for details.</t>
    </list></t>
</list></t>

<t>Observe that an ECDH public key is composed of the same sequence of fields that define an ECDSA key plus the KDF parameters field.</t>

<t>The secret key is this single multiprecision integer:</t>

<t><list style="symbols">
  <t>An MPI representing the secret key, in the curve-specific format described in <xref target="curve-specific-formats"/>.</t>
</list></t>

<section anchor="ecdh-secret-key-material"><name>ECDH Secret Key Material</name>

<t>When curve P-256, P-384, or P-521 are used in ECDH, their secret keys are represented as a simple integer in standard MPI form.
Other curves are presented on the wire differently (though still as a single MPI), as described below and in <xref target="curve-specific-formats"/>.</t>

<section anchor="curve25519-secrets"><name>Curve25519 ECDH Secret Key Material</name>

<t>A Curve25519 secret key is stored as a standard integer in big-endian MPI form.
Note that this form is in reverse octet order from the little-endian "native" form found in <xref target="RFC7748"/>.</t>

<t>Note also that the integer for a Curve25519 secret key for OpenPGP MUST have the appropriate form: that is, it MUST be divisible by 8, MUST be at least 2**254, and MUST be less than 2**255.
The length of this MPI in bits is by definition always 255, so the two leading octets of the MPI will always be <spanx style="verb">00 ff</spanx> and reversing the following 32 octets from the wire will produce the "native" form.</t>

<t>When generating a new Curve25519 secret key from 32 fully-random octets, the following pseudocode produces the MPI wire format (note the similarity to <spanx style="verb">decodeScalar25519</spanx> from <xref target="RFC7748"/>):</t>

<figure><artwork><![CDATA[
def curve25519_MPI_from_random(octet_list):
    octet_list[0] &= 248
    octet_list[31] &= 127
    octet_list[31] |= 64
    mpi_header = [ 0x00, 0xff ]
    return mpi_header || reversed(octet_list)
]]></artwork></figure>

</section>
<section anchor="x448-ecdh-secret-key-material"><name>X448 ECDH Secret Key Material</name>

<t>An X448 secret key is contained within its MPI as a prefixed octet string (see <xref target="ec-prefix"/>), which encapsulates the native secret key format found in <xref target="RFC7748"/>.
The full wire format (as an MPI) will thus be the three octets <spanx style="verb">01 c7 40</spanx> followed by the full 56 octet native secret key.</t>

<t>When generating a new X448 secret key from 56 fully-random octets, the following pseudocode produces the MPI wire format:</t>

<figure><artwork><![CDATA[
def X448_MPI_from_random(octet_list):
    prefixed_header = [ 0x01, 0xc7, 0x40 ]
    return prefixed_header || octet_list
]]></artwork></figure>

</section>
</section>
</section>
</section>
<section anchor="compressed-data"><name>Compressed Data Packet (Tag 8)</name>

<t>The Compressed Data packet contains compressed data.
Typically, this packet is found as the contents of an encrypted packet, or following a Signature or One-Pass Signature packet, and contains a literal data packet.</t>

<t>The body of this packet consists of:</t>

<t><list style="symbols">
  <t>One octet that gives the algorithm used to compress the packet.</t>
  <t>Compressed data, which makes up the remainder of the packet.</t>
</list></t>

<t>A Compressed Data Packet's body contains an block that compresses some set of packets.
See <xref target="packet-composition"/> for details on how messages are formed.</t>

<t>ZIP-compressed packets are compressed with raw <xref target="RFC1951"/> DEFLATE blocks.</t>

<t>ZLIB-compressed packets are compressed with <xref target="RFC1950"/> ZLIB-style blocks.</t>

<t>BZip2-compressed packets are compressed using the BZip2 <xref target="BZ2"/> algorithm.</t>

<t>An implementation that generates a Compressed Data packet MUST use the non-legacy format for packet framing (see <xref target="openpgp-packet-format"/>).
It MUST NOT generate a Compressed Data packet with Legacy format (<xref target="legacy-packet-format"/>)</t>

<t>An implementation that deals with either historic data or data generated by legacy implementations MAY interpret Compressed Data packets that use the Legacy format for packet framing.</t>

</section>
<section anchor="sed"><name>Symmetrically Encrypted Data Packet (Tag 9)</name>

<t>The Symmetrically Encrypted Data packet contains data encrypted with a symmetric-key algorithm.
When it has been decrypted, it contains other packets (usually a literal data packet or compressed data packet, but in theory other Symmetrically Encrypted Data packets or sequences of packets that form whole OpenPGP messages).</t>

<t>This packet is obsolete.
An implementation MUST NOT create this packet.
An implementation MAY process such a packet but it MUST return a clear diagnostic that a non-integrity protected packet has been processed.
The implementation SHOULD also return an error in this case and stop processing.</t>

<t>This packet format is impossible to handle safely in general because the ciphertext it provides is malleable.
See <xref target="ciphertext-malleability"/> about selecting a better OpenPGP encryption container that does not have this flaw.</t>

<t>The body of this packet consists of:</t>

<t><list style="symbols">
  <t>Encrypted data, the output of the selected symmetric-key cipher operating in OpenPGP's variant of Cipher Feedback (CFB) mode.</t>
</list></t>

<t>The symmetric cipher used may be specified in a Public-Key or Symmetric-Key Encrypted Session Key packet that precedes the Symmetrically Encrypted Data packet.
In that case, the cipher algorithm octet is prefixed to the session key before it is encrypted.
If no packets of these types precede the encrypted data, the IDEA algorithm is used with the session key calculated as the MD5 hash of the passphrase, though this use is deprecated.</t>

<t>The data is encrypted in CFB mode, with a CFB shift size equal to the cipher's block size.
The Initial Vector (IV) is specified as all zeros.
Instead of using an IV, OpenPGP prefixes a string of length equal to the block size of the cipher plus two to the data before it is encrypted.
The first block-size octets (for example, 8 octets for a 64-bit block length) are random, and the following two octets are copies of the last two octets of the IV.
For example, in an 8-octet block, octet 9 is a repeat of octet 7, and octet 10 is a repeat of octet 8.
In a cipher of length 16, octet 17 is a repeat of octet 15 and octet 18 is a repeat of octet 16.
As a pedantic clarification, in both these examples, we consider the first octet to be numbered 1.</t>

<t>After encrypting the first block-size-plus-two octets, the CFB state is resynchronized.
The last block-size octets of ciphertext are passed through the cipher and the block boundary is reset.</t>

<t>The repetition of 16 bits in the random data prefixed to the message allows the receiver to immediately check whether the session key is incorrect.
See <xref target="security-considerations"/> for hints on the proper use of this "quick check".</t>

</section>
<section anchor="marker-packet-tag-10"><name>Marker Packet (Tag 10)</name>

<t>The body of this packet consists of:</t>

<t><list style="symbols">
  <t>The three octets 0x50, 0x47, 0x50 (which spell "PGP" in UTF-8).</t>
</list></t>

<t>Such a packet MUST be ignored when received.</t>

</section>
<section anchor="literal-data-packet-tag-11"><name>Literal Data Packet (Tag 11)</name>

<t>A Literal Data packet contains the body of a message; data that is not to be further interpreted.</t>

<t>The body of this packet consists of:</t>

<t><list style="symbols">
  <t>A one-octet field that describes how the data is formatted.  <vspace blankLines='1'/>
If it is a <spanx style="verb">b</spanx> (0x62), then the Literal packet contains binary data.
If it is a <spanx style="verb">u</spanx> (0x75), then the Literal packet contains UTF-8-encoded text data, and thus may need line ends converted to local form, or other text mode changes.  <vspace blankLines='1'/>
Older versions of OpenPGP used <spanx style="verb">t</spanx> (0x74) to indicate textual data, but did not specify the character encoding.
Implementations SHOULD NOT emit this value.
An implementation that receives a literal data packet with this value in the format field SHOULD interpret the packet data as UTF-8 encoded text, unless reliable (not attacker-controlled) context indicates a specific alternate text encoding.
This mode is deprecated due to its ambiguity.  <vspace blankLines='1'/>
Early versions of PGP also defined a value of <spanx style="verb">l</spanx> as a 'local' mode for machine-local conversions.
<xref target="RFC1991"/> incorrectly stated this local mode flag as <spanx style="verb">1</spanx> (ASCII numeral one).
Both of these local modes are deprecated.</t>
  <t>File name as a string (one-octet length, followed by a file name).
This may be a zero-length string.
Commonly, if the source of the encrypted data is a file, this will be the name of the encrypted file.
An implementation MAY consider the file name in the Literal packet to be a more authoritative name than the actual file name.</t>
  <t>A four-octet number that indicates a date associated with the literal data.
Commonly, the date might be the modification date of a file, or the time the packet was created, or a zero that indicates no specific time.</t>
  <t>The remainder of the packet is literal data.  <vspace blankLines='1'/>
Text data is stored with &lt;CR&gt;&lt;LF&gt; text endings (that is, network-normal line endings).
These should be converted to native line endings by the receiving software.</t>
</list></t>

<t>Note that OpenPGP signatures do not include the formatting octet, the file name, and the date field of the literal packet in a signature hash and thus those fields are not protected against tampering in a signed document.
A receiving implementation MUST NOT treat those fields as though they were cryptographically secured by the surrounding signature either when representing them to the user or acting on them.</t>

<t>Due to their inherent malleability, an implementation that generates a literal data packet SHOULD avoid storing any significant data in these fields.
If the implementation is certain that the data is textual and is encoded with UTF-8 (for example, if it will follow this literal data packet with a signature packet of type 0x01 (see <xref target="signature-types"/>), it MAY set the format octet to <spanx style="verb">u</spanx>.
Otherwise, it SHOULD set the format octet to <spanx style="verb">b</spanx>.
It SHOULD set the filename to the empty string (encoded as a single zero octet), and the timestamp to zero (encoded as four zero octets).</t>

<t>An application that wishes to include such filesystem metadata within a signature is advised to sign an encapsulated archive (for example, <xref target="PAX"/>).</t>

<t>An implementation that generates a Literal Data packet MUST use the OpenPGP format for packet framing (see <xref target="openpgp-packet-format"/>).
It MUST NOT generate a Literal Data packet with Legacy format (<xref target="legacy-packet-format"/>)</t>

<t>An implementation that deals with either historic data or data generated by legacy implementations MAY interpret Literal Data packets that use the Legacy format for packet framing.</t>

<section anchor="special-filename-console-deprecated"><name>Special Filename _CONSOLE (Deprecated)</name>

<t>The Literal Data packet's filename field has a historical special case for the special name <spanx style="verb">_CONSOLE</spanx>.
When the filename field is <spanx style="verb">_CONSOLE</spanx>, the message is considered to be "for your eyes only".
This advises that the message data is unusually sensitive, and the receiving program should process it more carefully, perhaps avoiding storing the received data to disk, for example.</t>

<t>An OpenPGP deployment that generates literal data packets MUST NOT depend on this indicator being honored in any particular way.
It cannot be enforced, and the field itself is not covered by any cryptographic signature.</t>

<t>It is NOT RECOMMENDED to use this special filename in a newly-generated literal data packet.</t>

</section>
</section>
<section anchor="trust-packet-tag-12"><name>Trust Packet (Tag 12)</name>

<t>The Trust packet is used only within keyrings and is not normally exported.
Trust packets contain data that record the user's specifications of which key holders are trustworthy introducers, along with other information that implementing software uses for trust information.
The format of Trust packets is defined by a given implementation.</t>

<t>Trust packets SHOULD NOT be emitted to output streams that are transferred to other users, and they SHOULD be ignored on any input other than local keyring files.</t>

</section>
<section anchor="user-id-packet-tag-13"><name>User ID Packet (Tag 13)</name>

<t>A User ID packet consists of UTF-8 text that is intended to represent the name and email address of the key holder.
By convention, it includes an <xref target="RFC2822"/> mail name-addr, but there are no restrictions on its content.
The packet length in the header specifies the length of the User ID.</t>

</section>
<section anchor="user-attribute-packet"><name>User Attribute Packet (Tag 17)</name>

<t>The User Attribute packet is a variation of the User ID packet.
It is capable of storing more types of data than the User ID packet, which is limited to text.
Like the User ID packet, a User Attribute packet may be certified by the key owner ("self-signed") or any other key owner who cares to certify it.
Except as noted, a User Attribute packet may be used anywhere that a User ID packet may be used.</t>

<t>While User Attribute packets are not a required part of the OpenPGP standard, implementations SHOULD provide at least enough compatibility to properly handle a certification signature on the User Attribute packet.
A simple way to do this is by treating the User Attribute packet as a User ID packet with opaque contents, but an implementation may use any method desired.</t>

<t>The User Attribute packet is made up of one or more attribute subpackets.
Each subpacket consists of a subpacket header and a body.
The header consists of:</t>

<t><list style="symbols">
  <t>the subpacket length (1, 2, or 5 octets)</t>
  <t>the subpacket type (1 octet)</t>
</list></t>

<t>and is followed by the subpacket specific data.</t>

<t>The following table lists the currently known subpackets:</t>

<texttable title="User Attribute type registry">
      <ttcol align='right'>Type</ttcol>
      <ttcol align='left'>Attribute Subpacket</ttcol>
      <c>1</c>
      <c>Image Attribute Subpacket</c>
      <c>100-110</c>
      <c>Private/Experimental Use</c>
</texttable>

<t>An implementation SHOULD ignore any subpacket of a type that it does not recognize.</t>

<section anchor="uat-image"><name>The Image Attribute Subpacket</name>

<t>The Image Attribute subpacket is used to encode an image, presumably (but not required to be) that of the key owner.</t>

<t>The Image Attribute subpacket begins with an image header.
The first two octets of the image header contain the length of the image header.
Note that unlike other multi-octet numerical values in this document, due to a historical accident this value is encoded as a little-endian number.
The image header length is followed by a single octet for the image header version.
The only currently defined version of the image header is 1, which is a 16-octet image header.
The first three octets of a version 1 image header are thus 0x10, 0x00, 0x01.</t>

<t>The fourth octet of a version 1 image header designates the encoding format of the image.
The only currently defined encoding format is the value 1 to indicate JPEG.
Image format types 100 through 110 are reserved for private or experimental use.
The rest of the version 1 image header is made up of 12 reserved octets, all of which MUST be set to 0.</t>

<t>The rest of the image subpacket contains the image itself.
As the only currently defined image type is JPEG, the image is encoded in the JPEG File Interchange Format (JFIF), a standard file format for JPEG images <xref target="JFIF"/>.</t>

<t>An implementation MAY try to determine the type of an image by examination of the image data if it is unable to handle a particular version of the image header or if a specified encoding format value is not recognized.</t>

</section>
</section>
<section anchor="seipd"><name>Sym. Encrypted Integrity Protected Data Packet (Tag 18)</name>

<t>This packet contains integrity protected and encrypted data.
When it has been decrypted, it will contain other packets forming an OpenPGP Message (see <xref target="openpgp-messages"/>).</t>

<t>The first octet of this packet is always used to indicate the version number, but different versions contain differently-structured ciphertext.
Version 1 of this packet contains data encrypted with a symmetric-key algorithm and protected against modification by the SHA-1 hash algorithm.
This is a legacy OpenPGP mechanism that offers some protections against ciphertext malleability.</t>

<t>Version 2 of this packet contains data encrypted with an authenticated encryption and additional data (AEAD) construction.
This offers a more cryptographically rigorous defense against ciphertext malleability, but may not be as widely supported yet.
See <xref target="ciphertext-malleability"/> for more details on choosing between these formats.</t>

<section anchor="version-one-seipd"><name>Version 1 Sym. Encrypted Integrity Protected Data Packet Format</name>

<t>A version 1 Symmetrically Encrypted Integrity Protected Data packet consists of:</t>

<t><list style="symbols">
  <t>A one-octet version number with value 1.</t>
  <t>Encrypted data, the output of the selected symmetric-key cipher operating in Cipher Feedback mode with shift amount equal to the block size of the cipher (CFB-n where n is the block size).</t>
</list></t>

<t>The symmetric cipher used MUST be specified in a Public-Key or Symmetric-Key Encrypted Session Key packet that precedes the Symmetrically Encrypted Integrity Protected Data packet.
In either case, the cipher algorithm octet is prefixed to the session key before it is encrypted.</t>

<t>The data is encrypted in CFB mode, with a CFB shift size equal to the cipher's block size.
The Initial Vector (IV) is specified as all zeros.
Instead of using an IV, OpenPGP prefixes an octet string to the data before it is encrypted.
The length of the octet string equals the block size of the cipher in octets, plus two.
The first octets in the group, of length equal to the block size of the cipher, are random; the last two octets are each copies of their 2nd preceding octet.
For example, with a cipher whose block size is 128 bits or 16 octets, the prefix data will contain 16 random octets, then two more octets, which are copies of the 15th and 16th octets, respectively.
Unlike the Symmetrically Encrypted Data Packet, no special CFB resynchronization is done after encrypting this prefix data.
See <xref target="cfb-mode"/> for more details.</t>

<t>The repetition of 16 bits in the random data prefixed to the message allows the receiver to immediately check whether the session key is incorrect.</t>

<t>Two constant octets with the values 0xD3 and 0x14 are appended to the plaintext.
Then, the plaintext of the data to be encrypted is passed through the SHA-1 hash function.
The input to the hash function includes the prefix data described above; it includes all of the plaintext, including the trailing constant octets 0xD3, 0x14.
The 20 octets of the SHA-1 hash are then appended to the plaintext (after the constant octets 0xD3, 0x14) and encrypted along with the plaintext using the same CFB context.
This trailing checksum is known as the Modification Detection Code (MDC).</t>

<t>During decryption, the plaintext data should be hashed with SHA-1, including the prefix data as well as the trailing constant octets 0xD3, 0x14, but excluding the last 20 octets containing the SHA-1 hash.
The computed SHA-1 hash is then compared with the last 20 octets of plaintext.
A mismatch of the hash indicates that the message has been modified and MUST be treated as a security problem.
Any failure SHOULD be reported to the user.</t>

<ul empty="true"><li>
  <t>NON-NORMATIVE EXPLANATION</t>

  <t>The Modification Detection Code (MDC) system, as the integrity
  protection mechanism of version 1 of the Symmetrically Encrypted
  Integrity Protected Data packet is called, was created to
  provide an integrity mechanism that is less strong than a
  signature, yet stronger than bare CFB encryption.</t>

  <t>It is a limitation of CFB encryption that damage to the ciphertext
  will corrupt the affected cipher blocks and the block following.
  Additionally, if data is removed from the end of a CFB-encrypted
  block, that removal is undetectable.  (Note also that CBC mode has
  a similar limitation, but data removed from the front of the block
  is undetectable.)</t>

  <t>The obvious way to protect or authenticate an encrypted block is
  to digitally sign it.  However, many people do not wish to
  habitually sign data, for a large number of reasons beyond the
  scope of this document.  Suffice it to say that many people
  consider properties such as deniability to be as valuable as
  integrity.</t>

  <t>OpenPGP addresses this desire to have more security than raw
  encryption and yet preserve deniability with the MDC system.  An
  MDC is intentionally not a MAC.  Its name was not selected by
  accident.  It is analogous to a checksum.</t>

  <t>Despite the fact that it is a relatively modest system, it has
  proved itself in the real world.  It is an effective defense to
  several attacks that have surfaced since it has been created.  It
  has met its modest goals admirably.</t>

  <t>Consequently, because it is a modest security system, it has
  modest requirements on the hash function(s) it employs.  It does
  not rely on a hash function being collision-free, it relies on a
  hash function being one-way.  If a forger, Frank, wishes to send
  Alice a (digitally) unsigned message that says, "I've always
  secretly loved you, signed Bob", it is far easier for him to
  construct a new message than it is to modify anything intercepted
  from Bob.  (Note also that if Bob wishes to communicate secretly
  with Alice, but without authentication or identification and with
  a threat model that includes forgers, he has a problem that
  transcends mere cryptography.)</t>

  <t>Note also that unlike nearly every other OpenPGP subsystem, there
  are no parameters in the MDC system.  It hard-defines SHA-1 as its
  hash function.  This is not an accident.  It is an intentional
  choice to avoid downgrade and cross-grade attacks while making a
  simple, fast system.  (A downgrade attack would be an attack that
  replaced SHA2-256 with SHA-1, for example.  A cross-grade attack
  would replace SHA-1 with another 160-bit hash, such as
  RIPE-MD/160, for example.)</t>

  <t>However, no update will be needed because the MDC has been replaced
  by the AEAD encryption described in this document.</t>
</li></ul>

</section>
<section anchor="version-two-seipd"><name>Version 2 Sym. Encrypted Integrity Protected Data Packet Format</name>

<t>A version 2 Symmetrically Encrypted Integrity Protected Data packet consists of:</t>

<t><list style="symbols">
  <t>A one-octet version number with value 2.</t>
  <t>A one-octet cipher algorithm.</t>
  <t>A one-octet AEAD algorithm.</t>
  <t>A one-octet chunk size.</t>
  <t>Thirty-two octets of salt.
The salt is used to derive the message key and must be unique.</t>
  <t>Encrypted data, the output of the selected symmetric-key cipher operating in the given AEAD mode.</t>
  <t>A final, summary authentication tag for the AEAD mode.</t>
</list></t>

<t>The decrypted session key and the salt are used to derive an M-bit message key and N-64 bits used as initialization vector, where M is the key size of the symmetric algorithm and N is the nonce size of the AEAD algorithm.
M + N - 64 bits are derived using HKDF (see <xref target="RFC5869"/>).
The left-most M bits are used as symmetric algorithm key, the remaining N - 64 bits are used as initialization vector.
HKDF is used with SHA256 as hash algorithm, the session key as Initial Keying Material (IKM), the salt as salt, and the Packet Tag in OpenPGP format encoding (bits 7 and 6 set, bits 5-0 carry the packet tag), version number, cipher algorithm octet, AEAD algorithm octet, and chunk size octet as info parameter.</t>

<t>The KDF mechanism provides key separation between cipher and AEAD algorithms.
Furthermore, an implementation can securely reply to a message even if a recipients certificate is unknown by reusing the encrypted session key packets and replying with a different salt yielding a new, unique message key.</t>

<t>A v2 SEIPD packet consists of one or more chunks of data.
The plaintext of each chunk is of a size specified using the chunk size octet using the method specified below.</t>

<t>The encrypted data consists of the encryption of each chunk of plaintext, followed immediately by the relevant authentication tag.
If the last chunk of plaintext is smaller than the chunk size, the ciphertext for that data may be shorter; it is nevertheless followed by a full authentication tag.</t>

<t>For each chunk, the AEAD construction is given the Packet Tag in OpenPGP format encoding (bits 7 and 6 set, bits 5-0 carry the packet tag), version number, cipher algorithm octet, AEAD algorithm octet, and chunk size octet as additional data.
For example, the additional data of the first chunk using EAX and AES-128 with a chunk size of 2**16 octets consists of the octets 0xD2, 0x02, 0x07, 0x01, and 0x10.</t>

<t>After the final chunk, the AEAD algorithm is used to produce a final authentication tag encrypting the empty string.
This AEAD instance is given the additional data specified above, plus an eight-octet, big-endian value specifying the total number of plaintext octets encrypted.
This allows detection of a truncated ciphertext.</t>

<t>The chunk size octet specifies the size of chunks using the following formula (in C), where c is the chunk size octet:</t>

<figure><artwork><![CDATA[
  chunk_size = ((uint64_t)1 << (c + 6))
]]></artwork></figure>

<t>An implementation MUST accept chunk size octets with values from 0 to 16.
An implementation MUST NOT create data with a chunk size octet value larger than 16 (4 MiB chunks).</t>

<t>The nonce for AEAD mode consists of two parts.
Let N be the size of the nonce.
The left-most N - 64 bits are the initialization vector derived using HKDF.
The right-most 64 bits are the chunk index as big-endian value.
The index of the first chunk is zero.</t>

</section>
<section anchor="eax-mode"><name>EAX Mode</name>

<t>The EAX AEAD Algorithm used in this document is defined in <xref target="EAX"/>.</t>

<t>The EAX algorithm can only use block ciphers with 16-octet blocks.
The nonce is 16 octets long.
EAX authentication tags are 16 octets long.</t>

</section>
<section anchor="ocb-mode"><name>OCB Mode</name>

<t>The OCB AEAD Algorithm used in this document is defined in <xref target="RFC7253"/>.</t>

<t>The OCB algorithm can only use block ciphers with 16-octet blocks.
The nonce is 15 octets long.
OCB authentication tags are 16 octets long.</t>

</section>
<section anchor="gcm-mode"><name>GCM Mode</name>

<t>The GCM AEAD Algorithm used in this document is defined in <xref target="SP800-38D"/>.</t>

<t>The GCM algorithm can only use block ciphers with 16-octet blocks.
The nonce is 12 octets long.
GCM authentication tags are 16 octets long.</t>

</section>
</section>
<section anchor="padding-packet"><name>Padding Packet (Tag 21)</name>

<t>The Padding packet contains random data, and can be used to defend against traffic analysis (see <xref target="traffic-analysis"/>) on version 2 SEIPD messages (see <xref target="version-two-seipd"/>) and Transferable Public Keys (see <xref target="transferable-public-keys"/>).</t>

<t>Such a packet MUST be ignored when received.</t>

<t>Its contents SHOULD be random octets to make the length obfuscation it provides more robust even when compressed.</t>

<t>An implementation adding padding to an OpenPGP stream SHOULD place such a packet:</t>

<t><list style="symbols">
  <t>At the end of a v5 Transferable Public Key that is transferred over an encrypted channel (see <xref target="transferable-public-keys"/>).</t>
  <t>As the last packet of an Optionally Padded Message within a version 2 Symmetrically Encrypted Integrity Protected Data Packet (see <xref target="unwrapping"/>).</t>
</list></t>

<t>An implementation MUST be able to process padding packets anywhere else in an OpenPGP stream, so that future revisions of this document may specify further locations for padding.</t>

<t>Policy about how large to make such a packet to defend against traffic analysis is beyond the scope of this document.</t>

</section>
</section>
<section anchor="radix-64-conversions"><name>Radix-64 Conversions</name>

<t>As stated in the introduction, OpenPGP's underlying native representation for objects is a stream of arbitrary octets, and some systems desire these objects to be immune to damage caused by character set translation, data conversions, etc.</t>

<t>In principle, any printable encoding scheme that met the requirements of the unsafe channel would suffice, since it would not change the underlying binary bit streams of the native OpenPGP data structures.
The OpenPGP standard specifies one such printable encoding scheme to ensure interoperability.</t>

<t>OpenPGP's Radix-64 encoding is composed of two parts: a base64 encoding of the binary data and an optional checksum.
The base64 encoding is identical to the MIME base64 content-transfer-encoding <xref target="RFC2045"/>.</t>

<t>The optional checksum is a 24-bit Cyclic Redundancy Check (CRC) converted to four characters of radix-64 encoding by the same MIME base64 transformation, preceded by an equal sign (=).
The CRC is computed by using the generator 0x864CFB and an initialization of 0xB704CE.
The accumulation is done on the data before it is converted to radix-64, rather than on the converted data.
A sample implementation of this algorithm is in <xref target="sample-crc24"/>.</t>

<t>If present, the checksum with its leading equal sign MUST appear on the next line after the base64 encoded data.</t>

<t>Rationale for CRC-24: The size of 24 bits fits evenly into printable base64.
The nonzero initialization can detect more errors than a zero initialization.</t>

<section anchor="sample-crc24"><name>An Implementation of the CRC-24 in "C"</name>

<figure><sourcecode type="text/x-csrc" name="sample-crc24.c"><![CDATA[
#define CRC24_INIT 0xB704CEL
#define CRC24_GENERATOR 0x864CFBL

typedef unsigned long crc24;
crc24 crc_octets(unsigned char *octets, size_t len)
{
    crc24 crc = CRC24_INIT;
    int i;
    while (len--) {
        crc ^= (*octets++) << 16;
        for (i = 0; i < 8; i++) {
            crc <<= 1;
            if (crc & 0x1000000) {
                crc &= 0xffffff; /* Clear bit 25 to avoid overflow */
                crc ^= CRC24_GENERATOR;
            }
        }
    }
    return crc & 0xFFFFFFL;
}
]]></sourcecode></figure>

</section>
<section anchor="forming-ascii-armor"><name>Forming ASCII Armor</name>

<t>When OpenPGP encodes data into ASCII Armor, it puts specific headers around the Radix-64 encoded data, so OpenPGP can reconstruct the data later.
An OpenPGP implementation MAY use ASCII armor to protect raw binary data.
OpenPGP informs the user what kind of data is encoded in the ASCII armor through the use of the headers.</t>

<t>Concatenating the following data creates ASCII Armor:</t>

<t><list style="symbols">
  <t>An Armor Header Line, appropriate for the type of data</t>
  <t>Armor Headers</t>
  <t>A blank (zero-length, or containing only whitespace) line</t>
  <t>The ASCII-Armored data</t>
  <t>An Armor Checksum</t>
  <t>The Armor Tail, which depends on the Armor Header Line</t>
</list></t>

<t>An Armor Header Line consists of the appropriate header line text surrounded by five (5) dashes (<spanx style="verb">-</spanx>, 0x2D) on either side of the header line text.
The header line text is chosen based upon the type of data that is being encoded in Armor, and how it is being encoded.
Header line texts include the following strings:</t>

<dl newline="true">
  <dt>
BEGIN PGP MESSAGE  </dt>
  <dd>
    <t>Used for signed, encrypted, or compressed files.</t>
  </dd>
  <dt>
BEGIN PGP PUBLIC KEY BLOCK  </dt>
  <dd>
    <t>Used for armoring public keys.</t>
  </dd>
  <dt>
BEGIN PGP PRIVATE KEY BLOCK  </dt>
  <dd>
    <t>Used for armoring private keys.</t>
  </dd>
  <dt>
BEGIN PGP MESSAGE, PART X/Y  </dt>
  <dd>
    <t>Used for multi-part messages, where the armor is split amongst Y parts, and this is the Xth part out of Y.</t>
  </dd>
  <dt>
BEGIN PGP MESSAGE, PART X  </dt>
  <dd>
    <t>Used for multi-part messages, where this is the Xth part of an unspecified number of parts.
Requires the MESSAGE-ID Armor Header to be used.</t>
  </dd>
  <dt>
BEGIN PGP SIGNATURE  </dt>
  <dd>
    <t>Used for detached signatures, OpenPGP/MIME signatures, and cleartext signatures.</t>
  </dd>
</dl>

<t>Note that all these Armor Header Lines are to consist of a complete line.
That is to say, there is always a line ending preceding the starting five dashes, and following the ending five dashes.
The header lines, therefore, MUST start at the beginning of a line, and MUST NOT have text other than whitespace following them on the same line.
These line endings are considered a part of the Armor Header Line for the purposes of determining the content they delimit.
This is particularly important when computing a cleartext signature (see <xref target="cleartext-signature"/>).</t>

<t>The Armor Headers are pairs of strings that can give the user or the receiving OpenPGP implementation some information about how to decode or use the message.
The Armor Headers are a part of the armor, not a part of the message, and hence are not protected by any signatures applied to the message.</t>

<t>The format of an Armor Header is that of a key-value pair.
A colon (<spanx style="verb">:</spanx> 0x38) and a single space (0x20) separate the key and value.
OpenPGP should consider improperly formatted Armor Headers to be corruption of the ASCII Armor.
Unknown keys should be reported to the user, but OpenPGP should continue to process the message.</t>

<t>Note that some transport methods are sensitive to line length.
While there is a limit of 76 characters for the Radix-64 data (<xref target="encoding-binary-radix64"/>), there is no limit to the length of Armor Headers.
Care should be taken that the Armor Headers are short enough to survive transport.
One way to do this is to repeat an Armor Header Key multiple times with different values for each so that no one line is overly long.</t>

<t>Currently defined Armor Header Keys are as follows:</t>

<t><list style="symbols">
  <t>"Version", which states the OpenPGP implementation and version used to encode the message.
To minimize metadata, implementations SHOULD NOT emit this key and its corresponding value except for debugging purposes with explicit user consent.</t>
  <t>"Comment", a user-defined comment.
OpenPGP defines all text to be in UTF-8.
A comment may be any UTF-8 string.
However, the whole point of armoring is to provide seven-bit-clean data.
Consequently, if a comment has characters that are outside the US-ASCII range of UTF, they may very well not survive transport.</t>
  <t>"MessageID", a 32-character string of printable characters.
The string must be the same for all parts of a multi-part message that uses the "PART X" Armor Header.
MessageID strings should be unique enough that the recipient of the mail can associate all the parts of a message with each other.
A good checksum or cryptographic hash function is sufficient.  <vspace blankLines='1'/>
The MessageID SHOULD NOT appear unless it is in a multi-part message.
If it appears at all, it MUST be computed from the finished (encrypted, signed, etc.) message in a deterministic fashion, rather than contain a purely random value.
This is to allow the legitimate recipient to determine that the MessageID cannot serve as a covert means of leaking cryptographic key information.</t>
  <t>"Hash", a comma-separated list of hash algorithms used in this message.
This is used only in cleartext signed messages.</t>
  <t>"SaltedHash", a salt and hash algorithm used in this message.
This is used only in cleartext signed messages that are followed by a v5 Signature.</t>
  <t>"Charset", a description of the character set that the plaintext is in.
Please note that OpenPGP defines text to be in UTF-8.
An implementation will get best results by translating into and out of UTF-8.
However, there are many instances where this is easier said than done.
Also, there are communities of users who have no need for UTF-8 because they are all happy with a character set like ISO Latin-5 or a Japanese character set.
In such instances, an implementation MAY override the UTF-8 default by using this header key.
An implementation MAY implement this key and any translations it cares to; an implementation MAY ignore it and assume all text is UTF-8.</t>
</list></t>

<t>The Armor Tail Line is composed in the same manner as the Armor Header Line, except the string "BEGIN" is replaced by the string "END".</t>

</section>
<section anchor="encoding-binary-radix64"><name>Encoding Binary in Radix-64</name>

<t>The encoding process represents 24-bit groups of input bits as output strings of 4 encoded characters.
Proceeding from left to right, a 24-bit input group is formed by concatenating three 8-bit input groups.
These 24 bits are then treated as four concatenated 6-bit groups, each of which is translated into a single digit in the Radix-64 alphabet.
When encoding a bit stream with the Radix-64 encoding, the bit stream must be presumed to be ordered with the most significant bit first.
That is, the first bit in the stream will be the high-order bit in the first 8-bit octet, and the eighth bit will be the low-order bit in the first 8-bit octet, and so on.</t>

<figure><artwork><![CDATA[
┌──first octet──┬─second octet──┬──third octet──┐
│7 6 5 4 3 2 1 0│7 6 5 4 3 2 1 0│7 6 5 4 3 2 1 0│
├───────────┬───┴───────┬───────┴───┬───────────┤
│5 4 3 2 1 0│5 4 3 2 1 0│5 4 3 2 1 0│5 4 3 2 1 0│
└──1.index──┴──2.index──┴──3.index──┴──4.index──┘
]]></artwork></figure>

<t>Each 6-bit group is used as an index into an array of 64 printable characters from the table below.
The character referenced by the index is placed in the output string.</t>

<texttable title="Encoding for Radix-64">
      <ttcol align='right'>Value</ttcol>
      <ttcol align='left'>Encoding</ttcol>
      <ttcol align='left'>&#160;</ttcol>
      <ttcol align='right'>Value</ttcol>
      <ttcol align='left'>Encoding</ttcol>
      <ttcol align='left'>&#160;</ttcol>
      <ttcol align='right'>Value</ttcol>
      <ttcol align='left'>Encoding</ttcol>
      <ttcol align='left'>&#160;</ttcol>
      <ttcol align='right'>Value</ttcol>
      <ttcol align='left'>Encoding</ttcol>
      <c>0</c>
      <c>A</c>
      <c>&#160;</c>
      <c>17</c>
      <c>R</c>
      <c>&#160;</c>
      <c>34</c>
      <c>i</c>
      <c>&#160;</c>
      <c>51</c>
      <c>z</c>
      <c>1</c>
      <c>B</c>
      <c>&#160;</c>
      <c>18</c>
      <c>S</c>
      <c>&#160;</c>
      <c>35</c>
      <c>j</c>
      <c>&#160;</c>
      <c>52</c>
      <c>0</c>
      <c>2</c>
      <c>C</c>
      <c>&#160;</c>
      <c>19</c>
      <c>T</c>
      <c>&#160;</c>
      <c>36</c>
      <c>k</c>
      <c>&#160;</c>
      <c>53</c>
      <c>1</c>
      <c>3</c>
      <c>D</c>
      <c>&#160;</c>
      <c>20</c>
      <c>U</c>
      <c>&#160;</c>
      <c>37</c>
      <c>l</c>
      <c>&#160;</c>
      <c>54</c>
      <c>2</c>
      <c>4</c>
      <c>E</c>
      <c>&#160;</c>
      <c>21</c>
      <c>V</c>
      <c>&#160;</c>
      <c>38</c>
      <c>m</c>
      <c>&#160;</c>
      <c>55</c>
      <c>3</c>
      <c>5</c>
      <c>F</c>
      <c>&#160;</c>
      <c>22</c>
      <c>W</c>
      <c>&#160;</c>
      <c>39</c>
      <c>n</c>
      <c>&#160;</c>
      <c>56</c>
      <c>4</c>
      <c>6</c>
      <c>G</c>
      <c>&#160;</c>
      <c>23</c>
      <c>X</c>
      <c>&#160;</c>
      <c>40</c>
      <c>o</c>
      <c>&#160;</c>
      <c>57</c>
      <c>5</c>
      <c>7</c>
      <c>H</c>
      <c>&#160;</c>
      <c>24</c>
      <c>Y</c>
      <c>&#160;</c>
      <c>41</c>
      <c>p</c>
      <c>&#160;</c>
      <c>58</c>
      <c>6</c>
      <c>8</c>
      <c>I</c>
      <c>&#160;</c>
      <c>25</c>
      <c>Z</c>
      <c>&#160;</c>
      <c>42</c>
      <c>q</c>
      <c>&#160;</c>
      <c>59</c>
      <c>7</c>
      <c>9</c>
      <c>J</c>
      <c>&#160;</c>
      <c>26</c>
      <c>a</c>
      <c>&#160;</c>
      <c>43</c>
      <c>r</c>
      <c>&#160;</c>
      <c>60</c>
      <c>8</c>
      <c>10</c>
      <c>K</c>
      <c>&#160;</c>
      <c>27</c>
      <c>b</c>
      <c>&#160;</c>
      <c>44</c>
      <c>s</c>
      <c>&#160;</c>
      <c>61</c>
      <c>9</c>
      <c>11</c>
      <c>L</c>
      <c>&#160;</c>
      <c>28</c>
      <c>c</c>
      <c>&#160;</c>
      <c>45</c>
      <c>t</c>
      <c>&#160;</c>
      <c>62</c>
      <c>+</c>
      <c>12</c>
      <c>M</c>
      <c>&#160;</c>
      <c>29</c>
      <c>d</c>
      <c>&#160;</c>
      <c>46</c>
      <c>u</c>
      <c>&#160;</c>
      <c>63</c>
      <c>/</c>
      <c>13</c>
      <c>N</c>
      <c>&#160;</c>
      <c>30</c>
      <c>e</c>
      <c>&#160;</c>
      <c>47</c>
      <c>v</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>14</c>
      <c>O</c>
      <c>&#160;</c>
      <c>31</c>
      <c>f</c>
      <c>&#160;</c>
      <c>48</c>
      <c>w</c>
      <c>&#160;</c>
      <c>(pad)</c>
      <c>=</c>
      <c>15</c>
      <c>P</c>
      <c>&#160;</c>
      <c>32</c>
      <c>g</c>
      <c>&#160;</c>
      <c>49</c>
      <c>x</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>16</c>
      <c>Q</c>
      <c>&#160;</c>
      <c>33</c>
      <c>h</c>
      <c>&#160;</c>
      <c>50</c>
      <c>y</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
</texttable>

<t>The encoded output stream must be represented in lines of no more than 76 characters each.</t>

<t>Special processing is performed if fewer than 24 bits are available at the end of the data being encoded.
There are three possibilities:</t>

<t><list style="numbers">
  <t>The last data group has 24 bits (3 octets).
No special processing is needed.</t>
  <t>The last data group has 16 bits (2 octets).
The first two 6-bit groups are processed as above.
The third (incomplete) data group has two zero-value bits added to it, and is processed as above.
A pad character (=) is added to the output.</t>
  <t>The last data group has 8 bits (1 octet).
The first 6-bit group is processed as above.
The second (incomplete) data group has four zero-value bits added to it, and is processed as above.
Two pad characters (=) are added to the output.</t>
</list></t>

</section>
<section anchor="decoding-radix-64"><name>Decoding Radix-64</name>

<t>In Radix-64 data, characters other than those in the table, line breaks, and other white space probably indicate a transmission error, about which a warning message or even a message rejection might be appropriate under some circumstances.
Decoding software must ignore all white space.</t>

<t>Because it is used only for padding at the end of the data, the occurrence of any "=" characters may be taken as evidence that the end of the data has been reached (without truncation in transit).
No such assurance is possible, however, when the number of octets transmitted was a multiple of three and no "=" characters are present.</t>

</section>
<section anchor="examples-of-radix-64"><name>Examples of Radix-64</name>

<figure><artwork><![CDATA[
Input data:  0x14FB9C03D97E
Hex:     1   4    F   B    9   C     | 0   3    D   9    7   E
8-bit:   00010100 11111011 10011100  | 00000011 11011001 01111110
6-bit:   000101 001111 101110 011100 | 000000 111101 100101 111110
Decimal: 5      15     46     28       0      61     37     62
Output:  F      P      u      c        A      9      l      +
Input data:  0x14FB9C03D9
Hex:     1   4    F   B    9   C     | 0   3    D   9
8-bit:   00010100 11111011 10011100  | 00000011 11011001
                                                pad with 00
6-bit:   000101 001111 101110 011100 | 000000 111101 100100
Decimal: 5      15     46     28       0      61     36
                                                   pad with =
Output:  F      P      u      c        A      9      k      =
Input data:  0x14FB9C03
Hex:     1   4    F   B    9   C     | 0   3
8-bit:   00010100 11111011 10011100  | 00000011
                                       pad with 0000
6-bit:   000101 001111 101110 011100 | 000000 110000
Decimal: 5      15     46     28       0      48
                                            pad with =      =
Output:  F      P      u      c        A      w      =      =
]]></artwork></figure>

</section>
<section anchor="example-of-an-ascii-armored-message"><name>Example of an ASCII Armored Message</name>

<figure><artwork><![CDATA[
-----BEGIN PGP MESSAGE-----

yDgBO22WxBHv7O8X7O/jygAEzol56iUKiXmV+XmpCtmpqQUKiQrFqclFqUDBovzS
vBSFjNSiVHsuAA==
=njUN
-----END PGP MESSAGE-----
]]></artwork></figure>

<t>Note that this example has extra indenting; an actual armored message would have no leading whitespace.</t>

</section>
</section>
<section anchor="cleartext-signature"><name>Cleartext Signature Framework</name>

<t>It is desirable to be able to sign a textual octet stream without ASCII armoring the stream itself, so the signed text is still readable without special software.
In order to bind a signature to such a cleartext, this framework is used, which follows the same basic format and restrictions as the ASCII armoring described in <xref target="forming-ascii-armor"/>.
(Note that this framework is not intended to be reversible.
<xref target="RFC3156"/> defines another way to sign cleartext messages for environments that support MIME.)</t>

<t>The cleartext signed message consists of:</t>

<t><list style="symbols">
  <t>The cleartext header <spanx style="verb">-----BEGIN PGP SIGNED MESSAGE-----</spanx> on a single line,</t>
  <t>If the message is signed using v3 or v4 Signatures, one or more "Hash" Armor Headers,</t>
  <t>If the message is signed using v5 Signatures, one or more "SaltedHash" Armor Headers,</t>
  <t>Exactly one empty line not included into the message digest,</t>
  <t>The dash-escaped cleartext that is included into the message digest,</t>
  <t>The ASCII armored signature(s) including the <spanx style="verb">-----BEGIN PGP SIGNATURE-----</spanx> Armor Header and Armor Tail Lines.</t>
</list></t>

<t>If the "Hash" Armor Header is given, the specified message digest algorithm(s) are used for the signature.
If more than one message digest is used in the signature, the "Hash" armor header contains a comma-delimited list of used message digests.</t>

<t>If the "SaltedHash" Armor Header is given, the specified message digest algorithm and salt are used for a signature.
The message digest name is followed by a colon (<spanx style="verb">:</spanx>) followed by 22 characters of Radix-64 encoded salt without padding.
Note: The "SaltedHash" Armor Header contains digest algorithm and salt for a single signature; a second signature requires a second "SaltedHash" Armor Header.</t>

<t>Current message digest names are described with the algorithm IDs in <xref target="hash-algos"/>.</t>

<t>An implementation SHOULD add a line break after the cleartext, but MAY omit it if the cleartext ends with a line break.
This is for visual clarity.</t>

<section anchor="dash-escaped-text"><name>Dash-Escaped Text</name>

<t>The cleartext content of the message must also be dash-escaped.</t>

<t>Dash-escaped cleartext is the ordinary cleartext where every line starting with a <u>-</u> is prefixed by the sequence <u>-</u> and <u> </u>.
This prevents the parser from recognizing armor headers of the cleartext itself.
An implementation MAY dash-escape any line, SHOULD dash-escape lines commencing "From" followed by a space, and MUST dash-escape any line commencing in a dash.
The message digest is computed using the cleartext itself, not the dash-escaped form.</t>

<t>As with binary signatures on text documents, a cleartext signature is calculated on the text using canonical &lt;CR&gt;&lt;LF&gt; line endings.
The line ending (that is, the &lt;CR&gt;&lt;LF&gt;) before the <spanx style="verb">-----BEGIN PGP SIGNATURE-----</spanx> line that terminates the signed text is not considered part of the signed text.</t>

<t>When reversing dash-escaping, an implementation MUST strip the string <spanx style="verb">- </spanx> if it occurs at the beginning of a line, and SHOULD warn on <spanx style="verb">-</spanx> and any character other than a space at the beginning of a line.</t>

<t>Also, any trailing whitespace --- spaces (0x20) and tabs (0x09) --- at the end of any line is removed when the cleartext signature is generated.</t>

</section>
</section>
<section anchor="regular-expressions"><name>Regular Expressions</name>

<t>A regular expression is zero or more branches, separated by <spanx style="verb">|</spanx>.
It matches anything that matches one of the branches.</t>

<t>A branch is zero or more pieces, concatenated.
It matches a match for the first, followed by a match for the second, etc.</t>

<t>A piece is an atom possibly followed by <spanx style="verb">*</spanx>, <spanx style="verb">+</spanx>, or <spanx style="verb">?</spanx>.
An atom followed by <spanx style="verb">*</spanx> matches a sequence of 0 or more matches of the atom.
An atom followed by <spanx style="verb">+</spanx> matches a sequence of 1 or more matches of the atom.
An atom followed by <spanx style="verb">?</spanx> matches a match of the atom, or the null string.</t>

<t>An atom is a regular expression in parentheses (matching a match for the regular expression), a range (see below), <spanx style="verb">.</spanx> (matching any single character), <spanx style="verb">^</spanx> (matching the null string at the beginning of the input string), <spanx style="verb">$</spanx> (matching the null string at the end of the input string), a <spanx style="verb">\</spanx> followed by a single character (matching that character), or a single character with no other significance (matching that character).</t>

<t>A range is a sequence of characters enclosed in <spanx style="verb">[]</spanx>.
It normally matches any single character from the sequence.
If the sequence begins with <spanx style="verb">^</spanx>, it matches any single character not from the rest of the sequence.
If two characters in the sequence are separated by <spanx style="verb">-</spanx>, this is shorthand for the full list of ASCII characters between them (for example, <spanx style="verb">[0-9]</spanx> matches any decimal digit).
To include a literal <spanx style="verb">]</spanx> in the sequence, make it the first character (following a possible <spanx style="verb">^</spanx>).
To include a literal <spanx style="verb">-</spanx>, make it the first or last character.</t>

</section>
<section anchor="constants"><name>Constants</name>

<t>This section describes the constants used in OpenPGP.</t>

<t>Note that these tables are not exhaustive lists; an implementation MAY implement an algorithm not on these lists, so long as the algorithm numbers are chosen from the private or experimental algorithm range.</t>

<t>See <xref target="notes-on-algorithms"/> for more discussion of the algorithms.</t>

<section anchor="pubkey-algos"><name>Public-Key Algorithms</name>

<texttable title="Public-key algorithm registry">
      <ttcol align='right'>ID</ttcol>
      <ttcol align='left'>Algorithm</ttcol>
      <ttcol align='left'>Public Key Format</ttcol>
      <ttcol align='left'>Secret Key Format</ttcol>
      <ttcol align='left'>Signature Format</ttcol>
      <ttcol align='left'>PKESK Format</ttcol>
      <c>1</c>
      <c>RSA (Encrypt or Sign) <xref target="HAC"/></c>
      <c>MPI(n), MPI(e) [<xref target="key-rsa"/>]</c>
      <c>MPI(d), MPI(p), MPI(q), MPI(u)</c>
      <c>MPI(m**d mod n) [<xref target="sig-rsa"/>]</c>
      <c>MPI(m**e mod n) [<xref target="pkesk-rsa"/>]</c>
      <c>2</c>
      <c>RSA Encrypt-Only <xref target="HAC"/></c>
      <c>MPI(n), MPI(e) [<xref target="key-rsa"/>]</c>
      <c>MPI(d), MPI(p), MPI(q), MPI(u)</c>
      <c>N/A</c>
      <c>MPI(m**e mod n) [<xref target="pkesk-rsa"/>]</c>
      <c>3</c>
      <c>RSA Sign-Only <xref target="HAC"/></c>
      <c>MPI(n), MPI(e) [<xref target="key-rsa"/>]</c>
      <c>MPI(d), MPI(p), MPI(q), MPI(u)</c>
      <c>MPI(m**d mod n) [<xref target="sig-rsa"/>]</c>
      <c>N/A</c>
      <c>16</c>
      <c>Elgamal (Encrypt-Only) <xref target="ELGAMAL"/> <xref target="HAC"/></c>
      <c>MPI(p), MPI(g), MPI(y) [<xref target="key-elgamal"/>]</c>
      <c>MPI(x)</c>
      <c>N/A</c>
      <c>MPI(g**k mod p), MPI (m * y**k mod p) [<xref target="pkesk-elgamal"/>]</c>
      <c>17</c>
      <c>DSA (Digital Signature Algorithm) <xref target="FIPS186"/> <xref target="HAC"/></c>
      <c>MPI(p), MPI(q), MPI(g), MPI(y) [<xref target="key-dsa"/>]</c>
      <c>MPI(x)</c>
      <c>MPI(r), MPI(s) [<xref target="sig-dsa"/>]</c>
      <c>N/A</c>
      <c>18</c>
      <c>ECDH public key algorithm</c>
      <c>OID, MPI(point in curve-specific point format), KDFParams [see <xref target="curve-specific-formats"/>, <xref target="key-ecdh"/>]</c>
      <c>MPI(value in curve-specific format) [<xref target="curve-specific-formats"/>]</c>
      <c>N/A</c>
      <c>MPI(point in curve-specific point format), size octet, encoded key [<xref target="curve-specific-formats"/>, <xref target="pkesk-ecdh"/>, <xref target="ec-dh-algorithm-ecdh"/>]</c>
      <c>19</c>
      <c>ECDSA public key algorithm <xref target="FIPS186"/></c>
      <c>OID, MPI(point in SEC1 format) [<xref target="key-ecdsa"/>]</c>
      <c>MPI(value)</c>
      <c>MPI(r), MPI(s) [<xref target="sig-dsa"/>]</c>
      <c>N/A</c>
      <c>20</c>
      <c>Reserved (formerly Elgamal Encrypt or Sign)</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>21</c>
      <c>Reserved for Diffie-Hellman (X9.42, as defined for IETF-S/MIME)</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>22</c>
      <c>EdDSA  <xref target="RFC8032"/></c>
      <c>OID, MPI(point in prefixed native format) [see <xref target="ec-point-prefixed-native"/>, <xref target="key-eddsa"/>]</c>
      <c>MPI(value in curve-specific format) [see <xref target="curve-specific-formats"/>]</c>
      <c>MPI, MPI [see <xref target="curve-specific-formats"/>, <xref target="sig-eddsa"/>]</c>
      <c>N/A</c>
      <c>23</c>
      <c>Reserved (AEDH)</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>24</c>
      <c>Reserved (AEDSA)</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>100 to 110</c>
      <c>Private/Experimental algorithm</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
      <c>&#160;</c>
</texttable>

<t>Implementations MUST implement EdDSA (19) for signatures, and ECDH (18) for encryption.
Implementations SHOULD implement RSA (1) for signatures and encryption.</t>

<t>RSA Encrypt-Only (2) and RSA Sign-Only (3) are deprecated and SHOULD NOT be generated, but may be interpreted.
See <xref target="rsa-notes"/>.
See <xref target="reserved-notes"/> for notes on Elgamal Encrypt or Sign (20), and X9.42 (21).
Implementations MAY implement any other algorithm.</t>

<t>Note that an implementation conforming to the previous version of this standard (<xref target="RFC4880"/>) have only DSA (17) and Elgamal (16) as its MUST-implement algorithms.</t>

<t>A compatible specification of ECDSA is given in <xref target="RFC6090"/> as "KT-I Signatures" and in <xref target="SEC1"/>; ECDH is defined in <xref target="ec-dh-algorithm-ecdh"/> of this document.</t>

</section>
<section anchor="ec-curves"><name>ECC Curves for OpenPGP</name>

<t>The parameter curve OID is an array of octets that define a named curve.</t>

<t>The table below specifies the exact sequence of octets for each named curve referenced in this document.
It also specifies which public key algorithms the curve can be used with, as well as the size of expected elements in octets:</t>

<texttable title="ECC Curve OID and usage registry">
      <ttcol align='left'>ASN.1 Object Identifier</ttcol>
      <ttcol align='left'>OID len</ttcol>
      <ttcol align='left'>Curve OID octets in hexadecimal representation</ttcol>
      <ttcol align='left'>Curve name</ttcol>
      <ttcol align='left'>Usage</ttcol>
      <ttcol align='left'>Field Size (fsize)</ttcol>
      <c>1.2.840.10045.3.1.7</c>
      <c>8</c>
      <c>2A 86 48 CE 3D 03 01 07</c>
      <c>NIST P-256</c>
      <c>ECDSA, ECDH</c>
      <c>32</c>
      <c>1.3.132.0.34</c>
      <c>5</c>
      <c>2B 81 04 00 22</c>
      <c>NIST P-384</c>
      <c>ECDSA, ECDH</c>
      <c>48</c>
      <c>1.3.132.0.35</c>
      <c>5</c>
      <c>2B 81 04 00 23</c>
      <c>NIST P-521</c>
      <c>ECDSA, ECDH</c>
      <c>66</c>
      <c>1.3.6.1.4.1.11591.15.1</c>
      <c>9</c>
      <c>2B 06 01 04 01 DA 47 0F 01</c>
      <c>Ed25519</c>
      <c>EdDSA</c>
      <c>32</c>
      <c>1.3.101.113</c>
      <c>3</c>
      <c>2B 65 71</c>
      <c>Ed448</c>
      <c>EdDSA</c>
      <c>57</c>
      <c>1.3.6.1.4.1.3029.1.5.1</c>
      <c>10</c>
      <c>2B 06 01 04 01 97 55 01 05 01</c>
      <c>Curve25519</c>
      <c>ECDH</c>
      <c>32</c>
      <c>1.3.101.111</c>
      <c>3</c>
      <c>2B 65 6F</c>
      <c>X448</c>
      <c>ECDH</c>
      <c>56</c>
</texttable>

<t>The "Field Size (fsize)" column represents the field size of the group in number of octets, rounded up, such that x or y coordinates for a point on the curve, native point representations, or scalars with high enough entropy for the curve can be represented in that many octets.</t>

<t>The sequence of octets in the third column is the result of applying the Distinguished Encoding Rules (DER) to the ASN.1 Object Identifier with subsequent truncation.
The truncation removes the two fields of encoded Object Identifier.
The first omitted field is one octet representing the Object Identifier tag, and the second omitted field is the length of the Object Identifier body.
For example, the complete ASN.1 DER encoding for the NIST P-256 curve OID is "06 08 2A 86 48 CE 3D 03 01 07", from which the first entry in the table above is constructed by omitting the first two octets.
Only the truncated sequence of octets is the valid representation of a curve OID.</t>

<t>Implementations MUST implement Ed25519 for use with EdDSA, and Curve25519 for use with ECDH.
Implementations SHOULD implement Ed448 for use with EdDSA, and X448 for use with ECDH.</t>

<section anchor="curve-specific-formats"><name>Curve-Specific Wire Formats</name>

<t>Some Elliptic Curve Public Key Algorithms use different conventions for specific fields depending on the curve in use.
Each field is always formatted as an MPI, but with a curve-specific framing.
This table summarizes those distinctions.</t>

<texttable title="Curve-specific wire formats">
      <ttcol align='left'>Curve</ttcol>
      <ttcol align='left'>ECDH Point Format</ttcol>
      <ttcol align='left'>ECDH Secret Key MPI</ttcol>
      <ttcol align='left'>EdDSA Secret Key MPI</ttcol>
      <ttcol align='left'>EdDSA Signature first MPI</ttcol>
      <ttcol align='left'>EdDSA Signature second MPI</ttcol>
      <c>NIST P-256</c>
      <c>SEC1</c>
      <c>integer</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>NIST P-384</c>
      <c>SEC1</c>
      <c>integer</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>NIST P-521</c>
      <c>SEC1</c>
      <c>integer</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>Ed25519</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>32 octets of secret</c>
      <c>32 octets of R</c>
      <c>32 octets of S</c>
      <c>Ed448</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>prefixed 57 octets of secret</c>
      <c>prefixed 114 octets of signature</c>
      <c>0 [this is an unused placeholder]</c>
      <c>Curve25519</c>
      <c>prefixed native</c>
      <c>integer (see <xref target="curve25519-secrets"/>)</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>X448</c>
      <c>prefixed native</c>
      <c>prefixed 56 octets of secret</c>
      <c>N/A</c>
      <c>N/A</c>
      <c>N/A</c>
</texttable>

<t>For the native octet-string forms of EdDSA values, see <xref target="RFC8032"/>.
For the native octet-string forms of ECDH secret scalars and points, see <xref target="RFC7748"/>.</t>

</section>
</section>
<section anchor="symmetric-algos"><name>Symmetric-Key Algorithms</name>

<texttable title="Symmetric-key algorithm registry">
      <ttcol align='right'>ID</ttcol>
      <ttcol align='left'>Algorithm</ttcol>
      <c>0</c>
      <c>Plaintext or unencrypted data</c>
      <c>1</c>
      <c>IDEA <xref target="IDEA"/></c>
      <c>2</c>
      <c>TripleDES (DES-EDE, <xref target="SCHNEIER"/>, <xref target="HAC"/> - 168 bit key derived from 192)</c>
      <c>3</c>
      <c>CAST5 (128 bit key, as per <xref target="RFC2144"/>)</c>
      <c>4</c>
      <c>Blowfish (128 bit key, 16 rounds) <xref target="BLOWFISH"/></c>
      <c>5</c>
      <c>Reserved</c>
      <c>6</c>
      <c>Reserved</c>
      <c>7</c>
      <c>AES with 128-bit key <xref target="AES"/></c>
      <c>8</c>
      <c>AES with 192-bit key</c>
      <c>9</c>
      <c>AES with 256-bit key</c>
      <c>10</c>
      <c>Twofish with 256-bit key <xref target="TWOFISH"/></c>
      <c>11</c>
      <c>Camellia with 128-bit key <xref target="RFC3713"/></c>
      <c>12</c>
      <c>Camellia with 192-bit key</c>
      <c>13</c>
      <c>Camellia with 256-bit key</c>
      <c>100 to 110</c>
      <c>Private/Experimental algorithm</c>
      <c>253, 254 and 255</c>
      <c>Reserved to avoid collision with Secret Key Encryption (see <xref target="secret-key-encryption"/> and <xref target="secret-key-packet-formats"/>)</c>
</texttable>

<t>Implementations MUST implement AES-128.
Implementations SHOULD implement AES-256.
Implementations MUST NOT encrypt data with IDEA, TripleDES, or CAST5.
Implementations MAY decrypt data that uses IDEA, TripleDES, or CAST5 for the sake of reading older messages or new messages from legacy clients.
Implementations MAY implement any other algorithm.</t>

</section>
<section anchor="compression-algos"><name>Compression Algorithms</name>

<texttable title="Compression algorithm registry">
      <ttcol align='right'>ID</ttcol>
      <ttcol align='left'>Algorithm</ttcol>
      <c>0</c>
      <c>Uncompressed</c>
      <c>1</c>
      <c>ZIP <xref target="RFC1951"/></c>
      <c>2</c>
      <c>ZLIB <xref target="RFC1950"/></c>
      <c>3</c>
      <c>BZip2 <xref target="BZ2"/></c>
      <c>100 to 110</c>
      <c>Private/Experimental algorithm</c>
</texttable>

<t>Implementations MUST implement uncompressed data.
Implementations SHOULD implement ZLIB.
For interoperability reasons implementations SHOULD be able to decompress using ZIP.
Implementations MAY implement any other algorithm.</t>

</section>
<section anchor="hash-algos"><name>Hash Algorithms</name>

<texttable title="Hash algorithm registry">
      <ttcol align='right'>ID</ttcol>
      <ttcol align='left'>Algorithm</ttcol>
      <ttcol align='left'>Text Name</ttcol>
      <c>1</c>
      <c>MD5 <xref target="HAC"/></c>
      <c>"MD5"</c>
      <c>2</c>
      <c>SHA-1 <xref target="FIPS180"/></c>
      <c>"SHA1"</c>
      <c>3</c>
      <c>RIPE-MD/160 <xref target="HAC"/></c>
      <c>"RIPEMD160"</c>
      <c>4</c>
      <c>Reserved</c>
      <c>&#160;</c>
      <c>5</c>
      <c>Reserved</c>
      <c>&#160;</c>
      <c>6</c>
      <c>Reserved</c>
      <c>&#160;</c>
      <c>7</c>
      <c>Reserved</c>
      <c>&#160;</c>
      <c>8</c>
      <c>SHA2-256 <xref target="FIPS180"/></c>
      <c>"SHA256"</c>
      <c>9</c>
      <c>SHA2-384 <xref target="FIPS180"/></c>
      <c>"SHA384"</c>
      <c>10</c>
      <c>SHA2-512 <xref target="FIPS180"/></c>
      <c>"SHA512"</c>
      <c>11</c>
      <c>SHA2-224 <xref target="FIPS180"/></c>
      <c>"SHA224"</c>
      <c>12</c>
      <c>SHA3-256 <xref target="FIPS202"/></c>
      <c>"SHA3-256"</c>
      <c>13</c>
      <c>Reserved</c>
      <c>&#160;</c>
      <c>14</c>
      <c>SHA3-512 <xref target="FIPS202"/></c>
      <c>"SHA3-512"</c>
      <c>100 to 110</c>
      <c>Private/Experimental algorithm</c>
      <c>&#160;</c>
</texttable>

<t>Implementations MUST implement SHA2-256.
Implementations SHOULD implement SHA2-384 and SHA2-512.
Implementations MAY implement other algorithms.
Implementations SHOULD NOT create messages which require the use of SHA-1 with the exception of computing version 4 key fingerprints and for purposes of the Modification Detection Code (MDC) in version 1 Symmetrically Encrypted Integrity Protected Data packets.
Implementations MUST NOT generate signatures with MD5, SHA-1, or RIPE-MD/160.
Implementations MUST NOT use MD5, SHA-1, or RIPE-MD/160 as a hash function in an ECDH KDF.
Implementations MUST NOT validate any recent signature that depends on MD5, SHA-1, or RIPE-MD/160.
Implementations SHOULD NOT validate any old signature that depends on MD5, SHA-1, or RIPE-MD/160 unless the signature's creation date predates known weakness of the algorithm used, and the implementation is confident that the message has been in the secure custody of the user the whole time.</t>

</section>
<section anchor="aead-algorithms"><name>AEAD Algorithms</name>

<texttable title="AEAD algorithm registry">
      <ttcol align='right'>ID</ttcol>
      <ttcol align='left'>Algorithm</ttcol>
      <ttcol align='left'>IV length (octets)</ttcol>
      <ttcol align='left'>authentication tag length (octets)</ttcol>
      <c>1</c>
      <c>EAX <xref target="EAX"/></c>
      <c>16</c>
      <c>16</c>
      <c>2</c>
      <c>OCB <xref target="RFC7253"/></c>
      <c>15</c>
      <c>16</c>
      <c>3</c>
      <c>GCM <xref target="SP800-38D"/></c>
      <c>12</c>
      <c>16</c>
      <c>100 to 110</c>
      <c>Private/Experimental algorithm</c>
      <c>&#160;</c>
      <c>&#160;</c>
</texttable>

<t>Implementations MUST implement OCB.
Implementations MAY implement EAX, GCM and other algorithms.</t>

</section>
</section>
<section anchor="iana-considerations"><name>IANA Considerations</name>

<t>Because this document obsoletes <xref target="RFC4880"/>, IANA is requested to update all registration information that references <xref target="RFC4880"/> to instead reference this RFC.</t>

<t>OpenPGP is highly parameterized, and consequently there are a number of considerations for allocating parameters for extensions.
This section describes how IANA should look at extensions to the protocol as described in this document.</t>

<section anchor="new-string-to-key-specifier-types"><name>New String-to-Key Specifier Types</name>

<t>OpenPGP S2K specifiers contain a mechanism for new algorithms to turn a string into a key.
This specification creates a registry of S2K specifier types.
The registry includes the S2K type, the name of the S2K, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="s2k-types"/>.
Adding a new S2K specifier MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<t>IANA should add a column "Generate?" to the S2K type registry, with initial values taken from <xref target="s2k-types"/>.</t>

</section>
<section anchor="new-packets"><name>New Packets</name>

<t>Major new features of OpenPGP are defined through new packet types.
This specification creates a registry of packet types.
The registry includes the packet type, the name of the packet, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="packet-tags"/>.
Adding a new packet type MUST be done through the RFC REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<section anchor="user-attribute-types"><name>User Attribute Types</name>

<t>The User Attribute packet permits an extensible mechanism for other types of certificate identification.
This specification creates a registry of User Attribute types.
The registry includes the User Attribute type, the name of the User Attribute, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="user-attribute-packet"/>.
Adding a new User Attribute type MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<section anchor="image-format-subpacket-types"><name>Image Format Subpacket Types</name>

<t>Within User Attribute packets, there is an extensible mechanism for other types of image-based User Attributes.
This specification creates a registry of Image Attribute subpacket types.
The registry includes the Image Attribute subpacket type, the name of the Image Attribute subpacket, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="uat-image"/>.
Adding a new Image Attribute subpacket type MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
</section>
<section anchor="new-signature-subpackets"><name>New Signature Subpackets</name>

<t>OpenPGP signatures contain a mechanism for signed (or unsigned) data to be added to them for a variety of purposes in the Signature subpackets as discussed in <xref target="signature-subpacket"/>.
This specification creates a registry of Signature subpacket types.
The registry includes the Signature subpacket type, the name of the subpacket, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="signature-subpacket"/>.
Adding a new Signature subpacket MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<section anchor="signature-notation-data-subpackets"><name>Signature Notation Data Subpackets</name>

<t>OpenPGP signatures further contain a mechanism for extensions in signatures.
These are the Notation Data subpackets, which contain a key/value pair.
Notations contain a user space that is completely unmanaged and an IETF space.</t>

<t>This specification creates a registry of Signature Notation Data types.
The registry includes the Signature Notation Data type, the name of the Signature Notation Data, its allowed values, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="notation-data"/>.
Adding a new Signature Notation Data subpacket MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
<section anchor="signature-notation-data-subpacket-notation-flags"><name>Signature Notation Data Subpacket Notation Flags</name>

<t>This specification creates a new registry of Signature Notation Data Subpacket Notation Flags.
The registry includes the columns "Flag", "Description", "Security Recommended", "Interoperability Recommended", and "Reference".
The initial values for this registry can be found in <xref target="notation-data"/>.
Adding a new item MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
<section anchor="key-server-preference-extensions"><name>Key Server Preference Extensions</name>

<t>OpenPGP signatures contain a mechanism for preferences to be specified about key servers.
This specification creates a registry of key server preferences.
The registry includes the key server preference, the name of the preference, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="key-server-preferences"/>.
Adding a new key server preference MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
<section anchor="key-flags-extensions"><name>Key Flags Extensions</name>

<t>OpenPGP signatures contain a mechanism for flags to be specified about key usage.
This specification creates a registry of key usage flags.
The registry includes the key flags value, the name of the flag, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="key-flags"/>.
Adding a new key usage flag MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
<section anchor="reason-for-revocation-extensions"><name>Reason for Revocation Extensions</name>

<t>OpenPGP signatures contain a mechanism for flags to be specified about why a key was revoked.
This specification creates a registry of "Reason for Revocation" flags.
The registry includes the "Reason for Revocation" flags value, the name of the flag, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="reason-for-revocation"/>.
Adding a new feature flag MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
<section anchor="implementation-features"><name>Implementation Features</name>

<t>OpenPGP signatures contain a mechanism for flags to be specified stating which optional features an implementation supports.
This specification creates a registry of feature-implementation flags.
The registry includes the feature-implementation flags value, the name of the flag, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="features-subpacket"/>.
Adding a new feature-implementation flag MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<t>Also see <xref target="meta-considerations-for-expansion"/> for more information about when feature flags are needed.</t>

</section>
</section>
<section anchor="new-packet-versions"><name>New Packet Versions</name>

<t>The core OpenPGP packets all have version numbers, and can be revised by introducing a new version of an existing packet.
This specification creates a registry of packet types.
The registry includes the packet type, the number of the version, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="packet-types"/>.
Adding a new packet version MUST be done through the RFC REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
</section>
<section anchor="new-algorithms"><name>New Algorithms</name>

<t><xref target="constants"/> lists the core algorithms that OpenPGP uses.
Adding in a new algorithm is usually simple.
For example, adding in a new symmetric cipher usually would not need anything more than allocating a constant for that cipher.
If that cipher had other than a 64-bit or 128-bit block size, there might need to be additional documentation describing how OpenPGP-CFB mode would be adjusted.
Similarly, when DSA was expanded from a maximum of 1024-bit public keys to 3072-bit public keys, the revision of FIPS 186 contained enough information itself to allow implementation.
Changes to this document were made mainly for emphasis.</t>

<section anchor="public-key-algorithms"><name>Public-Key Algorithms</name>

<t>OpenPGP specifies a number of public-key algorithms.
This specification creates a registry of public-key algorithm identifiers.
The registry includes the algorithm name, its key sizes and parameters, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="pubkey-algos"/>.
Adding a new public-key algorithm MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<t>This document requests IANA register the following new public-key algorithm:</t>

<texttable title="New public-Key algorithms registered">
      <ttcol align='right'>ID</ttcol>
      <ttcol align='left'>Algorithm</ttcol>
      <ttcol align='left'>Reference</ttcol>
      <c>22</c>
      <c>EdDSA public key algorithm</c>
      <c>This doc, <xref target="eddsa"/></c>
</texttable>

<t>[ Note to RFC-Editor: Please remove the table above on publication.
]</t>

</section>
<section anchor="symmetric-key-algorithms"><name>Symmetric-Key Algorithms</name>

<t>OpenPGP specifies a number of symmetric-key algorithms.
This specification creates a registry of symmetric-key algorithm identifiers.
The registry includes the algorithm name, its key sizes and block size, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="symmetric-algos"/>.
Adding a new symmetric-key algorithm MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
<section anchor="hash-algorithms"><name>Hash Algorithms</name>

<t>OpenPGP specifies a number of hash algorithms.
This specification creates a registry of hash algorithm identifiers.
The registry includes the algorithm name, a text representation of that name, its block size, an OID hash prefix, and a reference to the defining specification.
The initial values for this registry can be found in <xref target="hash-algos"/> for the algorithm identifiers and text names, and <xref target="version-three-sig"/> for the OIDs and expanded signature prefixes.
Adding a new hash algorithm MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<t>This document requests IANA register the following hash algorithms:</t>

<texttable title="New hash algorithms registered">
      <ttcol align='right'>ID</ttcol>
      <ttcol align='left'>Algorithm</ttcol>
      <ttcol align='left'>Reference</ttcol>
      <c>12</c>
      <c>SHA3-256</c>
      <c>This doc</c>
      <c>13</c>
      <c>Reserved</c>
      <c>&#160;</c>
      <c>14</c>
      <c>SHA3-512</c>
      <c>This doc</c>
</texttable>

<t>[Notes to RFC-Editor: Please remove the table above on publication.
    It is desirable not to reuse old or reserved algorithms because some existing tools might print a wrong description.
    The ID 13 has been reserved so that the SHA3 algorithm IDs align nicely with their SHA2 counterparts.]</t>

</section>
<section anchor="compression-algorithms"><name>Compression Algorithms</name>

<t>OpenPGP specifies a number of compression algorithms.
This specification creates a registry of compression algorithm identifiers.
The registry includes the algorithm name and a reference to the defining specification.
The initial values for this registry can be found in <xref target="compression-algos"/>.
Adding a new compression key algorithm MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

</section>
<section anchor="elliptic-curve-algorithms"><name>Elliptic Curve Algorithms</name>

<t>This document requests IANA add a registry of elliptic curves for use in OpenPGP.</t>

<t>Each curve is identified on the wire by OID, and is acceptable for use in certain OpenPGP public key algorithms.
The table's initial headings and values can be found in <xref target="ec-curves"/>.
Adding a new elliptic curve algorithm to OpenPGP MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.
If the new curve can be used for ECDH or EdDSA, it must also be added to the "Curve-specific wire formats" table described in <xref target="curve-specific-formats"/>.</t>

</section>
</section>
<section anchor="elliptic-curve-point-and-scalar-wire-formats"><name>Elliptic Curve Point and Scalar Wire Formats</name>

<t>This document requests IANA add a registry of wire formats that represent elliptic curve points.
The table's initial headings and values can be found in <xref target="ec-point-wire-formats"/>.
Adding a new EC point wire format MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<t>This document also requests IANA add a registry of wire formats that represent scalars for use with elliptic curve cryptography.
The table's initial headings and values can be found in <xref target="ec-scalar-wire-formats"/>.
Adding a new EC scalar wire format MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>.</t>

<t>This document also requests that IANA add a registry mapping curve-specific MPI octet-string encoding conventions for ECDH and EdDSA.
The table's initial headings and values can be found in <xref target="curve-specific-formats"/>.
Adding a new elliptic curve algorithm to OpenPGP MUST be done through the SPECIFICATION REQUIRED method, as described in <xref target="RFC8126"/>, and requires adding an entry to this table if the curve is to be used with either EdDSA or ECDH.</t>

</section>
<section anchor="changes-to-existing-registries"><name>Changes to existing registries</name>

<t>This document requests IANA add the following wire format columns to the OpenPGP public-key algorithm registry:</t>

<t><list style="symbols">
  <t>Public Key Format</t>
  <t>Secret Key Format</t>
  <t>Signature Format</t>
  <t>PKESK Format</t>
</list></t>

<t>And populate them with the values found in <xref target="pubkey-algos"/>.</t>

</section>
</section>
<section anchor="packet-composition"><name>Packet Composition</name>

<t>OpenPGP packets are assembled into sequences in order to create messages and to transfer keys.
Not all possible packet sequences are meaningful and correct.
This section describes the rules for how packets should be placed into sequences.</t>

<section anchor="transferable-public-keys"><name>Transferable Public Keys</name>

<t>OpenPGP users may transfer public keys.
The essential elements of a transferable public key are as follows:</t>

<t><list style="symbols">
  <t>One Public-Key packet</t>
  <t>Zero or more revocation signatures</t>
  <t>Zero or more User ID packets</t>
  <t>After each User ID packet, zero or more Signature packets (certifications)</t>
  <t>Zero or more User Attribute packets</t>
  <t>After each User Attribute packet, zero or more Signature packets (certifications)</t>
  <t>Zero or more Subkey packets</t>
  <t>After each Subkey packet, one Signature packet, plus optionally a revocation</t>
  <t>An optional Padding packet</t>
</list></t>

<t>The Public-Key packet occurs first.
Each of the following User ID packets provides the identity of the owner of this public key.
If there are multiple User ID packets, this corresponds to multiple means of identifying the same unique individual user; for example, a user may have more than one email address, and construct a User ID for each one.
A transferable public key SHOULD include at least one User ID packet unless storage requirements prohibit this.</t>

<t>Immediately following each User ID packet, there are zero or more Signature packets.
Each Signature packet is calculated on the immediately preceding User ID packet and the initial Public-Key packet.
The signature serves to certify the corresponding public key and User ID.
In effect, the signer is testifying to his or her belief that this public key belongs to the user identified by this User ID.</t>

<t>Within the same section as the User ID packets, there are zero or more User Attribute packets.
Like the User ID packets, a User Attribute packet is followed by zero or more Signature packets calculated on the immediately preceding User Attribute packet and the initial Public-Key packet.</t>

<t>User Attribute packets and User ID packets may be freely intermixed in this section, so long as the signatures that follow them are maintained on the proper User Attribute or User ID packet.</t>

<t>After the User ID packet or Attribute packet, there may be zero or more Subkey packets.
In general, subkeys are provided in cases where the top-level public key is a signature-only key.
However, any V4 or V5 key may have subkeys, and the subkeys may be encryption-only keys, signature-only keys, or general-purpose keys.
V3 keys MUST NOT have subkeys.</t>

<t>Each Subkey packet MUST be followed by one Signature packet, which should be a subkey binding signature issued by the top-level key.
For subkeys that can issue signatures, the subkey binding signature MUST contain an Embedded Signature subpacket with a primary key binding signature (0x19) issued by the subkey on the top-level key.</t>

<t>Subkey and Key packets may each be followed by a revocation Signature packet to indicate that the key is revoked.
Revocation signatures are only accepted if they are issued by the key itself, or by a key that is authorized to issue revocations via a Revocation Key subpacket in a self-signature by the top-level key.</t>

<t>The optional trailing Padding packet is a mechanism to defend against traffic analysis (see <xref target="traffic-analysis"/>).
For maximum interoperability, if the Public-Key packet is a V4 key, the optional Padding packet SHOULD NOT be present unless the recipient has indicated that they are capable of ignoring it successfully.
An implementation that is capable of receiving a transferable public key with a V5 Public-Key primary key MUST be able to accept (and ignore) the trailing optional Padding packet.</t>

<t>Transferable public-key packet sequences may be concatenated to allow transferring multiple public keys in one operation.</t>

</section>
<section anchor="transferable-secret-keys"><name>Transferable Secret Keys</name>

<t>OpenPGP users may transfer secret keys.
The format of a transferable secret key is the same as a transferable public key except that secret-key and secret-subkey packets are used instead of the public key and public-subkey packets.
Implementations SHOULD include self-signatures on any User IDs and subkeys, as this allows for a complete public key to be automatically extracted from the transferable secret key.
Implementations MAY choose to omit the self-signatures, especially if a transferable public key accompanies the transferable secret key.</t>

</section>
<section anchor="openpgp-messages"><name>OpenPGP Messages</name>

<t>An OpenPGP message is a packet or sequence of packets that corresponds to the following grammatical rules (comma represents sequential composition, and vertical bar separates alternatives):</t>

<dl>
  <dt>
OpenPGP Message :-  </dt>
  <dd>
    <t>Encrypted Message | Signed Message | Compressed Message | Literal Message.</t>
  </dd>
  <dt>
Compressed Message :-  </dt>
  <dd>
    <t>Compressed Data Packet.</t>
  </dd>
  <dt>
Literal Message :-  </dt>
  <dd>
    <t>Literal Data Packet.</t>
  </dd>
  <dt>
ESK :-  </dt>
  <dd>
    <t>Public-Key Encrypted Session Key Packet | Symmetric-Key Encrypted Session Key Packet.</t>
  </dd>
  <dt>
ESK Sequence :-  </dt>
  <dd>
    <t>ESK | ESK Sequence, ESK.</t>
  </dd>
  <dt>
Encrypted Data :-  </dt>
  <dd>
    <t>Symmetrically Encrypted Data Packet | Symmetrically Encrypted Integrity Protected Data Packet</t>
  </dd>
  <dt>
Encrypted Message :-  </dt>
  <dd>
    <t>Encrypted Data | ESK Sequence, Encrypted Data.</t>
  </dd>
  <dt>
One-Pass Signed Message :-  </dt>
  <dd>
    <t>One-Pass Signature Packet, OpenPGP Message, Corresponding Signature Packet.</t>
  </dd>
  <dt>
Signed Message :-  </dt>
  <dd>
    <t>Signature Packet, OpenPGP Message | One-Pass Signed Message.</t>
  </dd>
  <dt>
Optionally Padded Message :-  </dt>
  <dd>
    <t>OpenPGP Message | OpenPGP Message, Padding Packet.</t>
  </dd>
</dl>

<section anchor="unwrapping"><name>Unwrapping Encrypted and Compressed Messages</name>

<t>In addition to the above grammar, certain messages can be "unwrapped" to yield new messages.
In particular:</t>

<t><list style="symbols">
  <t>Decrypting a version 2 Symmetrically Encrypted and Integrity Protected Data packet must yield a valid Optionally Padded Message.</t>
  <t>Decrypting a version 1 Symmetrically Encrypted and Integrity Protected Data packet or --- for historic data --- a Symmetrically Encrypted Data packet must yield a valid OpenPGP Message.</t>
  <t>Decompressing a Compressed Data packet must also yield a valid OpenPGP Message.</t>
</list></t>

<t>When either such unwrapping is performed, the resulting stream of octets is parsed into a series OpenPGP packets like any other stream of octets.
The packet boundaries found in the series of octets are expected to align with the length of the unwrapped octet stream.
An implementation MUST NOT interpret octets beyond the boundaries of the unwrapped octet stream as part of any OpenPGP packet.
If an implementation encounters a packet whose header length indicates that it would extend beyond the boundaries of the unwrapped octet stream, the implementation MUST reject that packet as malformed and unusable.</t>

</section>
<section anchor="additional-constraints-on-packet-sequences"><name>Additional Constraints on Packet Sequences</name>

<t>Note that some subtle combinations that are formally acceptable by this grammar are nonetheless unacceptable.</t>

<section anchor="encrypted-message-versions"><name>Packet Versions in Encrypted Messages</name>

<t>As noted above, an Encrypted Message is a sequence of zero or more PKESKs (<xref target="pkesk"/>) and SKESKs (<xref target="skesk"/>), followed by an SEIPD (<xref target="seipd"/>) payload.
In some historic data, the payload may be a deprecated SED (<xref target="sed"/>) packet instead of SEIPD, though implementations MUST NOT generate SED packets (see <xref target="ciphertext-malleability"/>).
The versions of the preceding ESK packets within an Encrypted Message MUST align with the version of the payload SEIPD packet, as described in this section.</t>

<t>v3 PKESK and v4 SKESK packets both contain in their cleartext the symmetric cipher algorithm identifier in addition to the session key for the subsequent SEIPD packet.
Since a v1 SEIPD does not contain a symmetric algorithm identifier, so all ESK packets preceding a v1 SEIPD payload MUST be either v3 PKESK or v4 SKESK.</t>

<t>On the other hand, the cleartext of the v5 ESK packets (either PKESK or SKESK) do not contain a symmetric cipher algorithm identifier, so they cannot be used in combination with a v1 SEIPD payload.
The payload following any v5 PKESK or v5 SKESK packet MUST be a v2 SEIPD.</t>

<t>Additionally, to avoid potentially conflicting cipher algorithm identifiers, and for simplicity, implementations MUST NOT precede a v2 SEIPD payload with either v3 PKESK or v4 SKESK packets.</t>

<t>The acceptable versions of packets in an Encrypted Message are summarized in the following table:</t>

<texttable title="Encrypted Message Packet Version Alignment">
      <ttcol align='left'>Version of Encrypted Data payload</ttcol>
      <ttcol align='left'>Version of preceding Symmetric-Key ESK (if any)</ttcol>
      <ttcol align='left'>Version of preceding Public-Key ESK (if any)</ttcol>
      <c>v1 SEIPD</c>
      <c>v4 SKESK</c>
      <c>v3 PKESK</c>
      <c>v2 SEIPD</c>
      <c>v5 SKESK</c>
      <c>v5 PKESK</c>
</texttable>

<t>An implementation processing an Encrypted Message MUST discard any preceding ESK packet with a version that does not align with the version of the payload.</t>

</section>
</section>
</section>
<section anchor="detached-signatures"><name>Detached Signatures</name>

<t>Some OpenPGP applications use so-called "detached signatures".
For example, a program bundle may contain a file, and with it a second file that is a detached signature of the first file.
These detached signatures are simply a Signature packet stored separately from the data for which they are a signature.</t>

</section>
</section>
<section anchor="enhanced-key-formats"><name>Enhanced Key Formats</name>

<section anchor="key-structures"><name>Key Structures</name>

<t>The format of an OpenPGP V3 key is as follows.
Entries in square brackets are optional and ellipses indicate repetition.</t>

<figure><artwork><![CDATA[
RSA Public Key
   [Revocation Self Signature]
    User ID [Signature ...]
   [User ID [Signature ...] ...]
]]></artwork></figure>

<t>Each signature certifies the RSA public key and the preceding User ID.
The RSA public key can have many User IDs and each User ID can have many signatures.
V3 keys are deprecated.
Implementations MUST NOT generate new V3 keys, but MAY continue to use existing ones.</t>

<t>The format of an OpenPGP V4 key that uses multiple public keys is similar except that the other keys are added to the end as "subkeys" of the primary key.</t>

<figure><artwork><![CDATA[
Primary-Key
   [Revocation Self Signature]
   [Direct Key Signature...]
   [User ID [Signature ...] ...]
   [User Attribute [Signature ...] ...]
   [[Subkey [Binding-Signature-Revocation ...]
           Subkey-Binding-Signature ...] ...]
]]></artwork></figure>

<t>A subkey always has at least one subkey binding signature after it that is issued using the primary key to tie the two keys together.
These binding signatures may be in either V3 or V4 format, but SHOULD be V4.
Subkeys that can issue signatures MUST have a V4 binding signature due to the REQUIRED embedded primary key binding signature.</t>

<t>In order to create self-signatures (see <xref target="self-sigs"/>), the primary key MUST be an algorithm capable of making signatures (that is, not an encryption-only algorithm).
The subkeys may be keys of any type.
For example, there may be a single-key RSA key, an EdDSA primary key with an RSA encryption key, or an EdDSA primary key with an ECDH subkey, etc.</t>

<t>It is also possible to have a signature-only subkey.
This permits a primary key that collects certifications (key signatures), but is used only for certifying subkeys that are used for encryption and signatures.</t>

</section>
<section anchor="key-ids-fingerprints"><name>Key IDs and Fingerprints</name>

<t>For a V3 key, the eight-octet Key ID consists of the low 64 bits of the public modulus of the RSA key.</t>

<t>The fingerprint of a V3 key is formed by hashing the body (but not the two-octet length) of the MPIs that form the key material (public modulus n, followed by exponent e) with MD5.
Note that both V3 keys and MD5 are deprecated.</t>

<t>A V4 fingerprint is the 160-bit SHA-1 hash of the octet 0x99, followed by the two-octet packet length, followed by the entire Public-Key packet starting with the version field.
The Key ID is the low-order 64 bits of the fingerprint.
Here are the fields of the hash material, with the example of an EdDSA key:</t>

<t>a.1) 0x99 (1 octet)</t>

<t>a.2) two-octet, big-endian scalar octet count of (b)-(e)</t>

<t>b) version number = 4 (1 octet);</t>

<t>c) timestamp of key creation (4 octets);</t>

<t>d) algorithm (1 octet): 22 = EdDSA (example);</t>

<t>e) Algorithm-specific fields.</t>

<t>Algorithm-Specific Fields for EdDSA keys (example):</t>

<t>e.1) A one-octet size of the following field;</t>

<t>e.2) The octets representing a curve OID, defined in <xref target="ec-curves"/>;</t>

<t>e.3) An MPI of an EC point representing a public key Q in prefixed native form (see <xref target="ec-point-prefixed-native"/>).</t>

<t>A V5 fingerprint is the 256-bit SHA2-256 hash of the octet 0x9A, followed by the four-octet packet length, followed by the entire Public-Key packet starting with the version field.
The Key ID is the high-order 64 bits of the fingerprint.
Here are the fields of the hash material, with the example of an EdDSA key:</t>

<t>a.1) 0x9A (1 octet)</t>

<t>a.2) four-octet scalar octet count of (b)-(f)</t>

<t>b) version number = 5 (1 octet);</t>

<t>c) timestamp of key creation (4 octets);</t>

<t>d) algorithm (1 octet): 22 = EdDSA (example);</t>

<t>e) four-octet scalar octet count for the following key material;</t>

<t>f) algorithm-specific fields.</t>

<t>Algorithm-Specific Fields for EdDSA keys (example):</t>

<t>f.1) A one-octet size of the following field;</t>

<t>f.2) The octets representing a curve OID, defined in <xref target="ec-curves"/>;</t>

<t>f.3) An MPI of an EC point representing a public key Q in prefixed native form (see <xref target="ec-point-prefixed-native"/>).</t>

<t>Note that it is possible for there to be collisions of Key IDs --- two different keys with the same Key ID.
Note that there is a much smaller, but still non-zero, probability that two different keys have the same fingerprint.</t>

<t>Also note that if V3, V4, and V5 format keys share the same RSA key material, they will have different Key IDs as well as different fingerprints.</t>

<t>Finally, the Key ID and fingerprint of a subkey are calculated in the same way as for a primary key, including the 0x99 (V4 key) or 0x9A (V5 key) as the first octet (even though this is not a valid packet ID for a public subkey).</t>

</section>
</section>
<section anchor="elliptic-curve-cryptography"><name>Elliptic Curve Cryptography</name>

<t>This section describes algorithms and parameters used with Elliptic Curve Cryptography (ECC) keys.
A thorough introduction to ECC can be found in <xref target="KOBLITZ"/>.</t>

<t>None of the ECC methods described in this document are allowed with deprecated V3 keys.
Refer to <xref target="FIPS186"/>, B.4.1, for the method to generate a uniformly distributed ECC private key.</t>

<section anchor="supported-ecc-curves"><name>Supported ECC Curves</name>

<t>This document references three named prime field curves defined in <xref target="FIPS186"/> as "Curve P-256", "Curve P-384", and "Curve P-521".
These three <xref target="FIPS186"/> curves can be used with ECDSA and ECDH public key algorithms.
Additionally, curve "Curve25519" and "Curve448" are referenced for use with Ed25519 and Ed448 (EdDSA signing, see <xref target="RFC8032"/>); and X25519 and X448 (ECDH encryption, see <xref target="RFC7748"/>).</t>

<t>The named curves are referenced as a sequence of octets in this document, called throughout, curve OID.
<xref target="ec-curves"/> describes in detail how this sequence of octets is formed.</t>

</section>
<section anchor="ec-point-wire-formats"><name>EC Point Wire Formats</name>

<t>A point on an elliptic curve will always be represented on the wire as an MPI.
Each curve uses a specific point format for the data within the MPI itself.
Each format uses a designated prefix octet to ensure that the high octet has at least one bit set to make the MPI a constant size.</t>

<texttable title="Elliptic Curve Point Wire Formats">
      <ttcol align='right'>Name</ttcol>
      <ttcol align='left'>Wire Format</ttcol>
      <ttcol align='left'>Reference</ttcol>
      <c>SEC1</c>
      <c>0x04 || x || y</c>
      <c><xref target="ec-point-sec1"/></c>
      <c>Prefixed native</c>
      <c>0x40 || native</c>
      <c><xref target="ec-point-prefixed-native"/></c>
</texttable>

<section anchor="ec-point-sec1"><name>SEC1 EC Point Wire Format</name>

<t>For a SEC1-encoded (uncompressed) point the content of the MPI is:</t>

<figure><artwork><![CDATA[
B = 04 || x || y
]]></artwork></figure>

<t>where x and y are coordinates of the point P = (x, y), and each is encoded in the big-endian format and zero-padded to the adjusted underlying field size.
The adjusted underlying field size is the underlying field size rounded up to the nearest 8-bit boundary, as noted in the "fsize" column in <xref target="ec-curves"/>.
This encoding is compatible with the definition given in <xref target="SEC1"/>.</t>

</section>
<section anchor="ec-point-prefixed-native"><name>Prefixed Native EC Point Wire Format</name>

<t>For a custom compressed point the content of the MPI is:</t>

<figure><artwork><![CDATA[
B = 40 || p
]]></artwork></figure>

<t>where p is the public key of the point encoded using the rules defined for the specified curve.
This format is used for ECDH keys based on curves expressed in Montgomery form, and for points when using EdDSA.</t>

</section>
<section anchor="notes-on-ec-point-wire-formats"><name>Notes on EC Point Wire Formats</name>

<t>Given the above definitions, the exact size of the MPI payload for an encoded point is 515 bits for "Curve P-256", 771 for "Curve P-384", 1059 for "Curve P-521", 263 for both "Curve25519" and "Ed25519", 463 for "Ed448", and 455 for "X448".
For example, the length of a EdDSA public key for the curve Ed25519 is 263 bits: 7 bits to represent the 0x40 prefix octet and 32 octets for the native value of the public key.</t>

<t>Even though the zero point, also called the point at infinity, may occur as a result of arithmetic operations on points of an elliptic curve, it SHALL NOT appear in data structures defined in this document.</t>

<t>Each particular curve uses a designated wire format for the point found in its public key or ECDH data structure.
An implementation MUST NOT use a different wire format for a point than the wire format associated with the curve.</t>

</section>
</section>
<section anchor="ec-scalar-wire-formats"><name>EC Scalar Wire Formats</name>

<t>Some non-curve values in elliptic curve cryptography (for example, secret keys and signature components) are not points on a curve, but are also encoded on the wire in OpenPGP as an MPI.</t>

<t>Because of different patterns of deployment, some curves treat these values as opaque bit strings with the high bit set, while others are treated as actual integers, encoded in the standard OpenPGP big-endian form.
The choice of encoding is specific to the public key algorithm in use.</t>

<texttable title="Elliptic Curve Scalar Encodings">
      <ttcol align='left'>Type</ttcol>
      <ttcol align='left'>Description</ttcol>
      <ttcol align='left'>Reference</ttcol>
      <c>integer</c>
      <c>An integer, big-endian encoded as a standard OpenPGP MPI</c>
      <c><xref target="mpi"/></c>
      <c>octet string</c>
      <c>An octet string of fixed length, that may be shorter on the wire due to leading zeros being stripped by the MPI encoding, and may need to be zero-padded before usage</c>
      <c><xref target="ec-octet-string"/></c>
      <c>prefixed N octets</c>
      <c>An octet string of fixed length N, prefixed with octet 0x40 to ensure no leading zero octet</c>
      <c><xref target="ec-prefix"/></c>
</texttable>

<section anchor="ec-octet-string"><name>EC Octet String Wire Format</name>

<t>Some opaque strings of octets are represented on the wire as an MPI by simply stripping the leading zeros and counting the remaining bits.
These strings are of known, fixed length.
They are represented in this document as <spanx style="verb">MPI(N octets of X)</spanx> where <spanx style="verb">N</spanx> is the expected length in octets of the octet string.</t>

<t>For example, a five-octet opaque string (<spanx style="verb">MPI(5 octets of X)</spanx>) where <spanx style="verb">X</spanx> has the value <spanx style="verb">00 02 ee 19 00</spanx> would be represented on the wire as an MPI like so: <spanx style="verb">00 1a 02 ee 19 00</spanx>.</t>

<t>To encode <spanx style="verb">X</spanx> to the wire format, we set the MPI's two-octet bit counter to the value of the highest set bit (bit 26, or 0x001a), and do not transfer the leading all-zero octet to the wire.</t>

<t>To reverse the process, an implementation that knows this value has an expected length of 5 octets can take the following steps:</t>

<t><list style="symbols">
  <t>ensure that the MPI's two-octet bitcount is less than or equal to 40 (5 octets of 8 bits)</t>
  <t>allocate 5 octets, setting all to zero initially</t>
  <t>copy the MPI data octets (without the two count octets) into the lower octets of the allocated space</t>
</list></t>

</section>
<section anchor="ec-prefix"><name>Elliptic Curve Prefixed Octet String Wire Format</name>

<t>Another way to ensure that a fixed-length bytestring is encoded simply to the wire while remaining in MPI format is to prefix the bytestring with a dedicated non-zero octet.
This specification uses 0x40 as the prefix octet.
This is represented in this standard as <spanx style="verb">MPI(prefixed N octets of X)</spanx>, where <spanx style="verb">N</spanx> is the known bytestring length.</t>

<t>For example, a five-octet opaque string using <spanx style="verb">MPI(prefixed 5 octets of X)</spanx> where <spanx style="verb">X</spanx> has the value <spanx style="verb">00 02 ee 19 00</spanx> would be written to the wire form as: <spanx style="verb">00 2f 40 00 02 ee 19 00</spanx>.</t>

<t>To encode the string, we prefix it with the octet 0x40 (whose 7th bit is set), then set the MPI's two-octet bit counter to 47 (0x002f, 7 bits for the prefix octet and 40 bits for the string).</t>

<t>To decode the string from the wire, an implementation that knows that the variable is formed in this way can:</t>

<t><list style="symbols">
  <t>ensure that the first three octets of the MPI (the two bit-count octets plus the prefix octet)  are <spanx style="verb">00 2f 40</spanx>, and</t>
  <t>use the remainder of the MPI directly off the wire.</t>
</list></t>

<t>Note that this is a similar approach to that used in the EC point encodings found in <xref target="ec-point-prefixed-native"/>.</t>

</section>
</section>
<section anchor="key-derivation-function"><name>Key Derivation Function</name>

<t>A key derivation function (KDF) is necessary to implement EC encryption.
The Concatenation Key Derivation Function (Approved Alternative 1) <xref target="SP800-56A"/> with the KDF hash function that is SHA2-256 <xref target="FIPS180"/> or stronger is REQUIRED.</t>

<t>For convenience, the synopsis of the encoding method is given below with significant simplifications attributable to the restricted choice of hash functions in this document.
However, <xref target="SP800-56A"/> is the normative source of the definition.</t>

<figure><artwork><![CDATA[
//   Implements KDF( X, oBits, Param );
//   Input: point X = (x,y)
//   oBits - the desired size of output
//   hBits - the size of output of hash function Hash
//   Param - octets representing the parameters
//   Assumes that oBits <= hBits
// Convert the point X to the octet string:
//   ZB' = 04 || x || y
// and extract the x portion from ZB'
ZB = x;
MB = Hash ( 00 || 00 || 00 || 01 || ZB || Param );
return oBits leftmost bits of MB.
]]></artwork></figure>

<t>Note that ZB in the KDF description above is the compact representation of X as defined in Section 4.2 of <xref target="RFC6090"/>.</t>

</section>
<section anchor="ec-dh-algorithm-ecdh"><name>EC DH Algorithm (ECDH)</name>

<t>The method is a combination of an ECC Diffie-Hellman method to establish a shared secret, a key derivation method to process the shared secret into a derived key, and a key wrapping method that uses the derived key to protect a session key used to encrypt a message.</t>

<t>The One-Pass Diffie-Hellman method C(1, 1, ECC CDH) <xref target="SP800-56A"/> MUST be implemented with the following restrictions: the ECC CDH primitive employed by this method is modified to always assume the cofactor is 1, the KDF specified in <xref target="key-derivation-function"/> is used, and the KDF parameters specified below are used.</t>

<t>The KDF parameters are encoded as a concatenation of the following 5 variable-length and fixed-length fields, which are compatible with the definition of the OtherInfo bitstring <xref target="SP800-56A"/>:</t>

<t><list style="symbols">
  <t>A variable-length field containing a curve OID, which is formatted as follows:  <list style="symbols">
      <t>A one-octet size of the following field,</t>
      <t>The octets representing a curve OID defined in <xref target="ec-curves"/>;</t>
    </list></t>
  <t>A one-octet public key algorithm ID defined in <xref target="pubkey-algos"/>;</t>
  <t>A variable-length field containing KDF parameters, which are identical to the corresponding field in the ECDH public key, and are formatted as follows:  <list style="symbols">
      <t>A one-octet size of the following fields; values 0 and 0xFF are reserved for future extensions,</t>
      <t>A one-octet value 0x01, reserved for future extensions,</t>
      <t>A one-octet hash function ID used with the KDF,</t>
      <t>A one-octet algorithm ID for the symmetric algorithm used to wrap the symmetric key for message encryption; see <xref target="ec-dh-algorithm-ecdh"/> for details;</t>
    </list></t>
  <t>20 octets representing the UTF-8 encoding of the string <spanx style="verb">Anonymous Sender    </spanx>, which is the octet sequence 41 6E 6F 6E 79 6D 6F 75 73 20 53 65 6E 64 65 72 20 20 20 20;</t>
  <t>A variable-length field containing the fingerprint of the recipient encryption subkey or a primary key fingerprint identifying the key material that is needed for decryption.
For version 4 keys, this field is 20 octets.
For version 5 keys, this field is 32 octets.</t>
</list></t>

<t>The size in octets of the KDF parameters sequence, defined above, for encrypting to a v4 key is either 54 for curve P-256, 51 for curves P-384 and P-521, 56 for Curve25519, or 49 for X448.
For encrypting to a v5 key, the size of the sequence is either 66 for curve P-256, 63 for curves P-384 and P-521, 68 for Curve25519, or 61 for X448.</t>

<t>The key wrapping method is described in <xref target="RFC3394"/>.
The KDF produces a symmetric key that is used as a key-encryption key (KEK) as specified in <xref target="RFC3394"/>.
Refer to <xref target="security-considerations"/> for the details regarding the choice of the KEK algorithm, which SHOULD be one of three AES algorithms.
Key wrapping and unwrapping is performed with the default initial value of <xref target="RFC3394"/>.</t>

<t>The input to the key wrapping method is the plaintext described in <xref target="pkesk"/>, "Public-Key Encrypted Session Key Packets (Tag 1)", padded using the method described in <xref target="PKCS5"/> to an 8-octet granularity.</t>

<t>For example, in a V4 Public-Key Encrypted Session Key packet, the following AES-256 session key, in which 32 octets are denoted from k0 to k31, is composed to form the following 40 octet sequence:</t>

<figure><artwork><![CDATA[
09 k0 k1 ... k31 s0 s1 05 05 05 05 05
]]></artwork></figure>

<t>The octets s0 and s1 above denote the checksum of the session key octets.
This encoding allows the sender to obfuscate the size of the symmetric encryption key used to encrypt the data.
For example, assuming that an AES algorithm is used for the session key, the sender MAY use 21, 13, and 5 octets of padding for AES-128, AES-192, and AES-256, respectively, to provide the same number of octets, 40 total, as an input to the key wrapping method.</t>

<t>In a V5 Public-Key Encrypted Session Key packet, the symmetric algorithm is not included, as described in <xref target="pkesk"/>.
For example, an AES-256 session key would be composed as follows:</t>

<figure><artwork><![CDATA[
k0 k1 ... k31 s0 s1 06 06 06 06 06 06
]]></artwork></figure>

<t>The octets k0 to k31 above again denote the session key, and the octets s0 and s1 denote the checksum.
In this case, assuming that an AES algorithm is used for the session key, the sender MAY use 22, 14, and 6 octets of padding for AES-128, AES-192, and AES-256, respectively, to provide the same number of octets, 40 total, as an input to the key wrapping method.</t>

<t>The output of the method consists of two fields.
The first field is the MPI containing the ephemeral key used to establish the shared secret.
The second field is composed of the following two subfields:</t>

<t><list style="symbols">
  <t>One octet encoding the size in octets of the result of the key wrapping method; the value 255 is reserved for future extensions;</t>
  <t>Up to 254 octets representing the result of the key wrapping method, applied to the 8-octet padded session key, as described above.</t>
</list></t>

<t>Note that for session key sizes 128, 192, and 256 bits, the size of the result of the key wrapping method is, respectively, 32, 40, and 48 octets, unless size obfuscation is used.</t>

<t>For convenience, the synopsis of the encoding method is given below; however, this section, <xref target="SP800-56A"/>, and <xref target="RFC3394"/> are the normative sources of the definition.</t>

<t><list style="symbols">
  <t>Obtain the authenticated recipient public key R</t>
  <t>Generate an ephemeral key pair {v, V=vG}</t>
  <t>Compute the shared point S = vR;</t>
  <t>m = symm_alg_ID || session key || checksum || pkcs5_padding;</t>
  <t>curve_OID_len = (octet)len(curve_OID);</t>
  <t>Param = curve_OID_len || curve_OID || public_key_alg_ID || 03 || 01 || KDF_hash_ID || KEK_alg_ID for AESKeyWrap || <spanx style="verb">Anonymous Sender    </spanx> || recipient_fingerprint;</t>
  <t>Z_len = the key size for the KEK_alg_ID used with AESKeyWrap</t>
  <t>Compute Z = KDF( S, Z_len, Param );</t>
  <t>Compute C = AESKeyWrap( Z, m ) as per <xref target="RFC3394"/></t>
  <t>VB = convert point V to the octet string</t>
  <t>Output (MPI(VB) || len(C) || C).</t>
</list></t>

<t>The decryption is the inverse of the method given.
Note that the recipient obtains the shared secret by calculating</t>

<figure><artwork><![CDATA[
S = rV = rvG, where (r,R) is the recipient's key pair.
]]></artwork></figure>

<t>Consistent with <xref target="seipd"/>, AEAD encryption or a Modification Detection Code (MDC) MUST be used anytime the symmetric key is protected by ECDH.</t>

</section>
</section>
<section anchor="notes-on-algorithms"><name>Notes on Algorithms</name>

<section anchor="pkcs-encoding"><name>PKCS#1 Encoding in OpenPGP</name>

<t>This standard makes use of the PKCS#1 functions EME-PKCS1-v1_5 and EMSA-PKCS1-v1_5.
However, the calling conventions of these functions has changed in the past.
To avoid potential confusion and interoperability problems, we are including local copies in this document, adapted from those in PKCS#1 v2.1 <xref target="RFC8017"/>.
<xref target="RFC8017"/> should be treated as the ultimate authority on PKCS#1 for OpenPGP.
Nonetheless, we believe that there is value in having a self-contained document that avoids problems in the future with needed changes in the conventions.</t>

<section anchor="eme-pkcs1-v15-encode"><name>EME-PKCS1-v1_5-ENCODE</name>

<t>Input:</t>

<dl>
  <dt>
k =  </dt>
  <dd>
    <t>the length in octets of the key modulus.</t>
  </dd>
  <dt>
M =  </dt>
  <dd>
    <t>message to be encoded, an octet string of length mLen, where mLen &lt;= k - 11.</t>
  </dd>
</dl>

<t>Output:</t>

<dl>
  <dt>
EM =  </dt>
  <dd>
    <t>encoded message, an octet string of length k.</t>
  </dd>
</dl>

<t>Error: "message too long".</t>

<t><list style="numbers">
  <t>Length checking: If mLen &gt; k - 11, output "message too long" and stop.</t>
  <t>Generate an octet string PS of length k - mLen - 3 consisting of pseudo-randomly generated nonzero octets.
The length of PS will be at least eight octets.</t>
  <t>Concatenate PS, the message M, and other padding to form an encoded message EM of length k octets as  <vspace blankLines='1'/>
    <figure><artwork><![CDATA[
EM = 0x00 || 0x02 || PS || 0x00 || M.
]]></artwork></figure>
  </t>
  <t>Output EM.</t>
</list></t>

</section>
<section anchor="eme-pkcs1-v15-decode"><name>EME-PKCS1-v1_5-DECODE</name>

<t>Input:</t>

<dl>
  <dt>
EM =  </dt>
  <dd>
    <t>encoded message, an octet string</t>
  </dd>
</dl>

<t>Output:</t>

<dl>
  <dt>
M =  </dt>
  <dd>
    <t>message, an octet string.</t>
  </dd>
</dl>

<t>Error: "decryption error".</t>

<t>To decode an EME-PKCS1_v1_5 message, separate the encoded message EM into an octet string PS consisting of nonzero octets and a message M as follows</t>

<figure><artwork><![CDATA[
  EM = 0x00 || 0x02 || PS || 0x00 || M.
]]></artwork></figure>

<t>If the first octet of EM does not have hexadecimal value 0x00, if the second octet of EM does not have hexadecimal value 0x02, if there is no octet with hexadecimal value 0x00 to separate PS from M, or if the length of PS is less than 8 octets, output "decryption error" and stop.
See also the security note in <xref target="security-considerations"/> regarding differences in reporting between a decryption error and a padding error.</t>

</section>
<section anchor="emsa-pkcs1-v15"><name>EMSA-PKCS1-v1_5</name>

<t>This encoding method is deterministic and only has an encoding operation.</t>

<t>Option:</t>

<dl>
  <dt>
Hash -  </dt>
  <dd>
    <t>a hash function in which hLen denotes the length in octets of the hash function output.</t>
  </dd>
</dl>

<t>Input:</t>

<dl>
  <dt>
M =  </dt>
  <dd>
    <t>message to be encoded.</t>
  </dd>
  <dt>
emLen =  </dt>
  <dd>
    <t>intended length in octets of the encoded message, at least tLen + 11, where tLen is the octet length of the DER encoding T of a certain value computed during the encoding operation.</t>
  </dd>
</dl>

<t>Output:</t>

<dl>
  <dt>
EM =  </dt>
  <dd>
    <t>encoded message, an octet string of length emLen.</t>
  </dd>
</dl>

<t>Errors: "message too long"; "intended encoded message length too short".</t>

<t>Steps:</t>

<t><list style="numbers">
  <t>Apply the hash function to the message M to produce a hash value H:  <vspace blankLines='1'/>
H = Hash(M).  <vspace blankLines='1'/>
If the hash function outputs "message too long," output "message too long" and stop.</t>
  <t>Using the list in <xref target="version-three-sig"/>, produce an ASN.1 DER value for the hash function used.
Let T be the full hash prefix from the list, and let tLen be the length in octets of T.</t>
  <t>If emLen &lt; tLen + 11, output "intended encoded message length too short" and stop.</t>
  <t>Generate an octet string PS consisting of emLen - tLen - 3 octets with hexadecimal value 0xFF.
The length of PS will be at least 8 octets.</t>
  <t>Concatenate PS, the hash prefix T, and other padding to form the encoded message EM as  <vspace blankLines='1'/>
    <figure><artwork><![CDATA[
EM = 0x00 || 0x01 || PS || 0x00 || T.
]]></artwork></figure>
  </t>
  <t>Output EM.</t>
</list></t>

</section>
</section>
<section anchor="symmetric-algorithm-preferences"><name>Symmetric Algorithm Preferences</name>

<t>The symmetric algorithm preference is an ordered list of algorithms that the keyholder accepts.
Since it is found on a self-signature, it is possible that a keyholder may have multiple, different preferences.
For example, Alice may have AES-128 only specified for "alice@work.com" but Camellia-256, Twofish, and AES-128 specified for "alice@home.org".
Note that it is also possible for preferences to be in a subkey's binding signature.</t>

<t>Since AES-128 is the MUST-implement algorithm, if it is not explicitly in the list, it is tacitly at the end.
However, it is good form to place it there explicitly.
Note also that if an implementation does not implement the preference, then it is implicitly an AES-128-only implementation.
Note further that implementations conforming to previous versions of this standard <xref target="RFC4880"/> have TripleDES as its only MUST-implement algorithm.</t>

<t>An implementation MUST NOT use a symmetric algorithm that is not in the recipient's preference list.
When encrypting to more than one recipient, the implementation finds a suitable algorithm by taking the intersection of the preferences of the recipients.
Note that the MUST-implement algorithm, AES-128, ensures that the intersection is not null.
The implementation may use any mechanism to pick an algorithm in the intersection.</t>

<t>If an implementation can decrypt a message that a keyholder doesn't have in their preferences, the implementation SHOULD decrypt the message anyway, but MUST warn the keyholder that the protocol has been violated.
For example, suppose that Alice, above, has software that implements all algorithms in this specification.
Nonetheless, she prefers subsets for work or home.
If she is sent a message encrypted with IDEA, which is not in her preferences, the software warns her that someone sent her an IDEA-encrypted message, but it would ideally decrypt it anyway.</t>

<section anchor="plaintext"><name>Plaintext</name>

<t>Algorithm 0, "plaintext", may only be used to denote secret keys that are stored in the clear.
Implementations MUST NOT use plaintext in encrypted data packets; they must use Literal Data packets to encode unencrypted literal data.</t>

</section>
</section>
<section anchor="other-algorithm-preferences"><name>Other Algorithm Preferences</name>

<t>Other algorithm preferences work similarly to the symmetric algorithm preference, in that they specify which algorithms the keyholder accepts.
There are two interesting cases that other comments need to be made about, though, the compression preferences and the hash preferences.</t>

<section anchor="compression-preferences"><name>Compression Preferences</name>

<t>Like the algorithm preferences, an implementation MUST NOT use an algorithm that is not in the preference vector.
If Uncompressed (0) is not explicitly in the list, it is tacitly at the end.
That is, uncompressed messages may always be sent.</t>

<t>Note that earlier implementations may assume that the absence of compression preferences means that [ZIP(1), Uncompressed(0)] are preferred, and default to ZIP compression.
Therefore, an implementation that prefers uncompressed data SHOULD explicitly state this in the preferred compression algorithms.</t>

<section anchor="uncompressed"><name>Uncompressed</name>

<t>Algorithm 0, "uncompressed", may only be used to denote a preference for uncompressed data.
Implementations MUST NOT use uncompressed in Compressed Data packets; they must use Literal Data packets to encode uncompressed literal data.</t>

</section>
</section>
<section anchor="hash-algorithm-preferences"><name>Hash Algorithm Preferences</name>

<t>Typically, the choice of a hash algorithm is something the signer does, rather than the verifier, because a signer rarely knows who is going to be verifying the signature.
This preference, though, allows a protocol based upon digital signatures ease in negotiation.</t>

<t>Thus, if Alice is authenticating herself to Bob with a signature, it makes sense for her to use a hash algorithm that Bob's software uses.
This preference allows Bob to state in his key which algorithms Alice may use.</t>

<t>Since SHA2-256 is the MUST-implement hash algorithm, if it is not explicitly in the list, it is tacitly at the end.
However, it is good form to place it there explicitly.</t>

</section>
</section>
<section anchor="rsa-notes"><name>RSA</name>

<t>There are algorithm types for RSA Sign-Only, and RSA Encrypt-Only keys.
These types are deprecated.
The "key flags" subpacket in a signature is a much better way to express the same idea, and generalizes it to all algorithms.
An implementation SHOULD NOT create such a key, but MAY interpret it.</t>

<t>An implementation SHOULD NOT implement RSA keys of size less than 1024 bits.</t>

</section>
<section anchor="dsa"><name>DSA</name>

<t>An implementation SHOULD NOT implement DSA keys of size less than 1024 bits.
It MUST NOT implement a DSA key with a q size of less than 160 bits.
DSA keys MUST also be a multiple of 64 bits, and the q size MUST be a multiple of 8 bits.
The Digital Signature Standard (DSS) <xref target="FIPS186"/> specifies that DSA be used in one of the following ways:</t>

<t><list style="symbols">
  <t>1024-bit key, 160-bit q, SHA-1, SHA2-224, SHA2-256, SHA2-384, or SHA2-512 hash</t>
  <t>2048-bit key, 224-bit q, SHA2-224, SHA2-256, SHA2-384, or SHA2-512 hash</t>
  <t>2048-bit key, 256-bit q, SHA2-256, SHA2-384, or SHA2-512 hash</t>
  <t>3072-bit key, 256-bit q, SHA2-256, SHA2-384, or SHA2-512 hash</t>
</list></t>

<t>The above key and q size pairs were chosen to best balance the strength of the key with the strength of the hash.
Implementations SHOULD use one of the above key and q size pairs when generating DSA keys.
If DSS compliance is desired, one of the specified SHA hashes must be used as well.
<xref target="FIPS186"/> is the ultimate authority on DSS, and should be consulted for all questions of DSS compliance.</t>

<t>Note that earlier versions of this standard only allowed a 160-bit q with no truncation allowed, so earlier implementations may not be able to handle signatures with a different q size or a truncated hash.</t>

</section>
<section anchor="elgamal"><name>Elgamal</name>

<t>An implementation SHOULD NOT implement Elgamal keys of size less than 1024 bits.</t>

</section>
<section anchor="eddsa"><name>EdDSA</name>

<t>Although the EdDSA algorithm allows arbitrary data as input, its use with OpenPGP requires that a digest of the message is used as input (pre-hashed).
See <xref target="computing-signatures"/> for details.
Truncation of the resulting digest is never applied; the resulting digest value is used verbatim as input to the EdDSA algorithm.</t>

<t>For clarity: while <xref target="RFC8032"/> describes different variants of EdDSA, OpenPGP uses the "pure" variant (PureEdDSA).
The hashing that happens with OpenPGP is done as part of the standard OpenPGP signature process, and that hash itself is fed as the input message to the PureEdDSA algorithm.</t>

<t>As specified in <xref target="RFC8032"/>, Ed448 also expects a "context string".
In OpenPGP, Ed448 is used with the empty string as a context string.</t>

</section>
<section anchor="reserved-notes"><name>Reserved Algorithm Numbers</name>

<t>A number of algorithm IDs have been reserved for algorithms that would be useful to use in an OpenPGP implementation, yet there are issues that prevent an implementer from actually implementing the algorithm.
These are marked in <xref target="pubkey-algos"/> as "reserved for".</t>

<t>The reserved public-key algorithm X9.42 (21) does not have the necessary parameters, parameter order, or semantics defined.
The same is currently true for reserved public-key algorithms AEDH (23) and AEDSA (24).</t>

<t>Previous versions of OpenPGP permitted Elgamal <xref target="ELGAMAL"/> signatures with a public-key identifier of 20.
These are no longer permitted.
An implementation MUST NOT generate such keys.
An implementation MUST NOT generate Elgamal signatures.
See <xref target="BLEICHENBACHER"/>.</t>

</section>
<section anchor="cfb-mode"><name>OpenPGP CFB Mode</name>

<t>When using a version 1 Symmetrically Encrypted Integrity Protected Data packet (<xref target="version-one-seipd"/>) or --- for historic data --- a Symmetrically Encrypted Data packet (<xref target="sed"/>), OpenPGP does symmetric encryption using a variant of Cipher Feedback mode (CFB mode).
This section describes the procedure it uses in detail.
This mode is what is used for Symmetrically Encrypted Integrity Protected Data Packets (and the dangerously malleable --- and deprecated --- Symmetrically Encrypted Data Packets).
Some mechanisms for encrypting secret-key material also use CFB mode, as described in <xref target="secret-key-encryption"/>.</t>

<t>In the description below, the value BS is the block size in octets of the cipher.
Most ciphers have a block size of 8 octets.
The AES and Twofish have a block size of 16 octets.
Also note that the description below assumes that the IV and CFB arrays start with an index of 1 (unlike the C language, which assumes arrays start with a zero index).</t>

<t>OpenPGP CFB mode uses an initialization vector (IV) of all zeros, and prefixes the plaintext with BS+2 octets of random data, such that octets BS+1 and BS+2 match octets BS-1 and BS.
It does a CFB resynchronization after encrypting those BS+2 octets.</t>

<t>Thus, for an algorithm that has a block size of 8 octets (64 bits), the IV is 10 octets long and octets 7 and 8 of the IV are the same as octets 9 and 10.
For an algorithm with a block size of 16 octets (128 bits), the IV is 18 octets long, and octets 17 and 18 replicate octets 15 and 16.
Those extra two octets are an easy check for a correct key.</t>

<t>Step by step, here is the procedure:</t>

<t><list style="numbers">
  <t>The feedback register (FR) is set to the IV, which is all zeros.</t>
  <t>FR is encrypted to produce FRE (FR Encrypted).
This is the encryption of an all-zero value.</t>
  <t>FRE is xored with the first BS octets of random data prefixed to the plaintext to produce C[1] through C[BS], the first BS octets of ciphertext.</t>
  <t>FR is loaded with C[1] through C[BS].</t>
  <t>FR is encrypted to produce FRE, the encryption of the first BS octets of ciphertext.</t>
  <t>The left two octets of FRE get xored with the next two octets of data that were prefixed to the plaintext.
This produces C[BS+1] and C[BS+2], the next two octets of ciphertext.</t>
  <t>(The resynchronization step) FR is loaded with C[3] through C[BS+2].</t>
  <t>FR is encrypted to produce FRE.</t>
  <t>FRE is xored with the first BS octets of the given plaintext, now that we have finished encrypting the BS+2 octets of prefixed data.
This produces C[BS+3] through C[BS+(BS+2)], the next BS octets of ciphertext.</t>
  <t>FR is loaded with C[BS+3] to C[BS + (BS+2)] (which is C11-C18 for an 8-octet block).</t>
  <t>FR is encrypted to produce FRE.</t>
  <t>FRE is xored with the next BS octets of plaintext, to produce the next BS octets of ciphertext.
These are loaded into FR, and the process is repeated until the plaintext is used up.</t>
</list></t>

</section>
<section anchor="private-or-experimental-parameters"><name>Private or Experimental Parameters</name>

<t>S2K specifiers, Signature subpacket types, User Attribute types, image format types, and algorithms described in <xref target="constants"/> all reserve the range 100 to 110 for private and experimental use.
Packet types reserve the range 60 to 63 for private and experimental use.
These are intentionally managed with the PRIVATE USE method, as described in <xref target="RFC8126"/>.</t>

<t>However, implementations need to be careful with these and promote them to full IANA-managed parameters when they grow beyond the original, limited system.</t>

</section>
<section anchor="meta-considerations-for-expansion"><name>Meta-Considerations for Expansion</name>

<t>If OpenPGP is extended in a way that is not backwards-compatible, meaning that old implementations will not gracefully handle their absence of a new feature, the extension proposal can be declared in the key holder's self-signature as part of the Features signature subpacket.</t>

<t>We cannot state definitively what extensions will not be upwards-compatible, but typically new algorithms are upwards-compatible, whereas new packets are not.</t>

<t>If an extension proposal does not update the Features system, it SHOULD include an explanation of why this is unnecessary.
If the proposal contains neither an extension to the Features system nor an explanation of why such an extension is unnecessary, the proposal SHOULD be rejected.</t>

</section>
</section>
<section anchor="security-considerations"><name>Security Considerations</name>

<t><list style="symbols">
  <t>As with any technology involving cryptography, you should check the current literature to determine if any algorithms used here have been found to be vulnerable to attack.</t>
  <t>This specification uses Public-Key Cryptography technologies.
It is assumed that the private key portion of a public-private key pair is controlled and secured by the proper party or parties.</t>
  <t>The MD5 hash algorithm has been found to have weaknesses, with collisions found in a number of cases.
MD5 is deprecated for use in OpenPGP.
Implementations MUST NOT generate new signatures using MD5 as a hash function.
They MAY continue to consider old signatures that used MD5 as valid.</t>
  <t>SHA2-224 and SHA2-384 require the same work as SHA2-256 and SHA2-512, respectively.
In general, there are few reasons to use them outside of DSS compatibility.
You need a situation where one needs more security than smaller hashes, but does not want to have the full 256-bit or 512-bit data length.</t>
  <t>Many security protocol designers think that it is a bad idea to use a single key for both privacy (encryption) and integrity (signatures).
In fact, this was one of the motivating forces behind the V4 key format with separate signature and encryption keys.
If you as an implementer promote dual-use keys, you should at least be aware of this controversy.</t>
  <t>The DSA algorithm will work with any hash, but is sensitive to the quality of the hash algorithm.
Verifiers should be aware that even if the signer used a strong hash, an attacker could have modified the signature to use a weak one.
Only signatures using acceptably strong hash algorithms should be accepted as valid.</t>
  <t>As OpenPGP combines many different asymmetric, symmetric, and hash algorithms, each with different measures of strength, care should be taken that the weakest element of an OpenPGP message is still sufficiently strong for the purpose at hand.
While consensus about the strength of a given algorithm may evolve, NIST Special Publication 800-57 <xref target="SP800-57"/> recommends the following list of equivalent strengths:</t>
</list></t>

<texttable title="Key length equivalences">
      <ttcol align='right'>Asymmetric key size</ttcol>
      <ttcol align='left'>Hash size</ttcol>
      <ttcol align='left'>Symmetric key size</ttcol>
      <c>1024</c>
      <c>160</c>
      <c>80</c>
      <c>2048</c>
      <c>224</c>
      <c>112</c>
      <c>3072</c>
      <c>256</c>
      <c>128</c>
      <c>7680</c>
      <c>384</c>
      <c>192</c>
      <c>15360</c>
      <c>512</c>
      <c>256</c>
</texttable>

<t><list style="symbols">
  <t>There is a somewhat-related potential security problem in signatures.
If an attacker can find a message that hashes to the same hash with a different algorithm, a bogus signature structure can be constructed that evaluates correctly.  <vspace blankLines='1'/>
For example, suppose Alice DSA signs message M using hash algorithm H.
Suppose that Mallet finds a message M' that has the same hash value as M with H'.
Mallet can then construct a signature block that verifies as Alice's signature of M' with H'.
However, this would also constitute a weakness in either H or H' or both.
Should this ever occur, a revision will have to be made to this document to revise the allowed hash algorithms.</t>
  <t>If you are building an authentication system, the recipient may specify a preferred signing algorithm.
However, the signer would be foolish to use a weak algorithm simply because the recipient requests it.</t>
  <t>Some of the encryption algorithms mentioned in this document have been analyzed less than others.
For example, although CAST5 is presently considered strong, it has been analyzed less than TripleDES.
Other algorithms may have other controversies surrounding them.</t>
  <t>In late summer 2002, Jallad, Katz, and Schneier published an interesting attack on older versions of the OpenPGP protocol and some of its implementations <xref target="JKS02"/>.
In this attack, the attacker modifies a message and sends it to a user who then returns the erroneously decrypted message to the attacker.
The attacker is thus using the user as a random oracle, and can often decrypt the message.
This attack is a particular form of ciphertext malleability.
See <xref target="ciphertext-malleability"/> for information on how to defend against such an attack using more recent versions of OpenPGP.</t>
  <t>PKCS#1 has been found to be vulnerable to attacks in which a system that reports errors in padding differently from errors in decryption becomes a random oracle that can leak the private key in mere millions of queries.
Implementations must be aware of this attack and prevent it from happening.
The simplest solution is to report a single error code for all variants of decryption errors so as not to leak information to an attacker.</t>
  <t>Some technologies mentioned here may be subject to government control in some countries.</t>
  <t>In winter 2005, Serge Mister and Robert Zuccherato from Entrust released a paper describing a way that the "quick check" in OpenPGP CFB mode can be used with a random oracle to decrypt two octets of every cipher block <xref target="MZ05"/>.
They recommend as prevention not using the quick check at all.  <vspace blankLines='1'/>
Many implementers have taken this advice to heart for any data that is symmetrically encrypted and for which the session key is public-key encrypted.
In this case, the quick check is not needed as the public-key encryption of the session key should guarantee that it is the right session key.
In other cases, the implementation should use the quick check with care.  <vspace blankLines='1'/>
On the one hand, there is a danger to using it if there is a random oracle that can leak information to an attacker.
In plainer language, there is a danger to using the quick check if timing information about the check can be exposed to an attacker, particularly via an automated service that allows rapidly repeated queries.  <vspace blankLines='1'/>
On the other hand, it is inconvenient to the user to be informed that they typed in the wrong passphrase only after a petabyte of data is decrypted.
There are many cases in cryptographic engineering where the implementer must use care and wisdom, and this is one.</t>
  <t>An implementation SHOULD only use an AES algorithm as a KEK algorithm, since backward compatibility of the ECDH format is not a concern.
The KEK algorithm is only used within the scope of a Public-Key Encrypted Session Key Packet, which represents an ECDH key recipient of a message.
Compare this with the algorithm used for the session key of the message, which MAY be different from a KEK algorithm.  <vspace blankLines='1'/>
Side channel attacks are a concern when a compliant application's use of the OpenPGP format can be modeled by a decryption or signing oracle, for example, when an application is a network service performing decryption to unauthenticated remote users.
ECC scalar multiplication operations used in ECDSA and ECDH are vulnerable to side channel attacks.
Countermeasures can often be taken at the higher protocol level, such as limiting the number of allowed failures or time-blinding of the operations associated with each network interface.
Mitigations at the scalar multiplication level seek to eliminate any measurable distinction between the ECC point addition and doubling operations.</t>
  <t>V5 signatures include a 128 bit salt that is hashed first.
This makes OpenPGP signatures non-deterministic and protects against a broad class of attacks that depend on creating a signature over a predictable message.
Hashing the salt first means that there is no attacker controlled hashed prefix.
An example of this kind of attack is described in the paper SHA-1 Is A Shambles (see <xref target="SHAMBLES"/>), which leverages a chosen prefix collision attack against SHA-1.</t>
</list></t>

<section anchor="ciphertext-malleability"><name>Avoiding Ciphertext Malleability</name>

<t>If ciphertext can be modified by an attacker but still subsequently decrypted to some new plaintext, it is considered "malleable".
A number of attacks can arise in any cryptosystem that uses malleable encryption, so modern OpenPGP offers mechanisms to defend against it.
However, legacy OpenPGP data may have been created before these mechanisms were available.
Because OpenPGP implementations deal with historic stored data, they may encounter malleable ciphertexts.</t>

<t>When an OpenPGP implementation discovers that it is decrypting data that appears to be malleable, it MUST indicate a clear error message that the integrity of the message is suspect, SHOULD NOT release decrypted data to the user, and SHOULD halt with an error.
An implementation that encounters malleable ciphertext MAY choose to release cleartext to the user if it is known to be dealing with historic archived legacy data, and the user is aware of the risks.</t>

<t>Any of the following OpenPGP data elements indicate that malleable ciphertext is present:</t>

<t><list style="symbols">
  <t>all Symmetrically Encrypted Data packets (<xref target="sed"/>).</t>
  <t>within any encrypted container, any Compressed Data packet (<xref target="compressed-data"/>) where there is a decompression failure.</t>
  <t>any version 1 Symmetrically Encrypted Integrity Protected Data packet (<xref target="version-one-seipd"/>) where the internal Modification Detection Code does not validate.</t>
  <t>any version 2 Symmetrically Encrypted Integrity Protected Data packet (<xref target="version-two-seipd"/>) where the authentication tag of any chunk fails, or where there is no final zero-octet chunk.</t>
  <t>any Secret Key packet with encrypted secret key material (<xref target="secret-key-encryption"/>) where there is an integrity failure, based on the value of the secret key protection octet:  <list style="symbols">
      <t>value 255 or raw cipher algorithm: where the trailing 2-octet checksum does not match.</t>
      <t>value 254: where the SHA1 checksum is mismatched.</t>
      <t>value 253: where the AEAD authentication tag is invalid.</t>
    </list></t>
</list></t>

<t>To avoid these circumstances, an implementation that generates OpenPGP encrypted data SHOULD select the encrypted container format with the most robust protections that can be handled by the intended recipients.
In particular:</t>

<t><list style="symbols">
  <t>The SED packet is deprecated, and MUST NOT be generated.</t>
  <t>When encrypting to one or more public keys:  <list style="symbols">
      <t>all recipient keys indicate support for version 2 of the Symmetrically Encrypted Integrity Protected Data packet in their Features subpacket (<xref target="features-subpacket"/>), or are v5 keys without a Features subpacket, or the implementation can otherwise infer that all recipients support v2 SEIPD packets, the implementation MUST encrypt using a v2 SEIPD packet.</t>
      <t>If one of the recipients does not support v2 SEIPD packets, then the message generator MAY use a v1 SEIPD packet instead.</t>
    </list></t>
  <t>Password-protected secret key material in a V5 Secret Key or V5 Secret Subkey packet SHOULD be protected with AEAD encryption (S2K usage octet 253) unless it will be transferred to an implementation that is known to not support AEAD.</t>
</list></t>

<t>Implementers should implement AEAD (v2 SEIPD and S2K usage octet 253) promptly and encourage its spread.</t>

<t>Users should migrate to AEAD with all due speed.</t>

</section>
<section anchor="escrowed-revocations"><name>Escrowed Revocation Signatures</name>

<t>A keyholder Alice may wish to designate a third party to be able to revoke Alice's own key.</t>

<t>The preferred way for her to do this is produce a specific Revocation Signature (signature types 0x20, 0x28, or 0x30) and distribute it securely to her preferred revoker who can hold it in escrow.
The preferred revoker can then publish the escrowed Revocation Signature at whatever time is deemed appropriate, rather than generating a revocation signature themselves.</t>

<t>There are multiple advantages of using an escrowed Revocation Signature over the deprecated Revocation Key subpacket (<xref target="revocation-key"/>):</t>

<t><list style="symbols">
  <t>The keyholder can constrain what types of revocation the preferred revoker can issue, by only escrowing those specific signatures.</t>
  <t>There is no public/visible linkage between the keyholder and the preferred revoker.</t>
  <t>Third parties can verify the revocation without needing to find the key of the preferred revoker.</t>
  <t>The preferred revoker doesn't even need to have a public OpenPGP key if some other secure transport is possible between them and the keyholder.</t>
  <t>Implementation support for enforcing a revocation from an authorized Revocation Key subpacket is uneven and unreliable.</t>
  <t>If the fingerprint mechanism suffers a cryptanalytic flaw, the escrowed Revocation Signature is not affected.</t>
</list></t>

<t>A Revocation Signature may also be split up into shares and distributed among multiple parties, requiring some subset of those parties to collaborate before the escrowed Revocation Signature is recreated.</t>

</section>
<section anchor="random-number-generation-and-seeding"><name>Random Number Generation and Seeding</name>

<t>OpenPGP requires a cryptographically secure pseudorandom number generator (CSPRNG).
In most cases, the operating system provides an appropriate facility such as a <spanx style="verb">getrandom()</spanx> syscall, which should be used absent other (for example, performance) concerns.
It is RECOMMENDED to use an existing CSPRNG implementation in preference to crafting a new one.
Many adequate cryptographic libraries are already available under favorable license terms.
Should those prove unsatisfactory, <xref target="RFC4086"/> provides guidance on the generation of random values.</t>

<t>OpenPGP uses random data with three different levels of visibility:</t>

<t><list style="symbols">
  <t>in publicly-visible fields such as nonces, IVs, public padding material, or salts,</t>
  <t>in shared-secret values, such as session keys for encrypted data or padding material within an encrypted packet, and</t>
  <t>in entirely private data, such as asymmetric key generation.</t>
</list></t>

<t>With a properly functioning CSPRNG, this does not present a security problem, as it is not feasible to determine the CSPRNG state from its output.
However, with a broken CSPRNG, it may be possible for an attacker to use visible output to determine the CSPRNG internal state and thereby predict less-visible data like keying material, as documented in <xref target="CHECKOWAY"/>.</t>

<t>An implementation can provide extra security against this form of attack by using separate CSPRNGs to generate random data with different levels of visibility.</t>

</section>
<section anchor="traffic-analysis"><name>Traffic Analysis</name>

<t>When sending OpenPGP data through the network, the size of the data may leak information to an attacker.
There are circumstances where such a leak could be unacceptable from a security perspective.</t>

<t>For example, if possible cleartext messages for a given protocol are known to be either <spanx style="verb">yes</spanx> (three octets) and <spanx style="verb">no</spanx> (two octets) and the messages are sent within a Symmetrically-Encrypted Integrity Protected Data packet, the length of the encrypted message will reveal the contents of the cleartext.</t>

<t>In another example, sending an OpenPGP Transferable Public Key over an encrypted network connection might reveal the length of the certificate.
Since the length of an OpenPGP certificate varies based on the content, an external observer interested in metadata (who is trying to contact who) may be able to guess the identity of the certificate sent, if its length is unique.</t>

<t>In both cases, an implementation can adjust the size of the compound structure by including a Padding packet (see <xref target="padding-packet"/>).</t>

</section>
</section>
<section anchor="implementation-nits"><name>Implementation Nits</name>

<t>This section is a collection of comments to help an implementer, particularly with an eye to backward compatibility.
Often the differences are small, but small differences are frequently more vexing than large differences.
Thus, this is a non-comprehensive list of potential problems and gotchas for a developer who is trying to be backward-compatible.</t>

<t><list style="symbols">
  <t>There are many ways possible for two keys to have the same key material, but different fingerprints (and thus Key IDs).
For example, since a V4 fingerprint is constructed by hashing the key creation time along with other things, two V4 keys created at different times, yet with the same key material will have different fingerprints.</t>
  <t>OpenPGP does not put limits on the size of public keys.
However, larger keys are not necessarily better keys.
Larger keys take more computation time to use, and this can quickly become impractical.
Different OpenPGP implementations may also use different upper bounds for public key sizes, and so care should be taken when choosing sizes to maintain interoperability.</t>
  <t>ASCII armor is an optional feature of OpenPGP.
The OpenPGP working group strives for a minimal set of mandatory-to-implement features, and since there could be useful implementations that only use binary object formats, this is not a "MUST" feature for an implementation.
For example, an implementation that is using OpenPGP as a mechanism for file signatures may find ASCII armor unnecessary.
OpenPGP permits an implementation to declare what features it does and does not support, but ASCII armor is not one of these.
Since most implementations allow binary and armored objects to be used indiscriminately, an implementation that does not implement ASCII armor may find itself with compatibility issues with general-purpose implementations.
Moreover, implementations of OpenPGP-MIME <xref target="RFC3156"/> already have a requirement for ASCII armor so those implementations will necessarily have support.</t>
  <t>What this document calls Legacy packet format <xref target="legacy-packet-format"/> is what older documents called the "old packet format".
It is the packet format of the legacy PGP 2 implementation.
Older RFCs called the current OpenPGP packet format <xref target="openpgp-packet-format"/> the "new packet format".</t>
</list></t>

</section>


  </middle>

  <back>

    <references title='Normative References'>

<reference anchor="AES" target="http://csrc.nist.gov/publications/fips/fips197/fips-197.{ps,pdf}">
  <front>
    <title>FIPS PUB 197, Advanced Encryption Standard (AES)</title>
    <author >
      <organization>NIST</organization>
    </author>
    <date year="2001" month="November"/>
  </front>
</reference>
<reference anchor="BLOWFISH" target="http://www.counterpane.com/bfsverlag.html">
  <front>
    <title>Description of a New Variable-Length Key, 64-Bit Block Cipher (Blowfish)</title>
    <author initials="B." surname="Schneier">
      <organization></organization>
    </author>
    <date year="1993" month="December"/>
  </front>
  <seriesInfo name="Fast Software Encryption, Cambridge Security Workshop Proceedings" value="Springer-Verlag, 1994, pp191-204"/>
</reference>
<reference anchor="BZ2" target="http://www.bzip.org/">
  <front>
    <title>The Bzip2 and libbzip2 home page</title>
    <author initials="J." surname="Seward" fullname="Julian Seward, jseward@acm.org">
      <organization></organization>
    </author>
    <date year="2010"/>
  </front>
</reference>
<reference anchor="EAX" >
  <front>
    <title>A Conventional Authenticated-Encryption Mode</title>
    <author initials="M." surname="Bellare">
      <organization></organization>
    </author>
    <author initials="P." surname="Rogaway">
      <organization></organization>
    </author>
    <author initials="D." surname="Wagner">
      <organization></organization>
    </author>
    <date year="2003" month="April"/>
  </front>
</reference>
<reference anchor="ELGAMAL" >
  <front>
    <title>A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms</title>
    <author initials="T." surname="Elgamal">
      <organization></organization>
    </author>
    <date year="1985"/>
  </front>
  <seriesInfo name="IEEE Transactions on Information Theory" value="v. IT-31, n. 4, 1985, pp. 469-472"/>
</reference>
<reference anchor="FIPS180" target="http://dx.doi.org/10.6028/NIST.FIPS.180-4">
  <front>
    <title>Secure Hash Standard (SHS), FIPS 180-4</title>
    <author >
      <organization>National Institute of Standards and Technology, U.S. Department of Commerce</organization>
    </author>
    <date year="2015" month="August"/>
  </front>
</reference>
<reference anchor="FIPS186" target="http://dx.doi.org/10.6028/NIST.FIPS.186-4">
  <front>
    <title>Digital Signature Standard (DSS), FIPS 186-4</title>
    <author >
      <organization>National Institute of Standards and Technology, U.S. Department of Commerce</organization>
    </author>
    <date year="2013" month="July"/>
  </front>
</reference>
<reference anchor="FIPS202" target="http://dx.doi.org/10.6028/NIST.FIPS.202">
  <front>
    <title>SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions, FIPS 202</title>
    <author >
      <organization>National Institute of Standards and Technology, U.S. Department of Commerce</organization>
    </author>
    <date year="2015" month="August"/>
  </front>
</reference>
<reference anchor="HAC" >
  <front>
    <title>Handbook of Applied Cryptography</title>
    <author initials="A.J." surname="Menezes" fullname="Alfred J. Menezes">
      <organization></organization>
    </author>
    <author initials="P.v." surname="Oorschot" fullname="Paul van Oorschot">
      <organization></organization>
    </author>
    <author initials="S." surname="Vanstone" fullname="Scott Vanstone">
      <organization></organization>
    </author>
    <date year="1996"/>
  </front>
</reference>
<reference anchor="IDEA" >
  <front>
    <title>On the design and security of block ciphers</title>
    <author initials="X." surname="Lai">
      <organization></organization>
    </author>
    <date year="1992"/>
  </front>
  <seriesInfo name="ETH Series in Information Processing, J.L. Massey (editor)" value="Vol. 1, Hartung-Gorre Verlag Konstanz, Technische Hochschule (Zurich)"/>
</reference>
<reference anchor="ISO10646" >
  <front>
    <title>Information Technology - Universal Multiple-octet coded Character Set (UCS) - Part 1: Architecture and Basic Multilingual Plane</title>
    <author >
      <organization>International Organization for Standardization</organization>
    </author>
    <date year="1993" month="May"/>
  </front>
  <seriesInfo name="ISO" value="Standard 10646-1"/>
</reference>
<reference anchor="JFIF" >
  <front>
    <title>JPEG File Interchange Format (Version 1.02).</title>
    <author initials="E.H.M." surname="CA" fullname="Eric Hamilton, Milpitas, CA">
      <organization>C-Cube Microsystems</organization>
    </author>
    <date year="1996" month="September"/>
  </front>
</reference>
<reference anchor="PKCS5" >
  <front>
    <title>PKCS #5 v2.0: Password-Based Cryptography Standard</title>
    <author >
      <organization>RSA Laboratories</organization>
    </author>
    <date year="1999" month="March" day="25"/>
  </front>
</reference>




<reference anchor='RFC1950' target='https://www.rfc-editor.org/info/rfc1950'>
<front>
<title>ZLIB Compressed Data Format Specification version 3.3</title>
<author fullname='P. Deutsch' initials='P.' surname='Deutsch'><organization/></author>
<author fullname='J-L. Gailly' initials='J-L.' surname='Gailly'><organization/></author>
<date month='May' year='1996'/>
<abstract><t>This specification defines a lossless compressed data format.  This memo provides information for the Internet community.  This memo does not specify an Internet standard of any kind.</t></abstract>
</front>
<seriesInfo name='RFC' value='1950'/>
<seriesInfo name='DOI' value='10.17487/RFC1950'/>
</reference>



<reference anchor='RFC1951' target='https://www.rfc-editor.org/info/rfc1951'>
<front>
<title>DEFLATE Compressed Data Format Specification version 1.3</title>
<author fullname='P. Deutsch' initials='P.' surname='Deutsch'><organization/></author>
<date month='May' year='1996'/>
<abstract><t>This specification defines a lossless compressed data format that compresses data using a combination of the LZ77 algorithm and Huffman coding, with efficiency comparable to the best currently available general-purpose compression methods.  This memo provides information for the Internet community.  This memo does not specify an Internet standard of any kind.</t></abstract>
</front>
<seriesInfo name='RFC' value='1951'/>
<seriesInfo name='DOI' value='10.17487/RFC1951'/>
</reference>



<reference anchor='RFC2045' target='https://www.rfc-editor.org/info/rfc2045'>
<front>
<title>Multipurpose Internet Mail Extensions (MIME) Part One: Format of Internet Message Bodies</title>
<author fullname='N. Freed' initials='N.' surname='Freed'><organization/></author>
<author fullname='N. Borenstein' initials='N.' surname='Borenstein'><organization/></author>
<date month='November' year='1996'/>
<abstract><t>This initial document specifies the various headers used to describe the structure of MIME messages.  [STANDARDS-TRACK]</t></abstract>
</front>
<seriesInfo name='RFC' value='2045'/>
<seriesInfo name='DOI' value='10.17487/RFC2045'/>
</reference>



<reference anchor='RFC2119' target='https://www.rfc-editor.org/info/rfc2119'>
<front>
<title>Key words for use in RFCs to Indicate Requirement Levels</title>
<author fullname='S. Bradner' initials='S.' surname='Bradner'><organization/></author>
<date month='March' year='1997'/>
<abstract><t>In many standards track documents several words are used to signify the requirements in the specification.  These words are often capitalized. This document defines these words as they should be interpreted in IETF documents.  This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements.</t></abstract>
</front>
<seriesInfo name='BCP' value='14'/>
<seriesInfo name='RFC' value='2119'/>
<seriesInfo name='DOI' value='10.17487/RFC2119'/>
</reference>



<reference anchor='RFC2144' target='https://www.rfc-editor.org/info/rfc2144'>
<front>
<title>The CAST-128 Encryption Algorithm</title>
<author fullname='C. Adams' initials='C.' surname='Adams'><organization/></author>
<date month='May' year='1997'/>
<abstract><t>There is a need in the Internet community for an unencumbered encryption algorithm with a range of key sizes that can provide security for a variety of cryptographic applications and protocols.  This document describes an existing algorithm that can be used to satisfy this requirement.  This memo provides information for the Internet community. This memo does not specify an Internet standard of any kind.</t></abstract>
</front>
<seriesInfo name='RFC' value='2144'/>
<seriesInfo name='DOI' value='10.17487/RFC2144'/>
</reference>



<reference anchor='RFC2822' target='https://www.rfc-editor.org/info/rfc2822'>
<front>
<title>Internet Message Format</title>
<author fullname='P. Resnick' initials='P.' role='editor' surname='Resnick'><organization/></author>
<date month='April' year='2001'/>
<abstract><t>This document specifies a syntax for text messages that are sent between computer users, within the framework of &quot;electronic mail&quot; messages. [STANDARDS-TRACK]</t></abstract>
</front>
<seriesInfo name='RFC' value='2822'/>
<seriesInfo name='DOI' value='10.17487/RFC2822'/>
</reference>



<reference anchor='RFC3156' target='https://www.rfc-editor.org/info/rfc3156'>
<front>
<title>MIME Security with OpenPGP</title>
<author fullname='M. Elkins' initials='M.' surname='Elkins'><organization/></author>
<author fullname='D. Del Torto' initials='D.' surname='Del Torto'><organization/></author>
<author fullname='R. Levien' initials='R.' surname='Levien'><organization/></author>
<author fullname='T. Roessler' initials='T.' surname='Roessler'><organization/></author>
<date month='August' year='2001'/>
<abstract><t>This document describes how the OpenPGP Message Format can be used to provide privacy and authentication using the Multipurpose Internet Mail Extensions (MIME) security content types described in RFC 1847. [STANDARDS-TRACK]</t></abstract>
</front>
<seriesInfo name='RFC' value='3156'/>
<seriesInfo name='DOI' value='10.17487/RFC3156'/>
</reference>



<reference anchor='RFC3394' target='https://www.rfc-editor.org/info/rfc3394'>
<front>
<title>Advanced Encryption Standard (AES) Key Wrap Algorithm</title>
<author fullname='J. Schaad' initials='J.' surname='Schaad'><organization/></author>
<author fullname='R. Housley' initials='R.' surname='Housley'><organization/></author>
<date month='September' year='2002'/>
</front>
<seriesInfo name='RFC' value='3394'/>
<seriesInfo name='DOI' value='10.17487/RFC3394'/>
</reference>



<reference anchor='RFC3629' target='https://www.rfc-editor.org/info/rfc3629'>
<front>
<title>UTF-8, a transformation format of ISO 10646</title>
<author fullname='F. Yergeau' initials='F.' surname='Yergeau'><organization/></author>
<date month='November' year='2003'/>
<abstract><t>ISO/IEC 10646-1 defines a large character set called the Universal Character Set (UCS) which encompasses most of the world's writing systems.  The originally proposed encodings of the UCS, however, were not compatible with many current applications and protocols, and this has led to the development of UTF-8, the object of this memo.  UTF-8 has the characteristic of preserving the full US-ASCII range, providing compatibility with file systems, parsers and other software that rely on US-ASCII values but are transparent to other values.  This memo obsoletes and replaces RFC 2279.</t></abstract>
</front>
<seriesInfo name='STD' value='63'/>
<seriesInfo name='RFC' value='3629'/>
<seriesInfo name='DOI' value='10.17487/RFC3629'/>
</reference>



<reference anchor='RFC3713' target='https://www.rfc-editor.org/info/rfc3713'>
<front>
<title>A Description of the Camellia Encryption Algorithm</title>
<author fullname='M. Matsui' initials='M.' surname='Matsui'><organization/></author>
<author fullname='J. Nakajima' initials='J.' surname='Nakajima'><organization/></author>
<author fullname='S. Moriai' initials='S.' surname='Moriai'><organization/></author>
<date month='April' year='2004'/>
<abstract><t>This document describes the Camellia encryption algorithm.  Camellia is a block cipher with 128-bit block size and 128-, 192-, and 256-bit keys.  The algorithm description is presented together with key scheduling part and data randomizing part.  This memo provides information for the Internet community.</t></abstract>
</front>
<seriesInfo name='RFC' value='3713'/>
<seriesInfo name='DOI' value='10.17487/RFC3713'/>
</reference>



<reference anchor='RFC4086' target='https://www.rfc-editor.org/info/rfc4086'>
<front>
<title>Randomness Requirements for Security</title>
<author fullname='D. Eastlake 3rd' initials='D.' surname='Eastlake 3rd'><organization/></author>
<author fullname='J. Schiller' initials='J.' surname='Schiller'><organization/></author>
<author fullname='S. Crocker' initials='S.' surname='Crocker'><organization/></author>
<date month='June' year='2005'/>
<abstract><t>Security systems are built on strong cryptographic algorithms that foil pattern analysis attempts.  However, the security of these systems is dependent on generating secret quantities for passwords, cryptographic keys, and similar quantities.  The use of pseudo-random processes to generate secret quantities can result in pseudo-security. A sophisticated attacker may find it easier to reproduce the environment that produced the secret quantities and to search the resulting small set of possibilities than to locate the quantities in the whole of the potential number space.</t><t>Choosing random quantities to foil a resourceful and motivated adversary is surprisingly difficult.  This document points out many pitfalls in using poor entropy sources or traditional pseudo-random number generation techniques for generating such quantities.  It recommends the use of truly random hardware techniques and shows that the existing hardware on many systems can be used for this purpose. It provides suggestions to ameliorate the problem when a hardware solution is not available, and it gives examples of how large such quantities need to be for some applications.  This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements.</t></abstract>
</front>
<seriesInfo name='BCP' value='106'/>
<seriesInfo name='RFC' value='4086'/>
<seriesInfo name='DOI' value='10.17487/RFC4086'/>
</reference>



<reference anchor='RFC7253' target='https://www.rfc-editor.org/info/rfc7253'>
<front>
<title>The OCB Authenticated-Encryption Algorithm</title>
<author fullname='T. Krovetz' initials='T.' surname='Krovetz'><organization/></author>
<author fullname='P. Rogaway' initials='P.' surname='Rogaway'><organization/></author>
<date month='May' year='2014'/>
<abstract><t>This document specifies OCB, a shared-key blockcipher-based encryption scheme that provides confidentiality and authenticity for plaintexts and authenticity for associated data.  This document is a product of the Crypto Forum Research Group (CFRG).</t></abstract>
</front>
<seriesInfo name='RFC' value='7253'/>
<seriesInfo name='DOI' value='10.17487/RFC7253'/>
</reference>



<reference anchor='RFC7748' target='https://www.rfc-editor.org/info/rfc7748'>
<front>
<title>Elliptic Curves for Security</title>
<author fullname='A. Langley' initials='A.' surname='Langley'><organization/></author>
<author fullname='M. Hamburg' initials='M.' surname='Hamburg'><organization/></author>
<author fullname='S. Turner' initials='S.' surname='Turner'><organization/></author>
<date month='January' year='2016'/>
<abstract><t>This memo specifies two elliptic curves over prime fields that offer a high level of practical security in cryptographic applications, including Transport Layer Security (TLS).  These curves are intended to operate at the ~128-bit and ~224-bit security level, respectively, and are generated deterministically based on a list of required properties.</t></abstract>
</front>
<seriesInfo name='RFC' value='7748'/>
<seriesInfo name='DOI' value='10.17487/RFC7748'/>
</reference>



<reference anchor='RFC8017' target='https://www.rfc-editor.org/info/rfc8017'>
<front>
<title>PKCS #1: RSA Cryptography Specifications Version 2.2</title>
<author fullname='K. Moriarty' initials='K.' role='editor' surname='Moriarty'><organization/></author>
<author fullname='B. Kaliski' initials='B.' surname='Kaliski'><organization/></author>
<author fullname='J. Jonsson' initials='J.' surname='Jonsson'><organization/></author>
<author fullname='A. Rusch' initials='A.' surname='Rusch'><organization/></author>
<date month='November' year='2016'/>
<abstract><t>This document provides recommendations for the implementation of public-key cryptography based on the RSA algorithm, covering cryptographic primitives, encryption schemes, signature schemes with appendix, and ASN.1 syntax for representing keys and for identifying the schemes.</t><t>This document represents a republication of PKCS #1 v2.2 from RSA Laboratories' Public-Key Cryptography Standards (PKCS) series.  By publishing this RFC, change control is transferred to the IETF.</t><t>This document also obsoletes RFC 3447.</t></abstract>
</front>
<seriesInfo name='RFC' value='8017'/>
<seriesInfo name='DOI' value='10.17487/RFC8017'/>
</reference>



<reference anchor='RFC8032' target='https://www.rfc-editor.org/info/rfc8032'>
<front>
<title>Edwards-Curve Digital Signature Algorithm (EdDSA)</title>
<author fullname='S. Josefsson' initials='S.' surname='Josefsson'><organization/></author>
<author fullname='I. Liusvaara' initials='I.' surname='Liusvaara'><organization/></author>
<date month='January' year='2017'/>
<abstract><t>This document describes elliptic curve signature scheme Edwards-curve Digital Signature Algorithm (EdDSA).  The algorithm is instantiated with recommended parameters for the edwards25519 and edwards448 curves.  An example implementation and test vectors are provided.</t></abstract>
</front>
<seriesInfo name='RFC' value='8032'/>
<seriesInfo name='DOI' value='10.17487/RFC8032'/>
</reference>



<reference anchor='RFC8126' target='https://www.rfc-editor.org/info/rfc8126'>
<front>
<title>Guidelines for Writing an IANA Considerations Section in RFCs</title>
<author fullname='M. Cotton' initials='M.' surname='Cotton'><organization/></author>
<author fullname='B. Leiba' initials='B.' surname='Leiba'><organization/></author>
<author fullname='T. Narten' initials='T.' surname='Narten'><organization/></author>
<date month='June' year='2017'/>
<abstract><t>Many protocols make use of points of extensibility that use constants to identify various protocol parameters.  To ensure that the values in these fields do not have conflicting uses and to promote interoperability, their allocations are often coordinated by a central record keeper.  For IETF protocols, that role is filled by the Internet Assigned Numbers Authority (IANA).</t><t>To make assignments in a given registry prudently, guidance describing the conditions under which new values should be assigned, as well as when and how modifications to existing values can be made, is needed.  This document defines a framework for the documentation of these guidelines by specification authors, in order to assure that the provided guidance for the IANA Considerations is clear and addresses the various issues that are likely in the operation of a registry.</t><t>This is the third edition of this document; it obsoletes RFC 5226.</t></abstract>
</front>
<seriesInfo name='BCP' value='26'/>
<seriesInfo name='RFC' value='8126'/>
<seriesInfo name='DOI' value='10.17487/RFC8126'/>
</reference>



<reference anchor='RFC8174' target='https://www.rfc-editor.org/info/rfc8174'>
<front>
<title>Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words</title>
<author fullname='B. Leiba' initials='B.' surname='Leiba'><organization/></author>
<date month='May' year='2017'/>
<abstract><t>RFC 2119 specifies common key words that may be used in protocol  specifications.  This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the  defined special meanings.</t></abstract>
</front>
<seriesInfo name='BCP' value='14'/>
<seriesInfo name='RFC' value='8174'/>
<seriesInfo name='DOI' value='10.17487/RFC8174'/>
</reference>



<reference anchor='RFC9106' target='https://www.rfc-editor.org/info/rfc9106'>
<front>
<title>Argon2 Memory-Hard Function for Password Hashing and Proof-of-Work Applications</title>
<author fullname='A. Biryukov' initials='A.' surname='Biryukov'><organization/></author>
<author fullname='D. Dinu' initials='D.' surname='Dinu'><organization/></author>
<author fullname='D. Khovratovich' initials='D.' surname='Khovratovich'><organization/></author>
<author fullname='S. Josefsson' initials='S.' surname='Josefsson'><organization/></author>
<date month='September' year='2021'/>
<abstract><t>This document describes the Argon2 memory-hard function for password hashing and proof-of-work applications.  We provide an implementer-oriented description with test vectors.  The purpose is to simplify adoption of Argon2 for Internet protocols.  This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF.</t></abstract>
</front>
<seriesInfo name='RFC' value='9106'/>
<seriesInfo name='DOI' value='10.17487/RFC9106'/>
</reference>


<reference anchor="SCHNEIER" >
  <front>
    <title>Applied Cryptography Second Edition: protocols, algorithms, and source code in C</title>
    <author initials="B." surname="Schneier" fullname="Bruce Schneier">
      <organization></organization>
    </author>
    <date year="1996"/>
  </front>
</reference>
<reference anchor="SP800-38D" >
  <front>
    <title>Recommendation for Block Cipher Modes of Operation: Galois/Counter Mode (GCM) and GMAC</title>
    <author initials="M." surname="Dworkin">
      <organization></organization>
    </author>
    <date year="2007" month="November"/>
  </front>
  <seriesInfo name="NIST Special Publication" value="800-38D"/>
</reference>
<reference anchor="SP800-56A" >
  <front>
    <title>Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography</title>
    <author initials="E." surname="Barker">
      <organization></organization>
    </author>
    <author initials="D." surname="Johnson">
      <organization></organization>
    </author>
    <author initials="M." surname="Smid">
      <organization></organization>
    </author>
    <date year="2007" month="March"/>
  </front>
  <seriesInfo name="NIST Special Publication" value="800-56A Revision 1"/>
</reference>
<reference anchor="TWOFISH" >
  <front>
    <title>The Twofish Encryption Algorithm</title>
    <author initials="B." surname="Schneier">
      <organization></organization>
    </author>
    <author initials="J." surname="Kelsey">
      <organization></organization>
    </author>
    <author initials="D." surname="Whiting">
      <organization></organization>
    </author>
    <author initials="D." surname="Wagner">
      <organization></organization>
    </author>
    <author initials="C." surname="Hall">
      <organization></organization>
    </author>
    <author initials="N." surname="Ferguson">
      <organization></organization>
    </author>
    <date year="1999"/>
  </front>
</reference>


    </references>

    <references title='Informative References'>

<reference anchor="BLEICHENBACHER" >
  <front>
    <title>Generating ElGamal Signatures Without Knowing the Secret Key</title>
    <author initials="D." surname="Bleichenbacher">
      <organization></organization>
    </author>
    <date year="1996"/>
  </front>
  <seriesInfo name="Lecture Notes in Computer Science" value="Volume 1070, pp. 10-18"/>
</reference>
<reference anchor="JKS02" target="http://www.counterpane.com/pgp-attack.html">
  <front>
    <title>Implementation of Chosen-Ciphertext Attacks against PGP and GnuPG</title>
    <author initials="K." surname="Jallad" fullname="Kahil Jallad">
      <organization></organization>
    </author>
    <author initials="J." surname="Katz" fullname="Jonathan Katz">
      <organization></organization>
    </author>
    <author initials="B." surname="Schneier" fullname="Bruce Schneier">
      <organization></organization>
    </author>
    <date year="2002"/>
  </front>
</reference>
<reference anchor="KOBLITZ" >
  <front>
    <title>A course in number theory and cryptography, Chapter VI. Elliptic Curves</title>
    <author initials="N." surname="Koblitz">
      <organization></organization>
    </author>
    <date year="1997"/>
  </front>
  <seriesInfo name="ISBN" value="0-387-96576-9"/>
</reference>
<reference anchor="MZ05" target="http://eprint.iacr.org/2005/033">
  <front>
    <title>An Attack on CFB Mode Encryption As Used By OpenPGP</title>
    <author initials="S." surname="Mister" fullname="Serge Mister">
      <organization></organization>
    </author>
    <author initials="R." surname="Zuccherato" fullname="Robert Zuccherato">
      <organization></organization>
    </author>
    <date year="2005" month="February" day="08"/>
  </front>
  <seriesInfo name="IACR ePrint Archive" value="Report 2005/033"/>
</reference>
<reference anchor="PAX" target="https://pubs.opengroup.org/onlinepubs/9699919799/utilities/pax.html">
  <front>
    <title>IEEE Standard for Information Technology--Portable Operating System Interface (POSIX(R)) Base Specifications, Issue 7: pax - portable archive interchange</title>
    <author >
      <organization>The Open Group</organization>
    </author>
    <date year="2018"/>
  </front>
  <seriesInfo name="IEEE Standard" value="1003.1-2017"/>
  <seriesInfo name="DOI" value="10.1109/IEEESTD.2018.8277153"/>
</reference>
<reference anchor="REGEX" >
  <front>
    <title>Mastering Regular Expressions</title>
    <author initials="J." surname="Friedl" fullname="Jeffrey Friedl">
      <organization>O'Reilly</organization>
    </author>
    <date year="2002" month="August"/>
  </front>
  <seriesInfo name="ISBN" value="0-596-00289-0"/>
</reference>




<reference anchor='RFC1991' target='https://www.rfc-editor.org/info/rfc1991'>
<front>
<title>PGP Message Exchange Formats</title>
<author fullname='D. Atkins' initials='D.' surname='Atkins'><organization/></author>
<author fullname='W. Stallings' initials='W.' surname='Stallings'><organization/></author>
<author fullname='P. Zimmermann' initials='P.' surname='Zimmermann'><organization/></author>
<date month='August' year='1996'/>
<abstract><t>This document describes the format of &quot;PGP files&quot;, i.e., messages that have been encrypted and/or signed with PGP.  This memo provides information for the Internet community.  This memo does not specify an Internet standard of any kind.</t></abstract>
</front>
<seriesInfo name='RFC' value='1991'/>
<seriesInfo name='DOI' value='10.17487/RFC1991'/>
</reference>



<reference anchor='RFC2440' target='https://www.rfc-editor.org/info/rfc2440'>
<front>
<title>OpenPGP Message Format</title>
<author fullname='J. Callas' initials='J.' surname='Callas'><organization/></author>
<author fullname='L. Donnerhacke' initials='L.' surname='Donnerhacke'><organization/></author>
<author fullname='H. Finney' initials='H.' surname='Finney'><organization/></author>
<author fullname='R. Thayer' initials='R.' surname='Thayer'><organization/></author>
<date month='November' year='1998'/>
<abstract><t>This document is maintained in order to publish all necessary information needed to develop interoperable applications based on the OpenPGP format.  [STANDARDS-TRACK]</t></abstract>
</front>
<seriesInfo name='RFC' value='2440'/>
<seriesInfo name='DOI' value='10.17487/RFC2440'/>
</reference>



<reference anchor='RFC4880' target='https://www.rfc-editor.org/info/rfc4880'>
<front>
<title>OpenPGP Message Format</title>
<author fullname='J. Callas' initials='J.' surname='Callas'><organization/></author>
<author fullname='L. Donnerhacke' initials='L.' surname='Donnerhacke'><organization/></author>
<author fullname='H. Finney' initials='H.' surname='Finney'><organization/></author>
<author fullname='D. Shaw' initials='D.' surname='Shaw'><organization/></author>
<author fullname='R. Thayer' initials='R.' surname='Thayer'><organization/></author>
<date month='November' year='2007'/>
<abstract><t>This document is maintained in order to publish all necessary information needed to develop interoperable applications based on the OpenPGP format.  It is not a step-by-step cookbook for writing an application.  It describes only the format and methods needed to read, check, generate, and write conforming packets crossing any network.  It does not deal with storage and implementation questions. It does, however, discuss implementation issues necessary to avoid security flaws.</t><t>OpenPGP software uses a combination of strong public-key and symmetric cryptography to provide security services for electronic communications and data storage.  These services include confidentiality, key management, authentication, and digital signatures.  This document specifies the message formats used in OpenPGP.  [STANDARDS-TRACK]</t></abstract>
</front>
<seriesInfo name='RFC' value='4880'/>
<seriesInfo name='DOI' value='10.17487/RFC4880'/>
</reference>



<reference anchor='RFC5869' target='https://www.rfc-editor.org/info/rfc5869'>
<front>
<title>HMAC-based Extract-and-Expand Key Derivation Function (HKDF)</title>
<author fullname='H. Krawczyk' initials='H.' surname='Krawczyk'><organization/></author>
<author fullname='P. Eronen' initials='P.' surname='Eronen'><organization/></author>
<date month='May' year='2010'/>
<abstract><t>This document specifies a simple Hashed Message Authentication Code (HMAC)-based key derivation function (HKDF), which can be used as a building block in various protocols and applications.  The key derivation function (KDF) is intended to support a wide range of applications and requirements, and is conservative in its use of cryptographic hash functions.  This document is not an Internet  Standards Track specification; it is published for informational  purposes.</t></abstract>
</front>
<seriesInfo name='RFC' value='5869'/>
<seriesInfo name='DOI' value='10.17487/RFC5869'/>
</reference>



<reference anchor='RFC6090' target='https://www.rfc-editor.org/info/rfc6090'>
<front>
<title>Fundamental Elliptic Curve Cryptography Algorithms</title>
<author fullname='D. McGrew' initials='D.' surname='McGrew'><organization/></author>
<author fullname='K. Igoe' initials='K.' surname='Igoe'><organization/></author>
<author fullname='M. Salter' initials='M.' surname='Salter'><organization/></author>
<date month='February' year='2011'/>
<abstract><t>This note describes the fundamental algorithms of Elliptic Curve Cryptography (ECC) as they were defined in some seminal references from 1994 and earlier.  These descriptions may be useful for implementing the fundamental algorithms without using any of the specialized methods that were developed in following years.  Only elliptic curves defined over fields of characteristic greater than three are in scope; these curves are those used in Suite B. This document is not an Internet Standards Track specification; it is published for informational purposes.</t></abstract>
</front>
<seriesInfo name='RFC' value='6090'/>
<seriesInfo name='DOI' value='10.17487/RFC6090'/>
</reference>


<reference anchor="SEC1" >
  <front>
    <title>SEC 1: Elliptic Curve Cryptography</title>
    <author >
      <organization>Standards for Efficient Cryptography Group</organization>
    </author>
    <date year="2000" month="September"/>
  </front>
</reference>
<reference anchor="SHAMBLES" target="https://sha-mbles.github.io/">
  <front>
    <title>Sha-1 is a shambles: First chosen-prefix collision on sha-1 and application to the PGP web of trust</title>
    <author initials="G." surname="Leurent" fullname="Gaëtan Leurent">
      <organization></organization>
    </author>
    <author initials="T." surname="Peyrin" fullname="Thomas Peyrin">
      <organization></organization>
    </author>
    <date year="2020"/>
  </front>
</reference>
<reference anchor="SP800-57" target="http://csrc.nist.gov/publications/nistpubs/800-57/SP800-57-Part{1,2}.pdf">
  <front>
    <title>Recommendation on Key Management</title>
    <author >
      <organization>NIST</organization>
    </author>
    <date year="2007" month="March"/>
  </front>
  <seriesInfo name="NIST Special Publication" value="800-57"/>
</reference>


<reference anchor='CHECKOWAY'>
  <front>
    <title>A Systematic Analysis of the Juniper Dual EC Incident</title>
    <author fullname='Stephen Checkoway' initials='S.' surname='Checkoway'>
      <organization/>
    </author>
    <author fullname='Jacob Maskiewicz' initials='J.' surname='Maskiewicz'>
      <organization/>
    </author>
    <author fullname='Christina Garman' initials='C.' surname='Garman'>
      <organization/>
    </author>
    <author fullname='Joshua Fried' initials='J.' surname='Fried'>
      <organization/>
    </author>
    <author fullname='Shaanan Cohney' initials='S.' surname='Cohney'>
      <organization/>
    </author>
    <author fullname='Matthew Green' initials='M.' surname='Green'>
      <organization/>
    </author>
    <author fullname='Nadia Heninger' initials='N.' surname='Heninger'>
      <organization/>
    </author>
    <author fullname='Ralf-Philipp Weinmann' initials='R.' surname='Weinmann'>
      <organization/>
    </author>
    <author fullname='Eric Rescorla' initials='E.' surname='Rescorla'>
      <organization/>
    </author>
    <author fullname='Hovav Shacham' initials='H.' surname='Shacham'>
      <organization/>
    </author>
    <date month='October' year='2016'/>
  </front>
  <seriesInfo name='Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications' value='Security'/>
  <seriesInfo name='DOI' value='10.1145/2976749.2978395'/>
</reference>




    </references>


<section anchor="test-vectors"><name>Test vectors</name>

<t>To help implementing this specification a non-normative example for the EdDSA algorithm is given.</t>

<section anchor="sample-eddsa-key"><name>Sample EdDSA key</name>

<t>The secret key used for this example is:</t>

<t>D: 1a8b1ff05ded48e18bf50166c664ab023ea70003d78d9e41f5758a91d850f8d2</t>

<t>Note that this is the raw secret key used as input to the EdDSA signing operation.
The key was created on 2014-08-19 14:28:27 and thus the fingerprint of the OpenPGP key is:</t>

<figure><artwork><![CDATA[
   C959 BDBA FA32 A2F8 9A15  3B67 8CFD E121 9796 5A9A
]]></artwork></figure>

<t>The algorithm specific input parameters without the MPI length headers are:</t>

<t>oid: 2b06010401da470f01</t>

<t>q: 403f098994bdd916ed4053197934e4a87c80733a1280d62f8010992e43ee3b2406</t>

<t>The entire public key packet is thus:</t>

<figure><artwork><![CDATA[
   98 33 04 53 f3 5f 0b 16  09 2b 06 01 04 01 da 47
   0f 01 01 07 40 3f 09 89  94 bd d9 16 ed 40 53 19
   79 34 e4 a8 7c 80 73 3a  12 80 d6 2f 80 10 99 2e
   43 ee 3b 24 06
]]></artwork></figure>

</section>
<section anchor="sample-eddsa-signature"><name>Sample EdDSA signature</name>

<t>The signature is created using the sample key over the input data "OpenPGP" on 2015-09-16 12:24:53 and thus the input to the hash function is:</t>

<t>m: 4f70656e504750040016080006050255f95f9504ff0000000c</t>

<t>Using the SHA2-256 hash algorithm yields the digest:</t>

<t>d: f6220a3f757814f4c2176ffbb68b00249cd4ccdc059c4b34ad871f30b1740280</t>

<t>Which is fed into the EdDSA signature function and yields this signature:</t>

<t>r: 56f90cca98e2102637bd983fdb16c131dfd27ed82bf4dde5606e0d756aed3366</t>

<t>s: d09c4fa11527f038e0f57f2201d82f2ea2c9033265fa6ceb489e854bae61b404</t>

<t>The entire signature packet is thus:</t>

<figure><artwork><![CDATA[
   88 5e 04 00 16 08 00 06  05 02 55 f9 5f 95 00 0a
   09 10 8c fd e1 21 97 96  5a 9a f6 22 01 00 56 f9
   0c ca 98 e2 10 26 37 bd  98 3f db 16 c1 31 df d2
   7e d8 2b f4 dd e5 60 6e  0d 75 6a ed 33 66 01 00
   d0 9c 4f a1 15 27 f0 38  e0 f5 7f 22 01 d8 2f 2e
   a2 c9 03 32 65 fa 6c eb  48 9e 85 4b ae 61 b4 04
]]></artwork></figure>

</section>
<section anchor="sample-aead-eax-encryption-and-decryption"><name>Sample AEAD-EAX encryption and decryption</name>

<t>This example encrypts the cleartext string <spanx style="verb">Hello, world!</spanx> with the password <spanx style="verb">password</spanx>, using AES-128 with AEAD-EAX encryption.</t>

<section anchor="sample-parameters"><name>Sample Parameters</name>

<t>S2K:</t>

<figure><artwork><![CDATA[
  Iterated and Salted S2K
]]></artwork></figure>

<t>Iterations:</t>

<figure><artwork><![CDATA[
  65011712 (255), SHA2-256
]]></artwork></figure>

<t>Salt:</t>

<figure><artwork><![CDATA[
  a5 ae 57 9d 1f c5 d8 2b
]]></artwork></figure>

</section>
<section anchor="sample-symmetric-key-encrypted-session-key-packet-v5"><name>Sample symmetric-key encrypted session key packet (v5)</name>

<t>Packet header:</t>

<figure><artwork><![CDATA[
  c3 40
]]></artwork></figure>

<t>Version, algorithms, S2K fields:</t>

<figure><artwork><![CDATA[
  05 1e 07 01 0b 03 08 a5 ae 57 9d 1f c5 d8 2b ff
  69 22
]]></artwork></figure>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  69 22 4f 91 99 93 b3 50 6f a3 b5 9a 6a 73 cf f8
]]></artwork></figure>

<t>Encrypted session key and AEAD tag:</t>

<figure><artwork><![CDATA[
  da 74 6b 88 e3 57 e8 ae 54 eb 87 e1 d7 05 75 d7
  2f 60 23 29 90 52 3e 9a 59 09 49 22 40 6b e1 c3
]]></artwork></figure>

</section>
<section anchor="starting-aead-eax-decryption-of-the-session-key"><name>Starting AEAD-EAX decryption of the session key</name>

<t>The derived key is:</t>

<figure><artwork><![CDATA[
  15 49 67 e5 90 aa 1f 92 3e 1c 0a c6 4c 88 f2 3d
]]></artwork></figure>

<t>HKDF info:</t>

<figure><artwork><![CDATA[
  c3 05 07 01
]]></artwork></figure>

<t>HKDF output:</t>

<figure><artwork><![CDATA[
  74 f0 46 03 63 a7 00 76 db 08 c4 92 ab f2 95 52
]]></artwork></figure>

<t>Authenticated Data:</t>

<figure><artwork><![CDATA[
  c3 05 07 01
]]></artwork></figure>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  69 22 4f 91 99 93 b3 50 6f a3 b5 9a 6a 73 cf f8
]]></artwork></figure>

<t>Decrypted session key:</t>

<figure><artwork><![CDATA[
  38 81 ba fe 98 54 12 45 9b 86 c3 6f 98 cb 9a 5e
]]></artwork></figure>

</section>
<section anchor="sample-v2-seipd-packet"><name>Sample v2 SEIPD packet</name>

<t>Packet header:</t>

<figure><artwork><![CDATA[
  d2 69
]]></artwork></figure>

<t>Version, AES-128, EAX, Chunk size octet:</t>

<figure><artwork><![CDATA[
  02 07 01 06
]]></artwork></figure>

<t>Salt:</t>

<figure><artwork><![CDATA[
  9f f9 0e 3b 32 19 64 f3 a4 29 13 c8 dc c6 61 93
  25 01 52 27 ef b7 ea ea a4 9f 04 c2 e6 74 17 5d
]]></artwork></figure>

<t>Chunk #0 encrypted data:</t>

<figure><artwork><![CDATA[
  4a 3d 22 6e d6 af cb 9c a9 ac 12 2c 14 70 e1 1c
  63 d4 c0 ab 24 1c 6a 93 8a d4 8b f9 9a 5a 99 b9
  0b ba 83 25 de
]]></artwork></figure>

<t>Chunk #0 authentication tag:</t>

<figure><artwork><![CDATA[
  61 04 75 40 25 8a b7 95 9a 95 ad 05 1d da 96 eb
]]></artwork></figure>

<t>Final (zero-sized chunk #1) authentication tag:</t>

<figure><artwork><![CDATA[
  15 43 1d fe f5 f5 e2 25 5c a7 82 61 54 6e 33 9a
]]></artwork></figure>

</section>
<section anchor="decryption-of-data"><name>Decryption of data</name>

<t>Starting AEAD-EAX decryption of data, using the session key.</t>

<t>HKDF info:</t>

<figure><artwork><![CDATA[
  d2 02 07 01 06
]]></artwork></figure>

<t>HKDF output:</t>

<figure><artwork><![CDATA[
  b5 04 22 ac 1c 26 be 9d dd 83 1d 5b bb 36 b6 4f
  78 b8 33 f2 e9 4a 60 c0
]]></artwork></figure>

<t>Message key:</t>

<figure><artwork><![CDATA[
  b5 04 22 ac 1c 26 be 9d dd 83 1d 5b bb 36 b6 4f
]]></artwork></figure>

<t>Initialization vector:</t>

<figure><artwork><![CDATA[
  78 b8 33 f2 e9 4a 60 c0
]]></artwork></figure>

<t>Chunk #0:</t>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  78 b8 33 f2 e9 4a 60 c0 00 00 00 00 00 00 00 00
]]></artwork></figure>

<t>Additional authenticated data:</t>

<figure><artwork><![CDATA[
  d2 02 07 01 06
]]></artwork></figure>

<t>Decrypted chunk #0.</t>

<t>Literal data packet with the string contents <spanx style="verb">Hello, world!</spanx>:</t>

<figure><artwork><![CDATA[
  cb 13 62 00 00 00 00 00 48 65 6c 6c 6f 2c 20 77
  6f 72 6c 64 21
]]></artwork></figure>

<t>Padding packet:</t>

<figure><artwork><![CDATA[
  d5 0e ae 5b f0 cd 67 05 50 03 55 81 6c b0 c8 ff
]]></artwork></figure>

<t>Authenticating final tag:</t>

<t>Final nonce:</t>

<figure><artwork><![CDATA[
  78 b8 33 f2 e9 4a 60 c0 00 00 00 00 00 00 00 01
]]></artwork></figure>

<t>Final additional authenticated data:</t>

<figure><artwork><![CDATA[
  d2 02 07 01 06 00 00 00 00 00 00 00 25
]]></artwork></figure>

</section>
<section anchor="complete-aead-eax-encrypted-packet-sequence"><name>Complete AEAD-EAX encrypted packet sequence</name>

<figure><artwork><![CDATA[
-----BEGIN PGP MESSAGE-----

w0AFHgcBCwMIpa5XnR/F2Cv/aSJPkZmTs1Bvo7WaanPP+Np0a4jjV+iuVOuH4dcF
ddcvYCMpkFI+mlkJSSJAa+HD0mkCBwEGn/kOOzIZZPOkKRPI3MZhkyUBUifvt+rq
pJ8EwuZ0F11KPSJu1q/LnKmsEiwUcOEcY9TAqyQcapOK1Iv5mlqZuQu6gyXeYQR1
QCWKt5Wala0FHdqW6xVDHf719eIlXKeCYVRuM5o=
=wG7F
-----END PGP MESSAGE-----
]]></artwork></figure>

</section>
</section>
<section anchor="sample-aead-ocb-encryption-and-decryption"><name>Sample AEAD-OCB encryption and decryption</name>

<t>This example encrypts the cleartext string <spanx style="verb">Hello, world!</spanx> with the password <spanx style="verb">password</spanx>, using AES-128 with AEAD-OCB encryption.</t>

<section anchor="sample-parameters-1"><name>Sample Parameters</name>

<t>S2K:</t>

<figure><artwork><![CDATA[
  Iterated and Salted S2K
]]></artwork></figure>

<t>Iterations:</t>

<figure><artwork><![CDATA[
  65011712 (255), SHA2-256
]]></artwork></figure>

<t>Salt:</t>

<figure><artwork><![CDATA[
  56 a2 98 d2 f5 e3 64 53
]]></artwork></figure>

</section>
<section anchor="sample-symmetric-key-encrypted-session-key-packet-v5-1"><name>Sample symmetric-key encrypted session key packet (v5)</name>

<t>Packet header:</t>

<figure><artwork><![CDATA[
  c3 3f
]]></artwork></figure>

<t>Version, algorithms, S2K fields:</t>

<figure><artwork><![CDATA[
  05 1d 07 02 0b 03 08 56 a2 98 d2 f5 e3 64 53 ff
  cf cc
]]></artwork></figure>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  cf cc 5c 11 66 4e db 9d b4 25 90 d7 dc 46 b0
]]></artwork></figure>

<t>Encrypted session key and AEAD tag:</t>

<figure><artwork><![CDATA[
  78 c5 c0 41 9c c5 1b 3a 46 87 cb 32 e5 b7 03 1c
  e7 c6 69 75 76 5b 5c 21 d9 2a ef 4c c0 5c 3f ea
]]></artwork></figure>

</section>
<section anchor="starting-aead-eax-decryption-of-the-session-key-1"><name>Starting AEAD-EAX decryption of the session key</name>

<t>The derived key is:</t>

<figure><artwork><![CDATA[
  e8 0d e2 43 a3 62 d9 3b 9d c6 07 ed e9 6a 73 56
]]></artwork></figure>

<t>HKDF info:</t>

<figure><artwork><![CDATA[
  c3 05 07 02
]]></artwork></figure>

<t>HKDF output:</t>

<figure><artwork><![CDATA[
  20 62 fb 76 31 ef be f4 df 81 67 ce d7 f3 a4 64
]]></artwork></figure>

<t>Authenticated Data:</t>

<figure><artwork><![CDATA[
  c3 05 07 02
]]></artwork></figure>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  cf cc 5c 11 66 4e db 9d b4 25 90 d7 dc 46 b0
]]></artwork></figure>

<t>Decrypted session key:</t>

<figure><artwork><![CDATA[
  28 e7 9a b8 23 97 d3 c6 3d e2 4a c2 17 d7 b7 91
]]></artwork></figure>

</section>
<section anchor="sample-v2-seipd-packet-1"><name>Sample v2 SEIPD packet</name>

<t>Packet header:</t>

<figure><artwork><![CDATA[
  d2 69
]]></artwork></figure>

<t>Version, AES-128, EAX, Chunk size octet:</t>

<figure><artwork><![CDATA[
  02 07 02 06
]]></artwork></figure>

<t>Salt:</t>

<figure><artwork><![CDATA[
  20 a6 61 f7 31 fc 9a 30 32 b5 62 33 26 02 7e 3a
  5d 8d b5 74 8e be ff 0b 0c 59 10 d0 9e cd d6 41
]]></artwork></figure>

<t>Chunk #0 encrypted data:</t>

<figure><artwork><![CDATA[
  ff 9f d3 85 62 75 80 35 bc 49 75 4c e1 bf 3f ff
  a7 da d0 a3 b8 10 4f 51 33 cf 42 a4 10 0a 83 ee
  f4 ca 1b 48 01
]]></artwork></figure>

<t>Chunk #0 authentication tag:</t>

<figure><artwork><![CDATA[
  a8 84 6b f4 2b cd a7 c8 ce 9d 65 e2 12 f3 01 cb
]]></artwork></figure>

<t>Final (zero-sized chunk #1) authentication tag:</t>

<figure><artwork><![CDATA[
  cd 98 fd ca de 69 4a 87 7a d4 24 73 23 f6 e8 57
]]></artwork></figure>

</section>
<section anchor="decryption-of-data-1"><name>Decryption of data</name>

<t>Starting AEAD-OCB decryption of data, using the session key.</t>

<t>HKDF info:</t>

<figure><artwork><![CDATA[
  d2 02 07 02 06
]]></artwork></figure>

<t>HKDF output:</t>

<figure><artwork><![CDATA[
  71 66 2a 11 ee 5b 4e 08 14 4e 6d e8 83 a0 09 99
  eb de 12 bb 57 0d cf
]]></artwork></figure>

<t>Message key:</t>

<figure><artwork><![CDATA[
  71 66 2a 11 ee 5b 4e 08 14 4e 6d e8 83 a0 09 99
]]></artwork></figure>

<t>Initialization vector:</t>

<figure><artwork><![CDATA[
  eb de 12 bb 57 0d cf
]]></artwork></figure>

<t>Chunk #0:</t>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  eb de 12 bb 57 0d cf 00 00 00 00 00 00 00 00
]]></artwork></figure>

<t>Additional authenticated data:</t>

<figure><artwork><![CDATA[
  d2 02 07 02 06
]]></artwork></figure>

<t>Decrypted chunk #0.</t>

<t>Literal data packet with the string contents <spanx style="verb">Hello, world!</spanx>:</t>

<figure><artwork><![CDATA[
  cb 13 62 00 00 00 00 00 48 65 6c 6c 6f 2c 20 77
  6f 72 6c 64 21
]]></artwork></figure>

<t>Padding packet:</t>

<figure><artwork><![CDATA[
  d5 0e ae 6a a1 64 9b 56 aa 83 5b 26 13 90 2b d2
]]></artwork></figure>

<t>Authenticating final tag:</t>

<t>Final nonce:</t>

<figure><artwork><![CDATA[
  eb de 12 bb 57 0d cf 00 00 00 00 00 00 00 01
]]></artwork></figure>

<t>Final additional authenticated data:</t>

<figure><artwork><![CDATA[
  d2 02 07 02 06 00 00 00 00 00 00 00 25
]]></artwork></figure>

</section>
<section anchor="complete-aead-eax-encrypted-packet-sequence-1"><name>Complete AEAD-EAX encrypted packet sequence</name>

<figure><artwork><![CDATA[
-----BEGIN PGP MESSAGE-----

wz8FHQcCCwMIVqKY0vXjZFP/z8xcEWZO2520JZDX3EaweMXAQZzFGzpGh8sy5bcD
HOfGaXV2W1wh2SrvTMBcP+rSaQIHAgYgpmH3MfyaMDK1YjMmAn46XY21dI6+/wsM
WRDQns3WQf+f04VidYA1vEl1TOG/P/+n2tCjuBBPUTPPQqQQCoPu9MobSAGohGv0
K82nyM6dZeIS8wHLzZj9yt5pSod61CRzI/boVw==
=K/pk
-----END PGP MESSAGE-----
]]></artwork></figure>

</section>
</section>
<section anchor="sample-aead-gcm-encryption-and-decryption"><name>Sample AEAD-GCM encryption and decryption</name>

<t>This example encrypts the cleartext string <spanx style="verb">Hello, world!</spanx> with the password <spanx style="verb">password</spanx>, using AES-128 with AEAD-GCM encryption.</t>

<section anchor="sample-parameters-2"><name>Sample Parameters</name>

<t>S2K:</t>

<figure><artwork><![CDATA[
  Iterated and Salted S2K
]]></artwork></figure>

<t>Iterations:</t>

<figure><artwork><![CDATA[
  65011712 (255), SHA2-256
]]></artwork></figure>

<t>Salt:</t>

<figure><artwork><![CDATA[
  e9 d3 97 85 b2 07 00 08
]]></artwork></figure>

</section>
<section anchor="sample-symmetric-key-encrypted-session-key-packet-v5-2"><name>Sample symmetric-key encrypted session key packet (v5)</name>

<t>Packet header:</t>

<figure><artwork><![CDATA[
  c3 3c
]]></artwork></figure>

<t>Version, algorithms, S2K fields:</t>

<figure><artwork><![CDATA[
  05 1a 07 03 0b 03 08 e9 d3 97 85 b2 07 00 08 ff
  b4 2e
]]></artwork></figure>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  b4 2e 7c 48 3e f4 88 44 57 cb 37 26
]]></artwork></figure>

<t>Encrypted session key and AEAD tag:</t>

<figure><artwork><![CDATA[
  0c 0c 4b f3 f2 cd 6c b7 b6 e3 8b 5b f3 34 67 c1
  c7 19 44 dd 59 03 46 66 2f 5a de 61 ff 84 bc e0
]]></artwork></figure>

</section>
<section anchor="starting-aead-eax-decryption-of-the-session-key-2"><name>Starting AEAD-EAX decryption of the session key</name>

<t>The derived key is:</t>

<figure><artwork><![CDATA[
  25 02 81 71 5b ba 78 28 ef 71 ef 64 c4 78 47 53
]]></artwork></figure>

<t>HKDF info:</t>

<figure><artwork><![CDATA[
  c3 05 07 03
]]></artwork></figure>

<t>HKDF output:</t>

<figure><artwork><![CDATA[
  de ec e5 81 8b c0 aa b9 0f 8a fb 02 fa 00 cd 13
]]></artwork></figure>

<t>Authenticated Data:</t>

<figure><artwork><![CDATA[
  c3 05 07 03
]]></artwork></figure>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  b4 2e 7c 48 3e f4 88 44 57 cb 37 26
]]></artwork></figure>

<t>Decrypted session key:</t>

<figure><artwork><![CDATA[
  19 36 fc 85 68 98 02 74 bb 90 0d 83 19 36 0c 77
]]></artwork></figure>

</section>
<section anchor="sample-v2-seipd-packet-2"><name>Sample v2 SEIPD packet</name>

<t>Packet header:</t>

<figure><artwork><![CDATA[
  d2 69
]]></artwork></figure>

<t>Version, AES-128, EAX, Chunk size octet:</t>

<figure><artwork><![CDATA[
  02 07 03 06
]]></artwork></figure>

<t>Salt:</t>

<figure><artwork><![CDATA[
  fc b9 44 90 bc b9 8b bd c9 d1 06 c6 09 02 66 94
  0f 72 e8 9e dc 21 b5 59 6b 15 76 b1 01 ed 0f 9f
]]></artwork></figure>

<t>Chunk #0 encrypted data:</t>

<figure><artwork><![CDATA[
  fc 6f c6 d6 5b bf d2 4d cd 07 90 96 6e 6d 1e 85
  a3 00 53 78 4c b1 d8 b6 a0 69 9e f1 21 55 a7 b2
  ad 62 58 53 1b
]]></artwork></figure>

<t>Chunk #0 authentication tag:</t>

<figure><artwork><![CDATA[
  57 65 1f d7 77 79 12 fa 95 e3 5d 9b 40 21 6f 69
]]></artwork></figure>

<t>Final (zero-sized chunk #1) authentication tag:</t>

<figure><artwork><![CDATA[
  a4 c2 48 db 28 ff 43 31 f1 63 29 07 39 9e 6f f9
]]></artwork></figure>

</section>
<section anchor="decryption-of-data-2"><name>Decryption of data</name>

<t>Starting AEAD-GCM decryption of data, using the session key.</t>

<t>HKDF info:</t>

<figure><artwork><![CDATA[
  d2 02 07 03 06
]]></artwork></figure>

<t>HKDF output:</t>

<figure><artwork><![CDATA[
  ea 14 38 80 3c b8 a4 77 40 ce 9b 54 c3 38 77 8d
  4d 2b dc 2b
]]></artwork></figure>

<t>Message key:</t>

<figure><artwork><![CDATA[
  ea 14 38 80 3c b8 a4 77 40 ce 9b 54 c3 38 77 8d
]]></artwork></figure>

<t>Initialization vector:</t>

<figure><artwork><![CDATA[
  4d 2b dc 2b
]]></artwork></figure>

<t>Chunk #0:</t>

<t>Nonce:</t>

<figure><artwork><![CDATA[
  4d 2b dc 2b 00 00 00 00 00 00 00 00
]]></artwork></figure>

<t>Additional authenticated data:</t>

<figure><artwork><![CDATA[
  d2 02 07 03 06
]]></artwork></figure>

<t>Decrypted chunk #0.</t>

<t>Literal data packet with the string contents <spanx style="verb">Hello, world!</spanx>:</t>

<figure><artwork><![CDATA[
  cb 13 62 00 00 00 00 00 48 65 6c 6c 6f 2c 20 77
  6f 72 6c 64 21
]]></artwork></figure>

<t>Padding packet:</t>

<figure><artwork><![CDATA[
  d5 0e 1c e2 26 9a 9e dd ef 81 03 21 72 b7 ed 7c
]]></artwork></figure>

<t>Authenticating final tag:</t>

<t>Final nonce:</t>

<figure><artwork><![CDATA[
  4d 2b dc 2b 00 00 00 00 00 00 00 01
]]></artwork></figure>

<t>Final additional authenticated data:</t>

<figure><artwork><![CDATA[
  d2 02 07 03 06 00 00 00 00 00 00 00 25
]]></artwork></figure>

</section>
<section anchor="complete-aead-eax-encrypted-packet-sequence-2"><name>Complete AEAD-EAX encrypted packet sequence</name>

<figure><artwork><![CDATA[
-----BEGIN PGP MESSAGE-----

wzwFGgcDCwMI6dOXhbIHAAj/tC58SD70iERXyzcmDAxL8/LNbLe244tb8zRnwccZ
RN1ZA0ZmL1reYf+EvODSaQIHAwb8uUSQvLmLvcnRBsYJAmaUD3LontwhtVlrFXax
Ae0Pn/xvxtZbv9JNzQeQlm5tHoWjAFN4TLHYtqBpnvEhVaeyrWJYUxtXZR/Xd3kS
+pXjXZtAIW9ppMJI2yj/QzHxYykHOZ5v+Q==
=ClBe
-----END PGP MESSAGE-----
]]></artwork></figure>

</section>
</section>
<section anchor="sample-message-encrypted-using-argon2"><name>Sample message encrypted using Argon2</name>

<t>These messages are the literal data "Hello, world!" encrypted using Argon2 and the passphrase "password", using different session key sizes.
In all cases, the Argon2 parameters are t = 1, p = 4, and m = 21.</t>

<t>AES-128:</t>

<figure><artwork><![CDATA[
-----BEGIN PGP MESSAGE-----
Comment: Encrypted using AES with 128-bit key
Comment: Session key: 01FE16BBACFD1E7B78EF3B865187374F

wycEBwScUvg8J/leUNU1RA7N/zE2AQQVnlL8rSLPP5VlQsunlO+ECxHSPgGYGKY+
YJz4u6F+DDlDBOr5NRQXt/KJIf4m4mOlKyC/uqLbpnLJZMnTq3o79GxBTdIdOzhH
XfA3pqV4mTzF
=uIks
-----END PGP MESSAGE-----
]]></artwork></figure>

<t>AES-192:</t>

<figure><artwork><![CDATA[
-----BEGIN PGP MESSAGE-----
Comment: Encrypted using AES with 192-bit key
Comment: Session key: 27006DAE68E509022CE45A14E569E91001C2955AF8DFE194

wy8ECAThTKxHFTRZGKli3KNH4UP4AQQVhzLJ2va3FG8/pmpIPd/H/mdoVS5VBLLw
F9I+AdJ1Sw56PRYiKZjCvHg+2bnq02s33AJJoyBexBI4QKATFRkyez2gldJldRys
LVg77Mwwfgl2n/d572WciAM=
=n8Ma
-----END PGP MESSAGE-----
]]></artwork></figure>

<t>AES-256:</t>

<figure><artwork><![CDATA[
-----BEGIN PGP MESSAGE-----
Comment: Encrypted using AES with 256-bit key
Comment: Session key: BBEDA55B9AAE63DAC45D4F49D89DACF4AF37FEFC13BAB2F1F8E18FB74580D8B0

wzcECQS4eJUgIG/3mcaILEJFpmJ8AQQVnZ9l7KtagdClm9UaQ/Z6M/5roklSGpGu
623YmaXezGj80j4B+Ku1sgTdJo87X1Wrup7l0wJypZls21Uwd67m9koF60eefH/K
95D1usliXOEm8ayQJQmZrjf6K6v9PWwqMQ==
=1fB/
-----END PGP MESSAGE-----
]]></artwork></figure>

</section>
</section>
<section anchor="acknowledgements"><name>Acknowledgements</name>

<t>This memo also draws on much previous work from a number of other authors, including: Derek Atkins, Charles Breed, Dave Del Torto, Marc Dyksterhouse, Gail Haspert, Gene Hoffman, Paul Hoffman, Ben Laurie, Raph Levien, Colin Plumb, Will Price, David Shaw, William Stallings, Mark Weaver, and Philip R. Zimmermann.</t>

</section>
<section anchor="document-workflow"><name>Document Workflow</name>

<t>This document is built from markdown using <eref target="https://rubygems.org/gems/kramdown-rfc2629">ruby-kramdown-rfc2629</eref>, and tracked using <eref target="https://git-scm.com/">git</eref>.
The markdown source under development can be found in the file <spanx style="verb">crypto-refresh.md</spanx> in the <spanx style="verb">main</spanx> branch of the <eref target="https://gitlab.com/openpgp-wg/rfc4880bis">git repository</eref>.
Discussion of this document should take place on the <eref target="https://www.ietf.org/mailman/listinfo/openpgp">openpgp@ietf.org mailing list</eref>.</t>

<t>A non-substantive editorial nit can be submitted directly as a <eref target="https://gitlab.com/openpgp-wg/rfc4880bis/-/merge_requests/new">merge request</eref>.
A substantive proposed edit may also be submitted as a merge request, but should simultaneously be sent to the mailing list for discussion.</t>

<t>An open problem can be recorded and tracked as <eref target="https://gitlab.com/openpgp-wg/rfc4880bis/-/issues">an issue</eref> in the gitlab issue tracker, but discussion of the issue should take place on the mailing list.</t>

<t>[Note to RFC-Editor: Please remove this section on publication.]</t>

</section>


  </back>

<!-- ##markdown-source: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-->

</rfc>

