]> BSI

Germany stavros.kousidis@bsi.bund.de

MTG AG

Germany johannes.roth@mtg.de

MTG AG

Germany falko.strenzke@mtg.de

Proton AG

Switzerland aron@wussler.it

sec Network Working Group Internet-Draft This document defines a post-quantum public-key algorithm extension for the OpenPGP protocol. Given the generally assumed threat of a cryptographically relevant quantum computer, this extension provides a basis for long-term secure OpenPGP signatures and ciphertexts. Specifically, it defines composite public-key encryption based on ML-KEM (formerly CRYSTALS-Kyber), composite public-key signatures based on ML-DSA (formerly CRYSTALS-Dilithium), both in combination with elliptic curve cryptography, and SLH-DSA (formerly SPHINCS+) as a standalone public key signature scheme. About This Document Status information for this document may be found at . Discussion of this document takes place on the WG Working Group mailing list (), which is archived at . Subscribe at . Source for this draft and an issue tracker can be found at .

Introduction The OpenPGP protocol supports various traditional public-key algorithms based on the factoring or discrete logarithm problem. As the security of algorithms based on these mathematical problems is endangered by the advent of quantum computers, there is a need to extend OpenPGP by algorithms that remain secure in the presence of quantum computers. Such cryptographic algorithms are referred to as post-quantum cryptography. The algorithms defined in this extension were chosen for standardization by the National Institute of Standards and Technology (NIST) in mid 2022 as the result of the NIST Post-Quantum Cryptography Standardization process initiated in 2016 . Namely, these are ML-KEM (formerly CRYSTALS-Kyber) as a Key Encapsulation Mechanism (KEM), a KEM being a modern building block for public-key encryption, and ML-DSA (formerly CRYSTALS-Dilithium) as well as SLH-DSA (formerly SPHINCS+) as signature schemes. For the two ML-* schemes, this document follows the conservative strategy to deploy post-quantum in combination with traditional schemes such that the security is retained even if all schemes but one in the combination are broken. In contrast, the stateless hash-based signature scheme SLH-DSA is considered to be sufficiently well understood with respect to its security assumptions in order to be used standalone. To this end, this document specifies the following new set: SLH-DSA standalone and the two ML-* as composite with ECC-based KEM and digital signature schemes. Here, the term "composite" indicates that any data structure or algorithm pertaining to the combination of the two components appears as single data structure or algorithm from the protocol perspective. The document specifies the conventions for interoperability between compliant OpenPGP implementations that make use of this extension and the newly defined algorithms or algorithm combinations.

Conventions used in this Document

Terminology for Multi-Algorithm Schemes The terminology in this document is oriented towards the definitions in . Specifically, the terms "multi-algorithm", "composite" and "non-composite" are used in correspondence with the definitions therein. The abbreviation "PQ" is used for post-quantum schemes. To denote the combination of post-quantum and traditional schemes, the abbreviation "PQ/T" is used. The short form "PQ(/T)" stands for PQ or PQ/T.

Post-Quantum Cryptography This section describes the individual post-quantum cryptographic schemes. All schemes listed here are believed to provide security in the presence of a cryptographically relevant quantum computer. However, the mathematical problems on which the two ML-* schemes and SLH-DSA are based, are fundamentally different, and accordingly the level of trust commonly placed in them as well as their performance characteristics vary. [Note to the reader: This specification refers to the NIST PQC draft standards FIPS 203, FIPS 204, and FIPS 205 as if they were a final specification. This is a temporary solution until the final versions of these documents are available. The goal is to provide a sufficiently precise specification of the algorithms already at the draft stage of this specification, so that it is possible for implementers to create interoperable implementations. Furthermore, we want to point out that, depending on possible future changes to the draft standards by NIST, this specification may be updated as soon as corresponding information becomes available.]

ML-KEM ML-KEM is based on the hardness of solving the learning-with-errors problem in module lattices (MLWE). The scheme is believed to provide security against cryptanalytic attacks by classical as well as quantum computers. This specification defines ML-KEM only in composite combination with ECC-based encryption schemes in order to provide a pre-quantum security fallback.

ML-DSA ML-DSA is a signature scheme that, like ML-KEM, is based on the hardness of solving the Learning With Errors problem and a variant of the Short Integer Solution problem in module lattices (MLWE and SelfTargetMSIS). Accordingly, this specification only defines ML-DSA in composite combination with ECC-based signature schemes.

SLH-DSA SLH-DSA is a stateless hash-based signature scheme. Its security relies on the hardness of finding preimages for cryptographic hash functions. This feature is generally considered to be a high security guarantee. Therefore, this specification defines SLH-DSA as a standalone signature scheme. In deployments the performance characteristics of SLH-DSA should be taken into account. We refer to for a discussion of the performance characteristics of this scheme.

Elliptic Curve Cryptography The ECC-based encryption is defined here as a KEM. This is in contrast to where the ECC-based encryption is defined as a public-key encryption scheme. All elliptic curves for the use in the composite combinations are taken from . However, as explained in the following, in the case of Curve25519 encoding changes are applied to the new composite schemes.

Curve25519 and Curve448 Curve25519 and Curve448 are defined in for use in a Diffie-Hellman key agreement scheme and defined in for use in a digital signature scheme. For Curve25519 this specification adapts the encoding of objects as defined in in contrast to .

Generic Prime Curves For interoperability this extension offers CRYSTALS-* in composite combinations with the NIST curves P-256, P-384 defined in and the Brainpool curves brainpoolP256r1, brainpoolP384r1 defined in .

Standalone and Multi-Algorithm Schemes This section provides a categorization of the new algorithms and their combinations.

Standalone and Composite Multi-Algorithm Schemes This specification introduces new cryptographic schemes, which can be categorized as follows:

• PQ/T multi-algorithm public-key encryption, namely a composite combination of ML-KEM with an ECC-based KEM,
• PQ/T multi-algorithm digital signature, namely composite combinations of ML-DSA with ECC-based signature schemes,
• PQ digital signature, namely SLH-DSA as a standalone cryptographic algorithm.

For each of the composite schemes, this specification mandates that the recipient has to successfully perform the cryptographic algorithms for each of the component schemes used in a cryptrographic message, in order for the message to be deciphered and considered as valid. This means that all component signatures must be verified successfully in order to achieve a successful verification of the composite signature. In the case of the composite public-key decryption, each of the component KEM decapsulation operations must succeed.

Non-Composite Algorithm Combinations As the OpenPGP protocol allows for multiple signatures to be applied to a single message, it is also possible to realize non-composite combinations of signatures. Furthermore, multiple OpenPGP signatures may be combined on the application layer. These latter two cases realize non-composite combinations of signatures. specifies how implementations should handle the verification of such combinations of signatures. Furthermore, the OpenPGP protocol also allows for parallel encryption to different keys held by the same recipient. Accordingly, if the sender makes use of this feature and sends an encrypted message with multiple PKESK packages for different encryption keys held by the same recipient, a non-composite multi-algorithm public-key encryption is realized where the recipient has to decrypt only one of the PKESK packages in order to decrypt the message. See for restrictions on parallel encryption mandated by this specification.

Preliminaries This section provides some preliminaries for the definitions in the subsequent sections.

Elliptic curves

SEC1 EC Point Wire Format Elliptic curve points of the generic prime curves are encoded using the SEC1 (uncompressed) format as the following octet string: where X and Y are coordinates of the elliptic curve point P = (X, Y), and each coordinate 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 "Field size" column in , , or . This encoding is compatible with the definition given in .

Measures to Ensure Secure Implementations In the following measures are described that ensure secure implementations according to existing best practices and standards defining the operations of Elliptic Curve Cryptography. 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 MUST NOT appear in any ECC data structure defined in this document. Furthermore, when performing the explicitly listed operations in , or it is REQUIRED to follow the specification and security advisory mandated from the respective elliptic curve specification.

Supported Public Key Algorithms This section specifies the composite ML-KEM + ECC and ML-DSA + ECC schemes as well as the standalone SLH-DSA signature scheme. The composite schemes are fully specified via their algorithm ID. The SLH-DSA signature schemes are fully specified by their algorithm ID and an additional parameter ID.

Algorithm Specifications For encryption, the following composite KEM schemes are specified: KEM algorithm specifications

ID	Algorithm	Requirement	Definition
29	ML-KEM-768 + X25519	MUST
30	ML-KEM-1024 + X448	SHOULD
31	ML-KEM-768 + ECDH-NIST-P-256	MAY
32	ML-KEM-1024 + ECDH-NIST-P-384	MAY
33	ML-KEM-768 + ECDH-brainpoolP256r1	MAY
34	ML-KEM-1024 + ECDH-brainpoolP384r1	MAY

For signatures, the following (composite) signature schemes are specified: Signature algorithm specifications

ID	Algorithm	Requirement	Definition
35	ML-DSA-65 + Ed25519	MUST
36	ML-DSA-87 + Ed448	SHOULD
37	ML-DSA-65 + ECDSA-NIST-P-256	MAY
38	ML-DSA-87 + ECDSA-NIST-P-384	MAY
39	ML-DSA-65 + ECDSA-brainpoolP256r1	MAY
40	ML-DSA-87 + ECDSA-brainpoolP384r1	MAY
41	SLH-DSA-SHA2	SHOULD
42	SLH-DSA-SHAKE	MAY

Parameter Specification

SLH-DSA-SHA2 For the SLH-DSA-SHA2 signature algorithm from , the following parameters are specified: SLH-DSA-SHA2 security parameters

Parameter ID	Parameter
1	SLH-DSA-SHA2-128s
2	SLH-DSA-SHA2-128f
3	SLH-DSA-SHA2-192s
4	SLH-DSA-SHA2-192f
5	SLH-DSA-SHA2-256s
6	SLH-DSA-SHA2-256f

All security parameters inherit the requirement of SLH-DSA-SHA2 from . That is, implementations SHOULD implement the parameters specified in . The values 0x00 and 0xFF are reserved for future extensions.

SLH-DSA-SHAKE For the SLH-DSA-SHAKE signature algorithm from , the following parameters are specified: SLH-DSA-SHAKE security parameters

Parameter ID	Parameter
1	SLH-DSA-SHAKE-128s
2	SLH-DSA-SHAKE-128f
3	SLH-DSA-SHAKE-192s
4	SLH-DSA-SHAKE-192f
5	SLH-DSA-SHAKE-256s
6	SLH-DSA-SHAKE-256f

All security parameters inherit the requirement of SLH-DSA-SHAKE from . That is, implementations MAY implement the parameters specified in . The values 0x00 and 0xFF are reserved for future extensions.

Algorithm Combinations

Composite KEMs The ML-KEM + ECC public-key encryption involves both the ML-KEM and an ECC-based KEM in an a priori non-separable manner. This is achieved via KEM combination, i.e. both key encapsulations/decapsulations are performed in parallel, and the resulting key shares are fed into a key combiner to produce a single shared secret for message encryption.

Parallel Public-Key Encryption As explained in , the OpenPGP protocol inherently supports parallel encryption to different keys of the same recipient. Implementations MUST NOT encrypt a message with a purely traditional public-key encryption key of a recipient if it is encrypted with a PQ/T key of the same recipient.

Composite Signatures The ML-DSA + ECC signature consists of independent ML-DSA and ECC signatures, and an implementation MUST successfully validate both signatures to state that the ML-DSA + ECC signature is valid.

Multiple Signatures The OpenPGP message format allows multiple signatures of a message, i.e. the attachment of multiple signature packets. An implementation MAY sign a message with a traditional key and a PQ(/T) key from the same sender. This ensures backwards compatibility due to Section 5.2.5, since a legacy implementation without PQ(/T) support can fall back on the traditional signature. Newer implementations with PQ(/T) support MAY ignore the traditional signature(s) during validation. Implementations SHOULD consider the message correctly signed if at least one of the non-ignored signatures validates successfully. [Note to the reader: The last requirement, that one valid signature is sufficient to identify a message as correctly signed, is an interpretation of Section 5.2.5.]

Composite KEM schemes

Building Blocks

ECC-Based KEMs In this section we define the encryption, decryption, and data formats for the ECDH component of the composite algorithms. , , and describe the ECC-KEM parameters and artifact lengths. The artefacts in follow the encodings described in . Montgomery curves parameters and artifact lengths

	X25519	X448
Algorithm ID reference	29	30
Field size	32 octets	56 octets
ECC-KEM	x25519Kem ()	x448Kem ()
ECDH public key	32 octets	56 octets
ECDH secret key	32 octets	56 octets
ECDH ephemeral	32 octets	56 octets
ECDH share	32 octets	56 octets
Key share	32 octets	64 octets
Hash	SHA3-256	SHA3-512

NIST curves parameters and artifact lengths

	NIST P-256	NIST P-384
Algorithm ID reference	31	32
Field size	32 octets	48 octets
ECC-KEM	ecdhKem ()	ecdhKem ()
ECDH public key	65 octets of SEC1-encoded public point	97 octets of SEC1-encoded public point
ECDH secret key	32 octets big-endian encoded secret scalar	48 octets big-endian encoded secret scalar
ECDH ephemeral	65 octets of SEC1-encoded ephemeral point	97 octets of SEC1-encoded ephemeral point
ECDH share	65 octets of SEC1-encoded shared point	97 octets of SEC1-encoded shared point
Key share	32 octets	64 octets
Hash	SHA3-256	SHA3-512

Brainpool curves parameters and artifact lengths

	brainpoolP256r1	brainpoolP384r1
Algorithm ID reference	33	34
Field size	32 octets	48 octets
ECC-KEM	ecdhKem ()	ecdhKem ()
ECDH public key	65 octets of SEC1-encoded public point	97 octets of SEC1-encoded public point
ECDH secret key	32 octets big-endian encoded secret scalar	48 octets big-endian encoded secret scalar
ECDH ephemeral	65 octets of SEC1-encoded ephemeral point	97 octets of SEC1-encoded ephemeral point
ECDH share	65 octets of SEC1-encoded shared point	97 octets of SEC1-encoded shared point
Key share	32 octets	64 octets
Hash	SHA3-256	SHA3-512

The SEC1 format for point encoding is defined in . The various procedures to perform the operations of an ECC-based KEM are defined in the following subsections. Specifically, each of these subsections defines the instances of the following operations: and To instantiate ECC-KEM, one must select a parameter set from , , or .

X25519-KEM The encapsulation and decapsulation operations of x25519kem are described using the function X25519() and encodings defined in . The eccSecretKey is denoted as r, the eccPublicKey as R, they are subject to the equation R = X25519(r, U(P)). Here, U(P) denotes the u-coordinate of the base point of Curve25519. The operation x25519Kem.Encaps() is defined as follows:

1. Generate an ephemeral key pair {v, V} via V = X25519(v,U(P)) where v is a random scalar
2. Compute the shared coordinate X = X25519(v, R) where R is the public key eccPublicKey
3. Set the output eccCipherText to V
4. Set the output eccKeyShare to SHA3-256(X || eccCipherText || eccPublicKey)

The operation x25519Kem.Decaps() is defined as follows:

1. Compute the shared coordinate X = X25519(r, V), where r is the eccSecretKey and V is the eccCipherText
2. Set the output eccKeyShare to SHA3-256(X || eccCipherText || eccPublicKey)

X448-KEM The encapsulation and decapsulation operations of x448kem are described using the function X448() and encodings defined in . The eccSecretKey is denoted as r, the eccPublicKey as R, they are subject to the equation R = X25519(r, U(P)). Here, U(P) denotes the u-coordinate of the base point of Curve448. The operation x448.Encaps() is defined as follows:

1. Generate an ephemeral key pair {v, V} via V = X448(v,U(P)) where v is a random scalar
2. Compute the shared coordinate X = X448(v, R) where R is the public key eccPublicKey
3. Set the output eccCipherText to V
4. Set the output eccKeyShare to SHA3-512(X || eccCipherText || eccPublicKey)

The operation x448Kem.Decaps() is defined as follows:

1. Compute the shared coordinate X = X448(r, V), where r is the eccSecretKey and V is the eccCipherText
2. Set the output eccKeyShare to SHA3-512(X || eccCipherText || eccPublicKey)

ECDH-KEM The operation ecdhKem.Encaps() is defined as follows:

1. Generate an ephemeral key pair {v, V=vG} as defined in or where v is a random scalar
2. Compute the shared point S = vR, where R is the component public key eccPublicKey, according to or
3. Extract the X coordinate from the SEC1 encoded point S = 04 || X || Y as defined in section
4. Set the output eccCipherText to the SEC1 encoding of V
5. Set the output eccKeyShare to Hash(X || eccCipherText || eccPublicKey), with Hash chosen according to or

The operation ecdhKem.Decaps() is defined as follows:

1. Compute the shared Point S as rV, where r is the eccSecretKey and V is the eccCipherText, according to or
2. Extract the X coordinate from the SEC1 encoded point S = 04 || X || Y as defined in section
3. Set the output eccKeyShare to Hash(X || eccCipherText || eccPublicKey), with Hash chosen according to or

ML-KEM ML-KEM features the following operations: and The above are the operations ML-KEM.Encaps and ML-KEM.Decaps defined in . Note that mlkemPublicKey is the encapsulation and mlkemSecretKey is the decapsulation key. ML-KEM has the parameterization with the corresponding artifact lengths in octets as given in . All artifacts are encoded as defined in . ML-KEM parameters artifact lengths in octets

Algorithm ID reference	ML-KEM	Public key	Secret key	Ciphertext	Key share
29, 31, 33	ML-KEM-768	1184	2400	1088	32
30, 32, 34	ML-KEM-1024	1568	3168	1568	32

To instantiate ML-KEM, one must select a parameter set from the column "ML-KEM" of . The procedure to perform ML-KEM.Encaps() is as follows:

1. Extract the encapsulation key mlkemPublicKey that is part of the recipient's composite public key
2. Invoke (mlkemCipherText, mlkemKeyShare) <- ML-KEM.Encaps(mlkemPublicKey)
3. Set mlkemCipherText as the ML-KEM ciphertext
4. Set mlkemKeyShare as the ML-KEM symmetric key share

The procedure to perform ML-KEM.Decaps() is as follows:

1. Invoke mlkemKeyShare <- ML-KEM.Decaps(mlkemCipherText, mlkemSecretKey)
2. Set mlkemKeyShare as the ML-KEM symmetric key share

Composite Encryption Schemes with ML-KEM specifies the following ML-KEM + ECC composite public-key encryption schemes: ML-KEM + ECC composite schemes

Algorithm ID reference	ML-KEM	ECC-KEM	ECC-KEM curve
29	ML-KEM-768	x25519Kem	Curve25519
30	ML-KEM-1024	x448Kem	Curve448
31	ML-KEM-768	ecdhKem	NIST P-256
32	ML-KEM-1024	ecdhKem	NIST P-384
33	ML-KEM-768	ecdhKem	brainpoolP256r1
34	ML-KEM-1024	ecdhKem	brainpoolP384r1

The ML-KEM + ECC composite public-key encryption schemes are built according to the following principal design:

• The ML-KEM encapsulation algorithm is invoked to create a ML-KEM ciphertext together with a ML-KEM symmetric key share.
• The encapsulation algorithm of an ECC-based KEM, namely one out of X25519-KEM, X448-KEM, or ECDH-KEM is invoked to create an ECC ciphertext together with an ECC symmetric key share.
• A Key-Encryption-Key (KEK) is computed as the output of a key combiner that receives as input both of the above created symmetric key shares and the protocol binding information.
• The session key for content encryption is then wrapped as described in using AES-256 as algorithm and the KEK as key.
• The PKESK package's algorithm-specific parts are made up of the ML-KEM ciphertext, the ECC ciphertext, and the wrapped session key.

Fixed information For the composite KEM schemes defined in the following procedure, justified in , MUST be used to derive a string to use as binding between the KEK and the communication parties.

Key combiner For the composite KEM schemes defined in the following procedure MUST be used to compute the KEK that wraps a session key. The construction is a one-step key derivation function compliant to Section 4, based on KMAC256 . It is given by the following algorithm. Note that the values eccKeyShare defined in and mlkemKeyShare defined in already use the relative ciphertext in the derivation. The ciphertext is by design included again in the key combiner to provide a robust security proof. The value of domSeparation is the UTF-8 encoding of the string "OpenPGPCompositeKeyDerivationFunction" and MUST be the following octet sequence: The value of counter MUST be set to the following octet sequence: The value of fixedInfo MUST be set according to . The value of customizationString is the UTF-8 encoding of the string "KDF" and MUST be set to the following octet sequence:

Key generation procedure The implementation MUST independently generate the ML-KEM and the ECC component keys. ML-KEM key generation follows the specification and the artifacts are encoded as fixed-length octet strings as defined in . For ECC this is done following the relative specification in , , or , and encoding the outputs as fixed-length octet strings in the format specified in , , or .

Encryption procedure The procedure to perform public-key encryption with a ML-KEM + ECC composite scheme is as follows:

1. Take the recipient's authenticated public-key packet pkComposite and sessionKey as input
2. Parse the algorithm ID from pkComposite
3. Extract the eccPublicKey and mlkemPublicKey component from the algorithm specific data encoded in pkComposite with the format specified in .
4. Instantiate the ECC-KEM and the ML-KEM depending on the algorithm ID according to
5. Compute (eccCipherText, eccKeyShare) := ECC-KEM.Encaps(eccPublicKey)
6. Compute (mlkemCipherText, mlkemKeyShare) := ML-KEM.Encaps(mlkemPublicKey)
7. Compute fixedInfo as specified in
8. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText, mlkemKeyShare, mlkemCipherText, fixedInfo, oBits=256) as defined in
9. Compute C := AESKeyWrap(KEK, sessionKey) with AES-256 as per that includes a 64 bit integrity check
10. Output eccCipherText || mlkemCipherText || len(C) || C

Decryption procedure The procedure to perform public-key decryption with a ML-KEM + ECC composite scheme is as follows:

1. Take the matching PKESK and own secret key packet as input
2. From the PKESK extract the algorithm ID and the encryptedKey
3. Check that the own and the extracted algorithm ID match
4. Parse the eccSecretKey and mlkemSecretKey from the algorithm specific data of the own secret key encoded in the format specified in
5. Instantiate the ECC-KEM and the ML-KEM depending on the algorithm ID according to
6. Parse eccCipherText, mlkemCipherText, and C from encryptedKey encoded as eccCipherText || mlkemCipherText || len(C) || C as specified in
7. Compute (eccKeyShare) := ECC-KEM.Decaps(eccCipherText, eccSecretKey)
8. Compute (mlkemKeyShare) := ML-KEM.Decaps(mlkemCipherText, mlkemSecretKey)
9. Compute fixedInfo as specified in
10. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText, mlkemKeyShare, mlkemCipherText, fixedInfo, oBits=256) as defined in
11. Compute sessionKey := AESKeyUnwrap(KEK, C) with AES-256 as per , aborting if the 64 bit integrity check fails
12. Output sessionKey

Packet specifications

Public-Key Encrypted Session Key Packets (Tag 1) The algorithm-specific fields consists of:

• A fixed-length octet string representing an ECC ephemeral public key in the format associated with the curve as specified in .
• A fixed-length octet string of the ML-KEM ciphertext, whose length depends on the algorithm ID as specified in .
• The one-octet algorithm identifier, if it is passed (in the case of a v3 PKESK packet).
• A variable-length field containing the wrapped session key:
  • A one-octet size of the following field;
  • The wrapped session key represented as an octet string, i.e., the output of the encryption procedure described in .

Note that unlike most public-key algorithms, in the case of a v3 PKESK packet, the symmetric algorithm identifier is not encrypted. Instead, it is prepended to the encrypted session key in plaintext. In this case, the symmetric algorithm used MUST be AES-128, AES-192 or AES-256 (algorithm ID 7, 8 or 9).

Key Material Packets The algorithm-specific public key is this series of values:

• A fixed-length octet string representing an EC point public key, in the point format associated with the curve specified in .
• A fixed-length octet string containing the ML-KEM public key, whose length depends on the algorithm ID as specified in .

The algorithm-specific secret key is these two values:

• A fixed-length octet string of the encoded secret scalar, whose encoding and length depend on the algorithm ID as specified in .
• A fixed-length octet string containing the ML-KEM secret key, whose length depends on the algorithm ID as specified in .

Composite Signature Schemes

Building blocks

EdDSA-Based signatures To sign and verify with EdDSA the following operations are defined: and The public and secret key, as well as the signature MUST be encoded according to as fixed-length octet strings. The following table describes the EdDSA parameters and artifact lengths: EdDSA parameters and artifact lengths in octets

Algorithm ID reference	Curve	Field size	Public key	Secret key	Signature
35	Ed25519	32	32	32	64
36	Ed448	57	57	57	114

ECDSA-Based signatures To sign and verify with ECDSA the following operations are defined: and The public keys MUST be encoded in SEC1 format as defined in section . The secret key, as well as both values R and S of the signature MUST each be encoded as a big-endian integer in a fixed-length octet string of the specified size. The following table describes the ECDSA parameters and artifact lengths: ECDSA parameters and artifact lengths in octets

Algorithm ID reference	Curve	Field size	Public key	Secret key	Signature value R	Signature value S
37	NIST P-256	32	65	32	32	32
38	NIST P-384	48	97	48	48	48
39	brainpoolP256r1	32	65	32	32	32
40	brainpoolP384r1	48	97	48	48	48

ML-DSA signatures For ML-DSA signature generation the default hedged version of ML-DSA.Sign given in is used. That is, to sign with ML-DSA the following operation is defined: For ML-DSA signature verification the algorithm ML-DSA.Verify given in is used. That is, to verify with ML-DSA the following operation is defined: ML-DSA has the parameterization with the corresponding artifact lengths in octets as given in . All artifacts are encoded as defined in . ML-DSA parameters and artifact lengths in octets

Algorithm ID reference	ML-DSA	Public key	Secret key	Signature value
35, 37, 39	ML-DSA-65	1952	4000	3293
36, 38, 40	ML-DSA-87	2592	4864	4595

Composite Signature Schemes with ML-DSA

Signature data digest Signature data (i.e. the data to be signed) is digested prior to signing operations, see Section 5.2.4. Composite ML-DSA + ECC signatures MUST use the associated hash algorithm as specified in for the signature data digest. Signatures using other hash algorithms MUST be considered invalid. An implementation supporting a specific ML-DSA + ECC algorithm MUST also support the matching hash algorithm. Binding between ML-DSA and signature data digest

Algorithm ID reference	Hash function	Hash function ID reference
35, 37, 39	SHA3-256	12
36, 38, 40	SHA3-512	14

Key generation procedure The implementation MUST independently generate the ML-DSA and the ECC component keys. ML-DSA key generation follows the specification and the artifacts are encoded as fixed-length octet strings as defined in . For ECC this is done following the relative specification in , , or , and encoding the artifacts as specified in or as fixed-length octet strings.

Signature Generation To sign a message M with ML-DSA + EdDSA the following sequence of operations has to be performed:

1. Generate dataDigest according to Section 5.2.4
2. Create the EdDSA signature over dataDigest with EdDSA.Sign() from
3. Create the ML-DSA signature over dataDigest with ML-DSA.Sign() from
4. Encode the EdDSA and ML-DSA signatures according to the packet structure given in .

To sign a message M with ML-DSA + ECDSA the following sequence of operations has to be performed:

1. Generate dataDigest according to Section 5.2.4
2. Create the ECDSA signature over dataDigest with ECDSA.Sign() from
3. Create the ML-DSA signature over dataDigest with ML-DSA.Sign() from
4. Encode the ECDSA and ML-DSA signatures according to the packet structure given in .

Signature Verification To verify a ML-DSA + EdDSA signature the following sequence of operations has to be performed:

1. Verify the EdDSA signature with EdDSA.Verify() from
2. Verify the ML-DSA signature with ML-DSA.Verify() from

To verify a ML-DSA + ECDSA signature the following sequence of operations has to be performed:

1. Verify the ECDSA signature with ECDSA.Verify() from
2. Verify the ML-DSA signature with ML-DSA.Verify() from

As specified in an implementation MUST validate both signatures, i.e. EdDSA/ECDSA and ML-DSA, to state that a composite ML-DSA + ECC signature is valid.

Packet Specifications

Signature Packet (Tag 2) The composite ML-DSA + ECC schemes MUST be used only with v6 signatures, as defined in . The algorithm-specific v6 signature parameters for ML-DSA + EdDSA signatures consists of:

• A fixed-length octet string representing the EdDSA signature, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string of the ML-DSA signature value, whose length depends on the algorithm ID as specified in .

The algorithm-specific v6 signature parameters for ML-DSA + ECDSA signatures consists of:

• A fixed-length octet string of the big-endian encoded ECDSA value R, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string of the big-endian encoded ECDSA value S, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string of the ML-DSA signature value, whose length depends on the algorithm ID as specified in .

Key Material Packets The composite ML-DSA + ECC schemes MUST be used only with v6 keys, as defined in . The algorithm-specific public key for ML-DSA + EdDSA keys is this series of values:

• A fixed-length octet string representing the EdDSA public key, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string containing the ML-DSA public key, whose length depends on the algorithm ID as specified in .

The algorithm-specific secret key for ML-DSA + EdDSA keys is this series of values:

• A fixed-length octet string representing the EdDSA secret key, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string containing the ML-DSA secret key, whose length depends on the algorithm ID as specified in .

The algorithm-specific public key for ML-DSA + ECDSA keys is this series of values:

• A fixed-length octet string representing the ECDSA public key in SEC1 format, as specified in section and with length specified in .
• A fixed-length octet string containing the ML-DSA public key, whose length depends on the algorithm ID as specified in .

The algorithm-specific secret key for ML-DSA + ECDSA keys is this series of values:

• A fixed-length octet string representing the ECDSA secret key as a big-endian encoded integer, whose length depends on the algorithm used as specified in .
• A fixed-length octet string containing the ML-DSA secret key, whose length depends on the algorithm ID as specified in .

SLH-DSA

The SLH-DSA Algorithms The following table describes the SLH-DSA parameters and artifact lengths: SLH-DSA parameters and artifact lengths in octets. The values equally apply to the parameter IDs of SLH-DSA-SHA2 and SLH-DSA-SHAKE.

Parameter ID reference	Parameter name suffix	SLH-DSA public key	SLH-DSA secret key	SLH-DSA signature
1	128s	32	64	7856
2	128f	32	64	17088
3	192s	48	96	16224
4	192f	48	96	35664
5	256s	64	128	29792
6	256f	64	128	49856

Signature Data Digest Signature data (i.e. the data to be signed) is digested prior to signing operations, see Section 5.2.4. SLH-DSA signatures MUST use the associated hash algorithm as specified in for the signature data digest. Signatures using other hash algorithms MUST be considered invalid. An implementation supporting a specific SLH-DSA algorithm and parameter MUST also support the matching hash algorithm. Binding between SLH-DSA and signature data digest

Algorithm ID reference	Parameter ID reference	Hash function	Hash function ID reference
41	1, 2	SHA-256	8
41	3, 4, 5, 6	SHA-512	10
42	1, 2	SHA3-256	12
42	3, 4, 5, 6	SHA3-512	14

Key generation SLH-DSA key generation is performed via the algorithm SLH-DSA.KeyGen as specified in , and the artifacts are encoded as fixed-length octet strings as defined in .

Signature Generation SLH-DSA signature generation is performed via the algorithm SLH-DSA.Sign as specified in . The variable opt_rand is set to PK.seed. See also . An implementation MUST set the Parameter ID in the signature equal to the issuing secret key Parameter ID.

Signature Verification SLH-DSA signature verification is performed via the algorithm SLH-DSA.Verify as specified in . An implementation MUST check that the Parameter ID in the signature and in the key match when verifying.

Packet specifications

Signature Packet (Tag 2) The SLH-DSA scheme MUST be used only with v6 signatures, as defined in Section 5.2.3. The algorithm-specific v6 Signature parameters consists of:

• A one-octet value specifying the SLH-DSA parameter ID defined in and . The values 0x00 and 0xFF are reserved for future extensions.
• A fixed-length octet string of the SLH-DSA signature value, whose length depends on the parameter ID in the format specified in .

Key Material Packets The SLH-DSA scheme MUST be used only with v6 keys, as defined in . The algorithm-specific public key is this series of values:

• A one-octet value specifying the SLH-DSA parameter ID defined in and . The values 0x00 and 0xFF are reserved for future extensions.
• A fixed-length octet string containing the SLH-DSA public key, whose length depends on the parameter ID as specified in .

The algorithm-specific secret key is this value:

• A fixed-length octet string containing the SLH-DSA secret key, whose length depends on the parameter ID as specified in .

Migration Considerations The post-quantum KEM algorithms defined in and the signature algorithms defined in are a set of new public key algorithms that extend the algorithm selection of . During the transition period, the post-quantum algorithms will not be supported by all clients. Therefore various migration considerations must be taken into account, in particular backwards compatibility to existing implementations that have not yet been updated to support the post-quantum algorithms.

Key preference Implementations SHOULD prefer PQ(/T) keys when multiple options are available. For instance, if encrypting for a recipient for which both a valid PQ/T and a valid ECC certificate are available, the implementation SHOULD choose the PQ/T certificate. In case a certificate has both a PQ/T and an ECC encryption-capable valid subkey, the PQ/T subkey SHOULD be preferred. An implementation MAY sign with both a PQ(/T) and an ECC key using multiple signatures over the same data as described in . Signing only with PQ(/T) key material is not backwards compatible. Note that the confidentiality of a message is not post-quantum secure when encrypting to multiple recipients if at least one recipient does not support PQ/T encryption schemes. An implementation SHOULD NOT abort the encryption process in this case to allow for a smooth transition to post-quantum cryptography.

Key generation strategies It is REQUIRED to generate fresh secrets when generating PQ(/T) keys. Reusing key material from existing ECC keys in PQ(/T) keys does not provide backwards compatibility, and the fingerprint will differ. An OpenPGP (v6) certificate is composed of a certification-capable primary key and one or more subkeys for signature, encryption, and authentication. Two migration strategies are recommended:

1. Generate two independent certificates, one for PQ(/T)-capable implementations, and one for legacy implementations. Implementations not understanding PQ(/T) certificates can use the legacy certificate, while PQ(/T)-capable implementations will prefer the newer certificate. This allows having an older v4 or v6 ECC certificate for compatibility and a v6 PQ(/T) certificate, at a greater complexity in key distribution.
2. Attach PQ(/T) encryption and signature subkeys to an existing v6 ECC certificate. Implementations understanding PQ(/T) will be able to parse and use the subkeys, while PQ(/T)-incapable implementations can gracefully ignore them. This simplifies key distribution, as only one certificate needs to be communicated and verified, but leaves the primary key vulnerable to quantum computer attacks.

Security Considerations

Hashing in ECC-KEM Our construction of the ECC-KEMs, in particular the inclusion of eccCipherText in the final hashing step in encapsulation and decapsulation that produces the eccKeyShare, is standard and known as hashed ElGamal key encapsulation, a hashed variant of ElGamal encryption. It ensures IND-CCA2 security in the random oracle model under some Diffie-Hellman intractability assumptions . The additional inclusion of eccPublicKey follows the security advice in Section 6.1 of .

Key combiner For the key combination in this specification limits itself to the use of KMAC. The sponge construction used by KMAC was proven to be indifferentiable from a random oracle . This means, that in contrast to SHA2, which uses a Merkle-Damgard construction, no HMAC-based construction is required for key combination. Except for a domain separation it is sufficient to simply process the concatenation of any number of key shares when using a sponge-based construction like KMAC. The construction using KMAC ensures a standardized domain separation. In this case, the processed message is then the concatenation of any number of key shares. More precisely, for a given capacity c the indifferentiability proof shows that assuming there are no weaknesses found in the Keccak permutation, an attacker has to make an expected number of 2^(c/2) calls to the permutation to tell KMAC from a random oracle. For a random oracle, a difference in only a single bit gives an unrelated, uniformly random output. Hence, to be able to distinguish a key K, derived from shared keys K1 and K2 (and ciphertexts C1 and C2) as from a random bit string, an adversary has to know (or correctly guess) both key shares K1 and K2, entirely. The proposed construction in preserves IND-CCA2 of any of its ingredient KEMs, i.e. the newly formed combined KEM is IND-CCA2 secure as long as at least one of the ingredient KEMs is. Indeed, the above stated indifferentiability from a random oracle qualifies Keccak as a split-key pseudorandom function as defined in . That is, Keccak behaves like a random function if at least one input shared secret is picked uniformly at random. Our construction can thus be seen as an instantiation of the IND-CCA2 preserving Example 3 in Figure 1 of , up to some reordering of input shared secrets and ciphertexts. In the random oracle setting, the reordering does not influence the arguments in .

Domain separation and binding The domSeparation information defined in provides the domain separation for the key combiner construction. This ensures that the input keying material is used to generate a KEK for a specific purpose or context. The fixedInfo defined in binds the derived KEK to the chosen algorithm and communication parties. The algorithm ID identifies univocally the algorithm, the parameters for its instantiation, and the length of all artifacts, including the derived key. This is in line with the Recommendation for ECC in section 5.5 of . Other fields included in the recommendation are not relevant for the OpenPGP protocol, since the sender is not required to have a key of their own, there are no pre-shared secrets, and all the other parameters are univocally defined by the algorithm ID. Furthermore, we do not require the recipients public key into the key combiner as the public key material is already included in the component key derivation functions. Given two KEMs which we assume to be multi-user secure, we combine their outputs using a KEM-combiner: Our aim is to preserve multi-user security. A common approach to this is to add the public key into the key derivation for K. However, it turns out that this is not necessary here. To break security of the combined scheme in the multi-user setting, the adversary has to distinguish a set of challenge keys K_u = H(K1_u, C1_u, K2_u, C2*_u) for users u in some set from random, also given ciphertexts C*_u = (C1*_u, C2*_u). For each of these K* it holds that if the adversary never makes a query they have a zero advantage over guessing. The only multi-user advantage that the adversary could gain therefore consists of queries to H that are meaningful for two different users u1 != u2 and their associated public keys. This is only the case if as the ciphertext values decide for which challenge the query is meaningful. This means that a ciphertext collision is needed between challenges. Assuming that the randomness used in the generation of the two challenges is uncorrelated, this is negligible. In consequence, the ciphertexts already work sufficiently well as domain-separator.

SLH-DSA Message Randomizer The specification of SLH-DSA prescribes an optional non-deterministic message randomizer. This is not used in this specification, as OpenPGP v6 signatures already provide a salted signature data digest of the appropriate size.

Binding hashes in signatures with signature algorithms In order not to extend the attack surface, we bind the hash algorithm used for signature data digestion to the hash algorithm used internally by the signature algorithm. ML-DSA internally uses a SHAKE256 digest, therefore we require SHA3 in the ML-DSA + ECC signature packet, see . Note that we bind a NIST security category 2 hash function to a signature algorithm that falls into NIST security category 3. This does not constitute a security bottleneck: because of the unpredictable random salt that is prepended to the digested data in v6 signatures, the hardness assumption is not collision resistance but second-preimage resistance. In the case of SLH-DSA the internal hash algorithm varies based on the algorithm and parameter ID, see .

Additional considerations

Performance Considerations for SLH-DSA This specification introduces both ML-DSA + ECC as well as SLH-DSA as PQ(/T) signature schemes. Generally, it can be said that ML-DSA + ECC provides a performance in terms of execution time requirements that is close to that of traditional ECC signature schemes. Regarding the size of signatures and public keys, though, ML-DSA has far greater requirements than traditional schemes like EC-based or even RSA signature schemes. Implementers may want to offer SLH-DSA for applications where a higher degree of trust in the signature scheme is required. However, SLH-DSA has performance characteristics in terms of execution time of the signature generation as well as space requirements for the signature that are even greater than those of ML-DSA + ECC signature schemes. Pertaining to the execution time, the particularly costly operation in SLH-DSA is the signature generation. In order to achieve short signature generation times, one of the parameter sets with the name ending in the letter "f" for "fast" should be chosen. This comes at the expense of a larger signature size. In order to minimize the space requirements of a SLH-DSA signature, a parameter set ending in "s" for "small" should be chosen. This comes at the expense of a longer signature generation time.

IANA Considerations IANA will add the following registries to the Pretty Good Privacy (PGP) registry group at https://www.iana.org/assignments/pgp-parameters:

• Registry name: SLH-DSA-SHA2 parameters Registration procedure: SPECIFICATION REQUIRED Values defined in this document, .
• Registry name: SLH-DSA-SHAKE parameters Registration procedure: SPECIFICATION REQUIRED Values defined in this document, .

Furthermore IANA will add the algorithm IDs defined in and to the registry Public Key Algorithms.

Changelog

draft-wussler-openpgp-pqc-01

• Shifted the algorithm IDs by 4 to align with the crypto-refresh.
• Renamed v5 packets into v6 to align with the crypto-refresh.
• Defined IND-CCA2 security for KDF and key combination.
• Added explicit key generation procedures.
• Changed the key combination KMAC salt.
• Mandated Parameter ID check in SPHINCS+ signature verification.
• Fixed key share size for Kyber-768.
• Added "Preliminaries" section.
• Fixed IANA considerations.

draft-wussler-openpgp-pqc-02

• Added the ephemeral and public key in the ECC key derivation function.
• Removed public key hash from key combiner.
• Allowed v3 PKESKs and v4 keys with PQ algorithms, limiting them to AES symmetric ciphers. for encryption with SEIPDv1, in line with the crypto-refresh.

draft-wussler-openpgp-pqc-03

• Replaced round 3 submission with NIST PQC Draft Standards FIPS 203, 204, 205.
• Added consideration about security level for hashes.

Contributors Stephan Ehlen (BSI)
Carl-Daniel Hailfinger (BSI)
Andreas Huelsing (TU Eindhoven)
Johannes Roth (MTG AG)

References Normative References 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. 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. 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). 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. This is the third edition of this document; it obsoletes RFC 5226. Aiven Proton AG Sequoia-PGP FSIJ 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. 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. This document obsoletes: RFC 4880 (OpenPGP), RFC 5581 (Camellia in OpenPGP) and RFC 6637 (Elliptic Curves in OpenPGP). Informative References This memo proposes several elliptic curve domain parameters over finite prime fields for use in cryptographic applications. The domain parameters are consistent with the relevant international standards, and can be used in X.509 certificates and certificate revocation lists (CRLs), for Internet Key Exchange (IKE), Transport Layer Security (TLS), XML signatures, and all applications or protocols based on the cryptographic message syntax (CMS). This document is not an Internet Standards Track specification; it is published for informational purposes. Standards for Efficient Cryptography Group National Institute of Standards and Technology National Institute of Standards and Technology National Institute of Standards and Technology

Acknowledgments Thanks to Daniel Huigens and Evangelos Karatsiolis for the early review and feedback on this document.