Internet-Draft PQC in OpenPGP February 2025
Kousidis, et al. Expires 10 August 2025 [Page]
Workgroup:
Network Working Group
Internet-Draft:
draft-ietf-openpgp-pqc-07
Published:
Intended Status:
Informational
Expires:
Authors:
S. Kousidis
BSI
J. Roth
MTG AG
F. Strenzke
MTG AG
A. Wussler
Proton AG

Post-Quantum Cryptography in OpenPGP

Abstract

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

This note is to be removed before publishing as an RFC.

Status information for this document may be found at https://datatracker.ietf.org/doc/draft-ietf-openpgp-pqc/.

Discussion of this document takes place on the WG Working Group mailing list (mailto:openpgp@ietf.org), which is archived at https://mailarchive.ietf.org/arch/browse/openpgp/. Subscribe at https://www.ietf.org/mailman/listinfo/openpgp/.

Source for this draft and an issue tracker can be found at https://github.com/openpgp-pqc/draft-openpgp-pqc.

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.

Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."

This Internet-Draft will expire on 10 August 2025.

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Table of Contents

1. 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 [NISTIR-8413] as the result of the NIST Post-Quantum Cryptography Standardization process initiated in 2016 [NIST-PQC]. Namely, these are ML-KEM [FIPS-203] as a Key Encapsulation Mechanism (KEM), a KEM being a modern building block for public-key encryption, and ML-DSA [FIPS-204] as well as SLH-DSA [FIPS-205] 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.

1.1. Conventions used in this Document

1.1.1. Terminology for Multi-Algorithm Schemes

The terminology in this document is oriented towards the definitions in [I-D.ietf-pquip-pqt-hybrid-terminology]. 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.

1.2. 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.]

1.2.1. ML-KEM

ML-KEM [FIPS-203] 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 ECDH encryption schemes in order to provide a pre-quantum security fallback.

1.2.2. ML-DSA

ML-DSA [FIPS-204] 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 EdDSA signature schemes.

1.2.3. SLH-DSA

SLH-DSA [FIPS-205] 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 Section 10.1 for a discussion of the performance characteristics of this scheme.

1.3. Elliptic Curve Cryptography

The ECDH encryption is defined here as a KEM via X25519 and X448 which are defined in [RFC7748]. EdDSA as defined in [RFC8032] is used as the elliptic curve-based digital signature scheme.

1.4. Standalone and Multi-Algorithm Schemes

This section provides a categorization of the new algorithms and their combinations.

1.4.1. 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 ECDH KEM,

  • PQ/T multi-algorithm digital signature, namely composite combinations of ML-DSA with EdDSA signature schemes,

  • PQ digital signature, namely SLH-DSA as a standalone cryptographic algorithm.

For each of the composite schemes, this specification mandates that the consuming party has to successfully perform the cryptographic algorithms for each of the component schemes used in a cryptographic 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.

1.4.2. Non-Composite Algorithm Combinations

As the OpenPGP protocol [RFC9580] 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. Section 3.3 specifies how implementations should handle the verification of such combinations of signatures.

Furthermore, the OpenPGP protocol also allows parallel encryption to different keys by using multiple PKESK packets, thus realizing non-composite multi-algorithm public-key encryption.

2. Supported Public Key Algorithms

This section specifies the composite ML-KEM + ECDH and ML-DSA + EdDSA schemes as well as the standalone SLH-DSA signature scheme. All of these schemes are fully specified via their algorithm ID, i.e., they are not parametrized.

2.1. Algorithm Specifications

For encryption, the following composite KEM schemes are specified:

Table 1: KEM algorithm specifications
ID Algorithm Requirement Definition
TBD (105 for testing) ML-KEM-768+X25519 MUST Section 4.2
TBD (106 for testing) ML-KEM-1024+X448 SHOULD Section 4.2

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

Table 2: Signature algorithm specifications
ID Algorithm Requirement Definition
30 ML-DSA-65+Ed25519 MUST Section 5.2
31 ML-DSA-87+Ed448 SHOULD Section 5.2
32 SLH-DSA-SHAKE-128s MAY Section 6.1
33 SLH-DSA-SHAKE-128f MAY Section 6.1
34 SLH-DSA-SHAKE-256s MAY Section 6.1

2.1.1. Experimental Codepoints for Interop Testing

[ Note: this section to be removed before publication ]

The use of private/experimental codepoints during development are intended to be used in non-released software only, for experimentation and interop testing purposes only. An OpenPGP implementation MUST NOT produce a formal release using these experimental codepoints. This draft will not be sent to IANA without every listed algorithm having a non-experimental codepoint.

3. Algorithm Combinations

3.1. Composite KEMs

The ML-KEM + ECDH public-key encryption involves both the ML-KEM and an ECDH 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.

As explained in Section 1.4.2, the OpenPGP protocol inherently supports parallel encryption to different keys. Note that the confidentiality of a message is not post-quantum secure when encrypting to different keys if at least one key does not support PQ/T encryption schemes. In Section 8.1 it is explained how to deal with multiple key scenarios.

3.2. Composite Signatures

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

3.3. 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 [RFC9580, 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 [RFC9580, Section 5.2.5].]

3.4. ECC requirements

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 Section 4.1.1.1 or Section 4.1.1.2 it is REQUIRED to follow the specification and security advisory mandated from the respective elliptic curve specification.

4. Composite KEM schemes

4.1. Building Blocks

4.1.1. ECDH KEMs

In this section we define the encryption, decryption, and data formats for the ECDH component of the composite algorithms.

Table 3 describes the ECDH-KEM parameters and artifact lengths. The artifacts in Table 3 follow the encodings described in [RFC7748].

Table 3: Montgomery curves parameters and artifact lengths
  X25519 X448
Algorithm ID reference TBD (105 for testing) TBD (106 for testing)
Field size 32 octets 56 octets
ECDH-KEM x25519Kem (Section 4.1.1.1) x448Kem (Section 4.1.1.2)
ECDH public key 32 octets [RFC7748] 56 octets [RFC7748]
ECDH secret key 32 octets [RFC7748] 56 octets [RFC7748]
ECDH ephemeral 32 octets [RFC7748] 56 octets [RFC7748]
ECDH key share 32 octets [RFC7748] 56 octets [RFC7748]

The various procedures to perform the operations of an ECDH KEM are defined in the following subsections. Specifically, each of these subsections defines the instances of the following operations:

(ecdhCipherText, ecdhKeyShare) <- ECDH-KEM.Encaps(ecdhPublicKey)

and

(ecdhKeyShare) <- ECDH-KEM.Decaps(ecdhSecretKey, ecdhCipherText, ecdhPublicKey)

To instantiate ECDH-KEM, one must select a parameter set from Table 3.

4.1.1.1. X25519-KEM

The encapsulation and decapsulation operations of x25519kem are described using the function X25519() and encodings defined in [RFC7748]. The ecdhSecretKey is denoted as r, the ecdhPublicKey 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 randomly generated octet string with a length of 32 octets

  2. Compute the shared coordinate X = X25519(v, R) where R is the recipient's public key ecdhPublicKey

  3. Set the output ecdhCipherText to V

  4. Set the output ecdhKeyShare to X

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

  1. Compute the shared coordinate X = X25519(r, V), where r is the ecdhSecretKey and V is the ecdhCipherText

  2. Set the output ecdhKeyShare to X

4.1.1.2. X448-KEM

The encapsulation and decapsulation operations of x448kem are described using the function X448() and encodings defined in [RFC7748]. The ecdhSecretKey is denoted as r, the ecdhPublicKey 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 randomly generated octet string with a length of 56 octets

  2. Compute the shared coordinate X = X448(v, R) where R is the recipient's public key ecdhPublicKey

  3. Set the output ecdhCipherText to V

  4. Set the output ecdhKeyShare to X

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

  1. Compute the shared coordinate X = X448(r, V), where r is the ecdhSecretKey and V is the ecdhCipherText

  2. Set the output ecdhKeyShare to X

4.1.2. ML-KEM

ML-KEM features the following operations:

(mlkemCipherText, mlkemKeyShare) <- ML-KEM.Encaps(mlkemPublicKey)

and

(mlkemKeyShare) <- ML-KEM.Decaps(mlkemCipherText, mlkemSecretKey)

The above are the operations ML-KEM.Encaps and ML-KEM.Decaps defined in [FIPS-203]. Note that mlkemPublicKey is the encapsulation and mlkemSecretKey is the decapsulation key.

ML-KEM has the parametrization with the corresponding artifact lengths in octets as given in Table 4. All artifacts are encoded as defined in [FIPS-203].

Table 4: ML-KEM parameters artifact lengths in octets
Algorithm ID reference ML-KEM Public key Secret key Ciphertext Key share
TBD (105 for testing) ML-KEM-768 1184 64 1088 32
TBD (106 for testing) ML-KEM-1024 1568 64 1568 32

To instantiate ML-KEM, one must select a parameter set from the column "ML-KEM" of Table 4.

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

  1. Invoke (mlkemCipherText, mlkemKeyShare) <- ML-KEM.Encaps(mlkemPublicKey), where mlkemPublicKey is the recipient's public key

  2. Set mlkemCipherText as the ML-KEM ciphertext

  3. 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

4.2. Composite Encryption Schemes with ML-KEM

Table 1 specifies the following ML-KEM + ECDH composite public-key encryption schemes:

Table 5: ML-KEM + ECDH composite schemes
Algorithm ID reference ML-KEM ECDH-KEM
TBD (105 for testing) ML-KEM-768 x25519Kem
TBD (106 for testing) ML-KEM-1024 x448Kem

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

  • The ML-KEM encapsulation algorithm is invoked to create an ML-KEM ciphertext together with an ML-KEM symmetric key share.

  • The encapsulation algorithm of an ECDH KEM, namely X25519-KEM or X448-KEM, is invoked to create an ECDH ciphertext together with an ECDH 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 [RFC3394] using AES-256 as algorithm and the KEK as key.

  • The PKESK packet's algorithm-specific parts are made up of the ML-KEM ciphertext, the ECDH ciphertext, and the wrapped session key.

4.2.1. Key combiner

For the composite KEM schemes defined in Table 1 the following procedure MUST be used to compute the KEK that wraps a session key. The construction is a key derivation function compliant to [SP800-56C], Section 4, based on SHA3-256. It is given by the following algorithm, which computes the key encryption key KEK that is used to wrap, i.e., encrypt, the session key.

//   multiKeyCombine(mlkemKeyShare, mlkemCipherText, mlkemPublicKey,
//                   ecdhKeyShare, ecdhCipherText, ecdhPublicKey, algId)
//
//   Input:
//   mlkemKeyShare   - the ML-KEM key share encoded as an octet string
//   mlkemCipherText - the ML-KEM ciphertext encoded as an octet string
//   mlkemPublicKey  - the ML-KEM public key of the recipient as an octet string
//   ecdhKeyShare    - the ECDH key share encoded as an octet string
//   ecdhCipherText  - the ECDH ciphertext encoded as an octet string
//   ecdhPublicKey   - the ECDH public key of the recipient as an octet string
//   algId           - the OpenPGP algorithm ID of the public-key encryption algorithm

KEK = SHA3-256( mlkemKeyShare || ecdhKeyShare || ecdhCipherText || ecdhPublicKey
                || mlkemCipherText || mlkemPublicKey || algId || domSep )
return KEK

The value domSep is a constant set to the UTF-8 encoding of the string "OpenPGPCompositeKDFv1", i.e.

domSep := 4F 70 65 6E 50 47 50 43 6F 6D 70 6F 73 69 74 65 4B 44 46 76 31

Note that this is in line with [I-D.ietf-lamps-pq-composite-kem] up to mlkemCipherText || mlkemPublicKey || algId || domSep being the OpenPGP-specific context information.

4.2.2. Key generation procedure

The implementation MUST generate the ML-KEM and the ECDH component keys independently. ML-KEM key generation follows the specification [FIPS-203] and the artifacts are encoded as fixed-length octet strings as defined in Section 4.1.2. For ECDH this is done following the relative specification in [RFC7748], and encoding the outputs as fixed-length octet strings in the format specified in Table 3.

4.2.3. Encryption procedure

The procedure to perform public-key encryption with an ML-KEM + ECDH 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 and set it as algId

  3. Extract the ecdhPublicKey and mlkemPublicKey component from the algorithm specific data encoded in pkComposite with the format specified in Section 4.3.2.

  4. Instantiate the ECDH-KEM and the ML-KEM depending on the algorithm ID according to Table 5

  5. Compute (ecdhCipherText, ecdhKeyShare) := ECDH-KEM.Encaps(ecdhPublicKey)

  6. Compute (mlkemCipherText, mlkemKeyShare) := ML-KEM.Encaps(mlkemPublicKey)

  7. Compute KEK := multiKeyCombine(mlkemKeyShare, mlkemCipherText, mlkemPublicKey, ecdhKeyShare, ecdhCipherText, ecdhPublicKey, algId, 256) as defined in Section 4.2.1

  8. Compute C := AESKeyWrap(KEK, sessionKey) with AES-256 as per [RFC3394] that includes a 64 bit integrity check

  9. Output the algorithm specific part of the PKESK as ecdhCipherText || mlkemCipherText || len(C, symAlgId) (|| symAlgId) || C, where both symAlgId and len(C, symAlgId) are single octet fields, symAlgId denotes the symmetric algorithm ID used and is present only for a v3 PKESK, and len(C, symAlgId) denotes the combined octet length of the fields specified as the arguments.

4.2.4. Decryption procedure

The procedure to perform public-key decryption with an ML-KEM + ECDH 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 as algId and the wrapped session key as encryptedKey

  3. Check that the own and the extracted algorithm ID match

  4. Parse the ecdhSecretKey and mlkemSecretKey from the algorithm specific data of the own secret key encoded in the format specified in Section 4.3.2

  5. Instantiate the ECDH-KEM and the ML-KEM depending on the algorithm ID according to Table 5

  6. Parse ecdhCipherText, mlkemCipherText, and C from encryptedKey encoded as ecdhCipherText || mlkemCipherText || len(C,symAlgId) (|| symAlgId) || C as specified in Section 4.3.1, where symAlgId is present only in the case of a v3 PKESK.

  7. Compute (ecdhKeyShare) := ECDH-KEM.Decaps(ecdhCipherText, ecdhSecretKey, ecdhPublicKey)

  8. Compute (mlkemKeyShare) := ML-KEM.Decaps(mlkemCipherText, mlkemSecretKey)

  9. Compute KEK := multiKeyCombine(mlkemKeyShare, mlkemCipherText, mlkemPublicKey, ecdhKeyShare, ecdhCipherText, ecdhPublicKey, algId) as defined in Section 4.2.1

  10. Compute sessionKey := AESKeyUnwrap(KEK, C) with AES-256 as per [RFC3394], aborting if the 64 bit integrity check fails

  11. Output sessionKey

4.3. Packet specifications

4.3.1. Public-Key Encrypted Session Key Packets (Tag 1)

The algorithm-specific fields consists of the output of the encryption procedure described in Section 4.2.3:

  • A fixed-length octet string representing an ECDH ephemeral public key in the format associated with the curve as specified in Section 4.1.1.

  • A fixed-length octet string of the ML-KEM ciphertext, whose length depends on the algorithm ID as specified in Table 4.

  • A one-octet size of the following fields.

  • Only in the case of a v3 PKESK packet: a one-octet symmetric algorithm identifier.

  • The wrapped session key represented as an octet string.

Note that like in the case of the algorithms X25519 and X448 specified in [RFC9580], for the ML-KEM composite schemes, in the case of a v3 PKESK packet, the symmetric algorithm identifier is not encrypted. Instead, it is placed in plaintext after the mlkemCipherText and before the length octet preceding the wrapped session key. In the case of v3 PKESK packets for ML-KEM composite schemes, the symmetric algorithm used MUST be AES-128, AES-192 or AES-256 (algorithm ID 7, 8 or 9).

In the case of a v3 PKESK, a receiving implementation MUST check if the length of the unwrapped symmetric key matches the symmetric algorithm identifier, and abort if this is not the case.

Implementations MUST NOT use the obsolete Symmetrically Encrypted Data packet (tag 9) to encrypt data protected with the algorithms described in this document.

4.3.2. Key Material Packets

The composite ML-KEM + ECDH schemes MUST be used only with v6 keys, as defined in [RFC9580], or newer versions defined by updates of that document.

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 Section 4.1.1.

  • A fixed-length octet string containing the ML-KEM public key, whose length depends on the algorithm ID as specified in Table 4.

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 Section 4.1.1.

  • A fixed-length octet string containing the ML-KEM secret key in seed format, whose length is 64 octets (compare Table 4). The seed format is defined in accordance with [FIPS-203], Section 3.3. Namely, the secret key is given by the concatenation of the values of d and z, generated in steps 1 and 2 of ML-KEM.KeyGen [FIPS-203], each of a length of 32 octets. Upon parsing the private key format, or before using the secret key, for the expansion of the key, the function ML-KEM.KeyGen_internal [FIPS-203] has to be invoked with the parsed values of d and z as input.

5. Composite Signature Schemes

5.1. Building blocks

5.1.1. EdDSA-Based signatures

Throughout this specification EdDSA refers to the PureEdDSA variant defined in [RFC8032].

To sign and verify with EdDSA the following operations are defined:

(eddsaSignature) <- EdDSA.Sign(eddsaSecretKey, dataDigest)

and

(verified) <- EdDSA.Verify(eddsaPublicKey, eddsaSignature, dataDigest)

The public and secret key, as well as the signature MUST be encoded according to [RFC8032] as fixed-length octet strings. The following table describes the EdDSA parameters and artifact lengths:

Table 6: EdDSA parameters and artifact lengths in octets
Algorithm ID reference Curve Field size Public key Secret key Signature
30 Ed25519 32 32 32 64
31 Ed448 57 57 57 114

5.1.2. ML-DSA signatures

Throughout this specification ML-DSA refers to the default pure and hedged version of ML-DSA, i.e., in contrast to the pre-hash or deterministic variant, defined in [FIPS-204].

For ML-DSA signature generation the default hedged version of ML-DSA.Sign given in [FIPS-204] is used. That is, to sign with ML-DSA the following operation is defined:

(mldsaSignature) <- ML-DSA.Sign(mldsaSecretKey, dataDigest)

For ML-DSA signature verification the algorithm ML-DSA.Verify given in [FIPS-204] is used. That is, to verify with ML-DSA the following operation is defined:

(verified) <- ML-DSA.Verify(mldsaPublicKey, dataDigest, mldsaSignature)

ML-DSA has the parametrization with the corresponding artifact lengths in octets as given in Table 7. All artifacts are encoded as defined in [FIPS-204].

Table 7: ML-DSA parameters and artifact lengths in octets
Algorithm ID reference ML-DSA Public key Secret key Signature value
30 ML-DSA-65 1952 32 3309
31 ML-DSA-87 2592 32 4627

5.2. Composite Signature Schemes with ML-DSA

5.2.1. Signature data digest

Signature data (i.e. the data to be signed) is digested prior to signing operations, see [RFC9580, Section 5.2.4]. Composite ML-DSA + EdDSA signatures MUST use the associated hash algorithm as specified in Table 8 for the signature data digest. Signatures using other hash algorithms MUST be considered invalid.

An implementation supporting a specific ML-DSA + EdDSA algorithm MUST also support the matching hash algorithm.

Table 8: Binding between ML-DSA + EdDSA and signature data digest
Algorithm ID reference Hash function Hash function ID reference
30 SHA3-256 12
31 SHA3-512 14

5.2.2. Key generation procedure

The implementation MUST generate the ML-DSA and the EdDSA component keys independently. ML-DSA key generation follows the specification [FIPS-204] and the artifacts are encoded as fixed-length octet strings as defined in Section 5.1.2. For EdDSA this is done following the relative specification in [RFC7748], and encoding the artifacts as specified in Section 5.1.1 as fixed-length octet strings.

5.2.3. 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 [RFC9580, Section 5.2.4]

  2. Create the EdDSA signature over dataDigest with EdDSA.Sign() from Section 5.1.1

  3. Create the ML-DSA signature over dataDigest with ML-DSA.Sign() from Section 5.1.2

  4. Encode the EdDSA and ML-DSA signatures according to the packet structure given in Section 5.3.1.

5.2.4. Signature Verification

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

  1. Verify the EdDSA signature with EdDSA.Verify() from Section 5.1.1

  2. Verify the ML-DSA signature with ML-DSA.Verify() from Section 5.1.2

As specified in Section 3.2 an implementation MUST validate both signatures, i.e. EdDSA and ML-DSA, successfully to state that a composite ML-DSA + EdDSA signature is valid.

5.3. Packet Specifications

5.3.1. Signature Packet (Tag 2)

The composite ML-DSA + EdDSA schemes MUST be used only with v6 signatures, as defined in [RFC9580], or newer versions defined by updates of that document.

The algorithm-specific v6 signature parameters for ML-DSA + EdDSA signatures consist of:

  • A fixed-length octet string representing the EdDSA signature, whose length depends on the algorithm ID as specified in Table 6.

  • A fixed-length octet string of the ML-DSA signature value, whose length depends on the algorithm ID as specified in Table 7.

5.3.2. Key Material Packets

The composite ML-DSA + EdDSA schemes MUST be used only with v6 keys, as defined in [RFC9580], or newer versions defined by updates of that document.

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 Table 6.

  • A fixed-length octet string containing the ML-DSA public key, whose length depends on the algorithm ID as specified in Table 7.

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 Table 6.

  • A fixed-length octet string containing the ML-DSA secret key in seed format, whose length is 32 octets (compare Table 7). The seed format is defined in accordance with [FIPS-204], Section 3.6.3. Namely, the secret key is given by the value xi generated in step 1 of ML-DSA.KeyGen [FIPS-204]. Upon parsing the private key format, or before using the secret key, for the expansion of the key, the function ML-DSA.KeyGen_internal [FIPS-204] has to be invoked with the parsed value of xi as input.

6. SLH-DSA

Throughout this specification SLH-DSA refers to the default pure and hedged version of SLH-DSA defined in [FIPS-205].

6.1. The SLH-DSA Algorithms

The following table lists the group of algorithm code points for the SLH-DSA signature scheme and the corresponding artifact lengths. This group of algorithms is henceforth referred to as "SLH-DSA code points".

Table 9: SLH-DSA algorithm code points and the corresponding artifact lengths in octets.
Algorithm ID reference SLH-DSA public key SLH-DSA secret key SLH-DSA signature
32 32 64 7856
33 32 64 17088
34 64 128 29792

6.1.1. Signature Data Digest

Signature data (i.e. the data to be signed) is digested prior to signing operations, see [RFC9580, Section 5.2.4]. SLH-DSA signatures MUST use the associated hash algorithm as specified in Table 10 for the signature data digest. Signatures using other hash algorithms MUST be considered invalid.

An implementation supporting a specific SLH-DSA algorithm code point MUST also support the matching hash algorithm.

Table 10: Binding between SLH-DSA algorithm code points and signature data hash algorithms
Algorithm ID reference Hash function Hash function ID reference
32 SHA3-256 12
33 SHA3-256 12
34 SHA3-512 14

6.1.2. Key generation

SLH-DSA key generation is performed via the algorithm SLH-DSA.KeyGen as specified in [FIPS-205], and the artifacts are encoded as fixed-length octet strings as defined in Section 6.1.

6.1.3. Signature Generation

SLH-DSA signature generation is performed via the algorithm SLH-DSA.Sign as specified in [FIPS-205].

6.1.4. Signature Verification

SLH-DSA signature verification is performed via the algorithm SLH-DSA.Verify as specified in [FIPS-205].

6.2. Packet specifications

6.2.1. Signature Packet (Tag 2)

The SLH-DSA algorithms MUST be used only with v6 signatures, as defined in [RFC9580, Section 5.2.3].

The algorithm-specific part of a signature packet for an SLH-DSA algorithm code point consists of:

  • A fixed-length octet string of the SLH-DSA signature value, whose length depends on the algorithm ID in the format specified in Table 9.

6.2.2. Key Material Packets

The SLH-DSA algorithms code points MUST be used only with v6 keys, as defined in [RFC9580], or newer versions defined by updates of that document.

The algorithm-specific part of the public key consists of:

  • A fixed-length octet string containing the SLH-DSA public key, whose length depends on the algorithm ID as specified in Table 9.

The algorithm-specific part of the secret key consists of:

  • A fixed-length octet string containing the SLH-DSA secret key, whose length depends on the algorithm ID as specified in Table 9.

7. Notes on Algorithms

7.1. Symmetric Algorithms for SEIPD Packets

Implementations MUST implement AES-256. An implementation SHOULD use AES-256 in the case of a v1 SEIPD packet, or AES-256 with any available AEAD mode in the case of a v2 SEIPD packet, if all recipient certificates indicate support for it (explicitly or implicitly).

A certificate that contains a PQ(/T) key SHOULD include AES-256 in the "Preferred Symmetric Ciphers for v1 SEIPD" subpacket and SHOULD include the pair AES-256 with OCB in the "Preferred AEAD Ciphersuites" subpacket.

If AES-256 is not explicitly in the list of the "Preferred Symmetric Ciphers for v1 SEIPD" subpacket, and if the certificate contains a PQ/T key, it is implicitly at the end of the list. This is justified since AES-256 is mandatory to implement. If AES-128 is also implicitly added to the list, it is added after AES-256.

If the pair AES-256 with OCB is not explicitly in the list of the "Preferred AEAD Ciphersuites" subpacket, and if the certificate contains a PQ/T key, it is implicitly at the end of the list. This is justified since AES-256 and OCB are mandatory to implement. If the pair AES-128 with OCB is also implicitly added to the list, it is added after the pair AES-256 with OCB.

7.2. Hash Algorithms for Key Binding Signatures

Subkey binding signatures over algorithms described in this document and primary key binding signatures made by algorithms described in this document MUST NOT be made with MD5, SHA-1, or RIPEMD-160. A receiving implementation MUST treat such a signature as invalid.

8. Migration Considerations

The post-quantum KEM algorithms defined in Table 1 and the signature algorithms defined in Table 2 are a set of new public key algorithms that extend the algorithm selection of [RFC9580]. 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.

8.1. Key preference

Implementations SHOULD prefer PQ(/T) keys when multiple options are available. When encrypting to a certificate that has both a valid PQ/T and a valid traditional encryption subkey, an implementation SHOULD use the PQ/T subkey only. Furthermore, if an application has any means to determine that encrypting to a PQ/T certificate and a traditional certificate is redundant, it should omit encrypting to the traditional certificate.

As specified in Section 3.1, the confidentiality of a message is not post-quantum secure when using multiple PKESKs if at least one does not use PQ/T encryption schemes. An implementation SHOULD NOT abort the encryption process when encrypting a message to both PQ/T and traditional keys to allow for a smooth transition to post-quantum cryptography.

An implementation MAY sign with both a PQ(/T) and an ECC key using multiple signatures over the same data as described in Section 3.3. Signing only with PQ(/T) key material is not backwards compatible.

8.2. Key generation strategies

It is RECOMMENDED to generate fresh secrets when generating PQ(/T) keys. Note that reusing key material from existing ECC keys in PQ(/T) keys does not provide backwards compatibility.

An OpenPGP 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 a traditional certificate for compatibility and a v6 PQ(/T) certificate, at a greater complexity in key distribution.

  2. Attach PQ(/T) encryption or signature subkeys to an existing traditional v6 OpenPGP 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.

9. Security Considerations

9.1. Security Aspects of Composite Signatures

When multiple signatures are applied to a message, the question of the protocol's resistance against signature stripping attacks naturally arises. In a signature stripping attack, an adversary removes one or more of the signatures such that only a subset of the signatures remain in the message at the point when it is verified. This amounts to a downgrade attack that potentially reduces the value of the signature. It should be noted that the composite signature schemes specified in this draft are not subject to a signature stripping vulnerability. This is due to the fact that in any OpenPGP signature, the hashed meta data includes the signature algorithm ID, as specified in [RFC9580, Section 5.2.4]. As a consequence, a component signature taken out of the context of a specific composite algorithm is not a valid signature for any message.

Furthermore, it is also not possible to craft a new signature for a message that was signed twice with a composite algorithm by interchanging (i.e., remixing) the component signatures, which would classify as a weak existential forgery. This is due to the fact that each v6 signatures also includes a random salt at the start of the hashed meta data, as also specified in the aforementioned reference.

9.2. Key combiner

For the key combination in Section 4.2.1 this specification limits itself to the use of SHA3-256 in a construction following [SP800-56C]. The sponge construction used by SHA3-256 was proven to be indifferentiable from a random oracle [BDPA08]. This means, that in contrast to SHA2, which uses a Merkle-Damgard construction, no HMAC-based construction is required for key combination. It is therefore sufficient to simply process the concatenation of any number of key shares with a domain separation when using a sponge-based construction like SHA3-256.

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 SHA3-256 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 secrets SS1 and SS2 (with ciphertexts CT1 and CT2 and public keys PK1 and PK2) as

K = SHA3-256(SS1 || SS2 || CT2 || PK2 || CT1 || PK1 || algId || domSep)

from a random bit string, an adversary has to know (or correctly guess) both secret shares SS1 and SS2, entirely.

The proposed construction in Section 4.2.1 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 [GHP18]. 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 [GHP18], up to some reordering of input shared secrets and ciphertexts. In the random oracle setting, the reordering does not influence the arguments in [GHP18]. That is, in the post-quantum setting the construction inherits its IND-CCA2 security from any ingredient post-quantum IND-CCA2-secure KEM.

Note that the ECDH-KEMs described in this specification are not IND-CCA2 secure as standalone schemes. However, regarding the pre-quantum setting, it is argued in [BCD_24] that the construction ensures IND-CCA2 security under some Diffie-Hellman intractability assumption in a nominal group. Note that Curve25519 and Curve448 qualify as such [ABH_21].

9.2.1. Domain separation and context binding

The domSep information defined in Section 4.2.1 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.

The algorithm ID, passed as the algID parameter to multiKeyCombine, binds the derived KEK to the chosen algorithm. The algorithm ID identifies unequivocally the algorithm, the parameters for its instantiation, and the length of all artifacts, including the derived key.

The input of the public keys into multiKeyCombine binds the KEK to the communication parties. The input of the ciphertexts binds the KEK to the specific session.

9.3. ML-DSA and SLH-DSA hedged variants

This specification makes use of the default "hedged" variants of ML-DSA and SLH-DSA, which mix fresh randomness into the respective signature-generation algorithm's internal hashing step. This has the advantage of an enhanced side-channel resistance of the signature operations according to [FIPS-204] and [FIPS-205].

9.4. 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 + EdDSA signature packet, see Section 5.2.1. 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 ID, see Section 6.1.1.

9.5. Symmetric Algorithms for SEIPD Packets

This specification mandates support for AES-256 for two reasons. First, AES-KeyWrap with AES-256 is already part of the composite KEM construction. Second, some of the PQ(/T) algorithms target the security level of AES-256.

For the same reasons, this specification further recommends the use of AES-256 if it is supported by all recipient certificates, regardless of what the implementation would otherwise choose based on the recipients' preferences. This recommendation should be understood as a clear and simple rule for the selection of AES-256 for encryption. Implementations may also make more nuanced decisions.

9.6. Key generation

When generating keys, this specification requires component keys to be generated independently, and recommends not to reuse existing keys for any of the components. Note that reusing a key across different protocols may lead to signature confusion vulnerabilities, that formally classify as signature forgeries. Generally, reusing a key for different purposes may lead to subtle vulnerabilities.

10. Additional considerations

10.1. Performance Considerations for SLH-DSA

This specification introduces both ML-DSA + EdDSA as well as SLH-DSA as PQ(/T) signature schemes.

Generally, it can be said that ML-DSA + EdDSA 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 the weaker security assumptions of a hash-based signature scheme are required – namely only the 2nd preimage resistance of a hash function – and thus a potentially higher degree of trust in the long-term security of signatures is achieved. 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 + EdDSA signature schemes.

Pertaining to the execution time, the particularly costly operation in SLH-DSA is the signature generation. Depending on the parameter set, it can range from approximately the one hundred fold to more than the two thousand fold of that of ML-DSA-87. These number are based on the performance measurements published in the NIST submissions for SLH-DSA and ML-DSA. In order to achieve fast signature generation times, the algorithm SLH-DSA-SHAKE-128f ("f" standing for "fast") should be chosen. This comes at the expense of a larger signature size. This choice can be relevant in applications where mass signing occurs or a small latency is required.

In order to minimize the space requirements of an SLH-DSA signature, an algorithm ID with the name ending in "s" for "small" should be chosen. This comes at the expense of a longer signature generation time. In particular, SLH-DSA-SHAKE-128s achieves the smallest possible signature size, which is about the double size of an ML-DSA-87 signature. Where a higher security level than 128 bit is needed, SLH-DSA-SHAKE-256s can be used.

Unlike the signature generation time, the signature verification time of SLH-DSA is not that much larger than that of other PQC schemes. Based on the performance measurements published in the NIST submissions for SLH-DSA and ML-DSA, the verification time of the SLH-DSA is, for the parameters covered by this specification, larger than that of ML-DSA-87 by a factor ranging from four (for -128s) over nine (for -256s) to twelve (for -128f).

11. IANA Considerations

IANA is requested to add the algorithm IDs defined in Table 11 to the existing registry OpenPGP Public Key Algorithms. The field specifications enclosed in brackets for the ML-KEM + ECDH composite algorithms denote fields that are only conditionally contained in the data structure.

Table 11: IANA updates for registry 'OpenPGP Public Key Algorithms'
ID Algorithm Public Key Format Secret Key Format Signature Format PKESK Format Reference
TBD ML-KEM-768+X25519 32 octets X25519 public key (Table 3), 1184 octets ML-KEM-768 public key (Table 4) 32 octets X25519 secret key (Table 3), 2400 octets ML-KEM-768 secret-key (Table 4) N/A 32 octets X25519 ciphertext, 1088 octets ML-KEM-768 ciphertext [, 1 octet algorithm ID in case of v3 PKESK], 1 octet length field of value n, n octets wrapped session key (Section 4.3.1) Section 4.2
TBD ML-KEM-1024+X448 56 octets X448 public key (Table 3), 1568 octets ML-KEM-1024 public key (Table 4) 56 octets X448 secret key (Table 3), 3168 octets ML-KEM-1024 secret-key (Table 4) N/A 56 octets X448 ciphertext, 1568 octets ML-KEM-1024 ciphertext [, 1 octet algorithm ID in case of v3 PKESK], 1 octet length field of value n, n octets wrapped session key (Section 4.3.1) Section 4.2
30 ML-DSA-65+Ed25519 32 octets Ed25519 public key (Table 6), 1952 octets ML-DSA-65 public key (Table 7) 32 octets Ed25519 secret key (Table 6), 4032 octets ML-DSA-65 secret (Table 7) 64 octets Ed25519 signature (Table 6), 3293 octets ML-DSA-65 signature (Table 7) N/A Section 5.2
31 ML-DSA-87+Ed448 57 octets Ed448 public key (Table 6), 2592 octets ML-DSA-87 public key (Table 7) 57 octets Ed448 secret key (Table 6), 4896 octets ML-DSA-87 secret (Table 7) 114 octets Ed448 signature (Table 6), 4595 octets ML-DSA-87 signature (Table 7) N/A Section 5.2
32 SLH-DSA-SHAKE-128s 32 octets public key (Table 9) 64 octets secret key (Table 9) 7856 octets signature (Table 9) N/A Section 6.1
33 SLH-DSA-SHAKE-128f 32 octets public key (Table 9) 64 octets secret key (Table 9) 17088 octets signature (Table 9) N/A Section 6.1
34 SLH-DSA-SHAKE-256s 64 octets public key (Table 9) 128 octets secret key (Table 9) 29792 octets signature (Table 9) N/A Section 6.1

12. Changelog

12.1. 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.

12.2. 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.

12.3. 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.

12.4. draft-wussler-openpgp-pqc-04

  • Added Johannes Roth as author

12.6. draft-ietf-openpgp-pqc-01

  • Mandated AES-256 as mandatory to implement.

  • Added AES-256 / AES-128 with OCB implicitly to v1/v2 SEIPD preferences of "PQ(/T) certificates".

  • Added a recommendation to use AES-256 when possible.

  • Swapped the optional v3 PKESK algorithm identifier with length octet in order to align with X25519 and X448.

  • Fixed ML-DSA private key size.

  • Added test vectors.

  • Correction and completion of IANA instructions.

12.7. draft-ietf-openpgp-pqc-02

  • Removed git rebase artifact.

12.8. draft-ietf-openpgp-pqc-03

  • Updated SLH-DSA by removing parametrization and restricting to three SLH-DSA-SHAKE algorithm code points.

  • Removed NIST and Brainpool curve hybrids, dropped ECDSA from the current specification.

  • Updated KDF as proposed at IETF 119.

  • Removed whitespaces from composite algorithm names.

  • Explicitly disallowed SED (tag 9) and weak hashes when using PQ algorithms.

12.9. draft-ietf-openpgp-pqc-04

  • Fixed ML-DSA signature size.

  • Fixed parameters order in PKESK description.

  • Fixed missing inputs into KEM combination description.

  • Improved parallel encryption guidance.

  • Improved SED deprecation decscription.

  • Added ML-DSA test vectors.

12.10. draft-ietf-openpgp-pqc-05

  • Reworked KEM combiner for the purpose of NIST-compliance.

  • Mandated v6 keys for ML-KEM + ECDH algorithms.

  • Defined private key seed format for ML-KEM and ML-DSA.

  • Added key generation security considerations.

  • Replaced initial public drafts with FIPS 203, 204, 205.

12.11. draft-ietf-openpgp-pqc-06

  • Fixed and improved test vectors.

12.12. draft-ietf-openpgp-pqc-07

  • Assign code points 30 - 34 for ML-DSA and SLH-DSA algorithms.

  • Align KEM combiner with LAMPS

  • Drop CCA-conversion of X25519/X448

  • Switch to hedged variant also for SLH-DSA

13. Contributors

Stephan Ehlen (BSI)
Carl-Daniel Hailfinger (BSI)
Andreas Huelsing (TU Eindhoven)

14. References

14.1. Normative References

[RFC3394]
Schaad, J. and R. Housley, "Advanced Encryption Standard (AES) Key Wrap Algorithm", RFC 3394, DOI 10.17487/RFC3394, , <https://www.rfc-editor.org/rfc/rfc3394>.
[RFC7748]
Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, , <https://www.rfc-editor.org/rfc/rfc7748>.
[RFC8032]
Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital Signature Algorithm (EdDSA)", RFC 8032, DOI 10.17487/RFC8032, , <https://www.rfc-editor.org/rfc/rfc8032>.
[RFC9580]
Wouters, P., Ed., Huigens, D., Winter, J., and Y. Niibe, "OpenPGP", RFC 9580, DOI 10.17487/RFC9580, , <https://www.rfc-editor.org/rfc/rfc9580>.

14.2. Informative References

[ABH_21]
Alwen, J., Blanchet, B., Hauck, E., Kiltz, E., Lipp, B., and D. Riepel, "Analysing the HPKE Standard", , <https://doi.org/10.1007/978-3-030-77870-5_4>.
[BCD_24]
Barbosa, M., Connolly, D., Duarte, J. D., Kaiser, A., Schwabe, P., Varner, K., and B. Westerbaan, "X-Wing The Hybrid KEM You’ve Been Looking For", , <https://doi.org/10.62056/a3qj89n4e>.
[BDPA08]
Bertoni, G., Daemen, J., Peters, M., and G. Assche, "On the Indifferentiability of the Sponge Construction", , <https://doi.org/10.1007/978-3-540-78967-3_11>.
[FIPS-203]
National Institute of Standards and Technology, "Module-Lattice-Based Key-Encapsulation Mechanism Standard", , <https://doi.org/10.6028/NIST.FIPS.203>.
[FIPS-204]
National Institute of Standards and Technology, "Module-Lattice-Based Digital Signature Standard", , <https://doi.org/10.6028/NIST.FIPS.204>.
[FIPS-205]
National Institute of Standards and Technology, "Stateless Hash-Based Digital Signature Standard", , <https://doi.org/10.6028/NIST.FIPS.205>.
[GHP18]
Giacon, F., Heuer, F., and B. Poettering, "KEM Combiners", , <https://doi.org/10.1007/978-3-319-76578-5_7>.
[I-D.ietf-lamps-pq-composite-kem]
Ounsworth, M., Gray, J., Pala, M., Klaußner, J., and S. Fluhrer, "Composite ML-KEM for use in X.509 Public Key Infrastructure and CMS", Work in Progress, Internet-Draft, draft-ietf-lamps-pq-composite-kem-05, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-pq-composite-kem-05>.
[I-D.ietf-pquip-pqt-hybrid-terminology]
D, F., P, M., and B. Hale, "Terminology for Post-Quantum Traditional Hybrid Schemes", Work in Progress, Internet-Draft, draft-ietf-pquip-pqt-hybrid-terminology-06, , <https://datatracker.ietf.org/doc/html/draft-ietf-pquip-pqt-hybrid-terminology-06>.
[NIST-PQC]
Chen, L., Moody, D., and Y. Liu, "Post-Quantum Cryptography Standardization", , <https://csrc.nist.gov/projects/post-quantum-cryptography/post-quantum-cryptography-standardization>.
[NISTIR-8413]
Alagic, G., Apon, D., Cooper, D., Dang, Q., Dang, T., Kelsey, J., Lichtinger, J., Miller, C., Moody, D., Peralta, R., Perlner, R., Robinson, A., Smith-Tone, D., and Y. Liu, "Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process", NIST IR 8413 , , <https://doi.org/10.6028/NIST.IR.8413-upd1>.
[SP800-56A]
Barker, E., Chen, L., Roginsky, A., Vassilev, A., and R. Davis, "Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography", NIST Special Publication 800-56A Rev. 3 , , <https://doi.org/10.6028/NIST.SP.800-56Ar3>.
[SP800-56C]
Barker, E., Chen, L., Roginsky, A., and R. Davis, "Recommendation for Key-Derivation Methods in Key-Establishment Schemes", NIST Special Publication 800-56C Rev. 2 , , <https://doi.org/10.6028/NIST.SP.800-56Cr2>.

Appendix A. Test Vectors

To help implementing this specification a set of non-normative examples follow here.

A.1. Sample Ed25519 with ML-KEM-768+X25519 Data

A.1.1. Transferable Secret Key

Here is a Transferable Secret Key consisting of:

  • A v6 Ed25519 Private-Key packet

  • A v6 direct key self-signature

  • A User ID packet

  • A v6 positive certification self-signature

  • A v6 X25519 Private-Subkey packet

  • A v6 subkey binding signature

  • A v6 ML-KEM-768+X25519 Private-Subkey packet

  • A v6 subkey binding signature

The primary key has the fingerprint 7f81f9d0db7cf905ed375ba0057928075faff433a70b88c0a30a022ddeaf3ac9.

The first subkey has the fingerprint e3ed45a07c5af795b7cc5a156738efb42301c10df886a341ede80fca4c99baa3. The second subkey has the fingerprint fecb6e4f8a9ad135c6b45e63d9016daf7706d7e8322fd6ed1d8b028f61d57ebe.

-----BEGIN PGP PRIVATE KEY BLOCK-----
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icmhn1FLNZvCmwYYGwoAAAAsBYJR0MaAApsMIqEGf4H50Nt8+QXtN1ugBXkoB1+v
9DOnC4jAowoCLd6vOskAAAAA/LYgqcJuYY5yvHWF9wtB9SGpMO0hXHQzL7bp2Og+
F4Ja0Aop+8942LLOhjHAL42gt447zQ1I8Hqr6cIr/h/VmIXxK8yif/zEPDOwDi8W
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W9xd5SBng+NidMfAF5kK5CMG0IU4ocJaqJV6O+xSO6QyqLXFslBIAfeUHJWC6Epz
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C5uvQ2SJ3ikdLVudFzsx3GYfAaVFK6p3ypRwqWstujBqPvUkDJx1JflAqxAHz0Mj
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xTNyTHqC7vFnXqxPItan1PwgCnFNwAuY+fI51KZBani/ADUeFulwNLJFmevIBNKF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-----END PGP PRIVATE KEY BLOCK-----

A.1.2. Transferable Public Key

Here is the corresponding Transferable Public Key for Appendix A.1.1 consisting of:

  • A v6 Ed25519 Public-Key packet

  • A v6 direct key self-signature

  • A User ID packet

  • A v6 positive certification self-signature

  • A v6 X25519 Public-Subkey packet

  • A v6 subkey binding signature

  • A v6 ML-KEM-768+X25519 Public-Subkey packet

  • A v6 subkey binding signature

-----BEGIN PGP PUBLIC KEY BLOCK-----

xioGUdDGgBsAAAAgDZb3fPA4Y7G87USs+N4VIxWY1uy4Rn4P/NA5x1KZCcvCrwYf
GwoAAABABYJR0MaAAwsJBwMVCggCFgACmwMCHgkioQZ/gfnQ23z5Be03W6AFeSgH
X6/0M6cLiMCjCgIt3q86yQUnCQIHAgAAAAA9ACA/zE1ayus/liv6a8+PSW8Cl2JU
v1+A6IL/wq20pJWaNG4Iyt+G4yxRfN6ca8WMIi8StUzcK1eo7CyX3Kvtj6dfqhJ4
5wlnV6A1VROojA9jcGIuFG9u3ttf1hnnzlM1ngjNLlBRQyB1c2VyIChUZXN0IEtl
eSkgPHBxYy10ZXN0LWtleUBleGFtcGxlLmNvbT7CmwYTGwoAAAAsBYJR0MaAAhkB
IqEGf4H50Nt8+QXtN1ugBXkoB1+v9DOnC4jAowoCLd6vOskAAAAAqtUgo0qTqXJP
VEDyLu74FId3ETgVp5gfNd1U/7aTBx6vGSCI2JOujbCaJC9HgG/tJXPhOlP05HPc
NvLyx8XrxTrJY9cPtZS1iVYpGULAUzvoy0eaAVPa6cxXtsSOdjNEVHsLzioGUdDG
gBkAAAAg/qSQQXVt99z6jqGnnJ9qY/fh3WeuYA8K0U2gT3LabCTCmwYYGwoAAAAs
BYJR0MaAApsMIqEGf4H50Nt8+QXtN1ugBXkoB1+v9DOnC4jAowoCLd6vOskAAAAA
/LYgqcJuYY5yvHWF9wtB9SGpMO0hXHQzL7bp2Og+F4Ja0Aop+8942LLOhjHAL42g
t447zQ1I8Hqr6cIr/h/VmIXxK8yif/zEPDOwDi8W3LdfentYkUodyJKo0X2v2LUv
9+oKzsQKBlHQxoBpAAAEwCMsYaegNwansYJa+5DkfTa/feM6uCuBqWv+/6Nw+R45
PaG6MPW0KdXNZuJfVMkRuAp9qdxoy8B2XTKm9SOeW9xd5SBng+NidMfAF5kK5CMG
0IU4ocJaqJV6O+xSO6QyqLXFslBIAfeUHJWC6EpzIEVnNBYDTSZstIzKpvs99geq
tpYvEbulJXO3uHRIA2sfaupCRJhPLyWJkKoGVOED96JZPYeoUTxmUemeoBF9eeKS
R7o8BymcZ2OcBLbIeyBPI4tlvPC5gRXLg6eZ8aOiC5uvQ2SJ3ikdLVudFzsx3GYf
AaVFK6p3ypRwqWstujBqPvUkDJx1JflAqxAHz0MjDGocypQfU1cM3iqBmCIs5UWU
SakAFMerb5BUh3aoDAhKwdksvntGPMuyUcO1jxxbxTNyTHqC7vFnXqxPItan1Pwg
CnFNwAuY+fI51KZBani/ADUeFulwNLJFmevIBNKFI5akhpeq7Hl+YngF6jfI5jnA
tSbGKLGshgKZvJs2mFhmHTsDEZw+4ZNDOYByqciACsGv0EI4R/LCMyo8lWJordtD
RsFd+hmXWeKp1bIVL2MNV8HF62hFjfiM30xv8IG8FaBh9/yAGcWhjHB/Q5Vyu1ik
I6o0pYelotGH8eEa4beoLSmAgGXMPYgArlWEaydYM2h8CQIq6IBh1wY6d6GeNwcv
w8d+P+McQ9AfuFAm6EcCaMVBOGTImTmEr5uvLYOD1eh6fYCLg3plbzJkqgYR+LrG
ruO/EUgJUvzElLCSRqMnjZhmyfe7PSAHXwrM4CV1VOBdNdOxkyqnhVAk2aVmPJBc
YJgkz1WWzshQHiQpr4ynbIJLnKJ8iqqvlaqSo1MJ5VvDonuowToiv+cj3tZl4Vy2
CcAEgBx+84BkiIBhaGie7rIRH9gN0dOqZQfO1KmoAma1/+BIFIUO+YsvvTRrpOlk
DukeXKvKSuYALhxPgAFReYNzNvCpQ3jCxiooldAvtkt54Utsy3nHKDOlQ3a0YQFT
n3QcIeCQCBImGnRxUyN9BQMc/sOJE+tu6EzBvVgPfApAeLliCLEs8aCsl8BUW2tu
WeYkTukNu5oMPecrLjzHyMpyHgQzr2rE6ZjPttITe3YLPwG2DYF28lhCNgGMu3Er
Rzpumkqx2jQi17ORLeQaVjmqBmi53ge4hWOxp4gKilsYbhqQvTpKuStYNTdEB7ZT
itiC4bZ+JVwqv6IuJvUYhSoYiChzwrtBtgt9KkF7JZvL+TU/q4UTnaTMt7AQ80cN
djEN9XIGmpoz0/R2iRc2R8uCLhnMK0WGoIeS9vIdwQMZo5M/2stSBRxZWXCjNuKr
veQLtaemMTWNxESGKtADjeMoUCminmmPttS0/ruMdLa4gzWFQraINml1RaaWdSUj
f1sBD1V6cXM1oZVZJhK9cJe60Tck6xFb6+eZpeY8ddiYLMTBqCCaB5YKRqe0ERgN
e7XPUGkaVGKN1Tk4DrG2MLu5xwUdKttJkpJZdzZip8cnWIwUODIzY/FeoFU6C/Vd
wpEGSxwUCTeY+IFsc9MhJtpxhMeOfvKChjmH/aWB+DUBU1Jcv+wn0wmMFfp/x6PL
kkTEIVHpaT/1Bt6tDft9d8lUNG3FwO1h1EnwgFt/3b3CmwYYGwoAAAAsBYJR0MaA
ApsMIqEGf4H50Nt8+QXtN1ugBXkoB1+v9DOnC4jAowoCLd6vOskAAAAAqrwg1X+V
iqXXTOl14ZRsOaxaYhsrVXzRQjWPY4Sq7J9vN0qlC4tFb7NjDWNBCB0XFeFLzXET
1NdhcJVhhVMq7c2hqq6rjtEn7VWKEBsaDQm3CK57RyQ+Nitq9guQlGXjUyQE
-----END PGP PUBLIC KEY BLOCK-----

A.1.3. Encrypted and Signed Message

Here is a signed message "Testing\n" encrypted to the certificate Appendix A.1.2 and signed by the secret key Appendix A.1.1:

  • A v3 PKESK

  • A v1 SEIPD

The hex-encoded mlkemKeyShare input to multiKeyCombine is 925fd46093bf8a785b89f3757fedaa8dd9190766471d7e68c426630851d9621e.

The hex-encoded ecdhKeyShare input to multiKeyCombine is d98c39a18dad9840e255c0b34c846089435617ee47f5764fad66e89abede9955.

The hex-encoded output of multiKeyCombine is 64ff5bc957bc99a784d455cb5575ca2898071bc6c0cf0332b269e23e7280e5ae.

The hex-encoded session key is 401aee9fa99486b10ee774fc5445ccc997fab51b19e05577304228351ffd5e0e.

-----BEGIN PGP MESSAGE-----
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-----END PGP MESSAGE-----

A.2. Sample ML-DSA-65+Ed25519 with ML-KEM-768+X25519 Data

A.2.1. Transferable Secret Key

Here is a Transferable Secret Key consisting of:

  • A v6 ML-DSA-65+Ed25519 Private-Key packet

  • A v6 direct key self-signature

  • A User ID packet

  • A v6 positive certification self-signature

  • A v6 ML-KEM-768+X25519 Private-Subkey packet

  • A v6 subkey binding signature

The primary key has the fingerprint eef4c85ce59af6a4520432960079697ebbcd521dffc500e945209a284f535791.

The subkey has the fingerprint 5718270f6330b5482f4f5c24ca8ea2d826650ad202f39c91638c348e20a03aad.

-----BEGIN PGP PRIVATE KEY BLOCK-----
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sl/P8EbzzPv72MZlbpk3qgRotnFCeaM+ZvP659TbqvYfdnO/+Qeq/SDJAxemG8gZ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s7lnA7234sbpvYYf8+N0HsPpZ0QMQKBR/YTGjkI6Zf26bCdRxHUaIkNUtJJVNIfI
JAXyEnB7G6dKwpM2w/bWKyQ2OC1rnMVBAjlMXR/PBBXK6B7uj7Kn4aVVwGfW8DnL
XTJzE9Q1CsJSSOFprxlNlG+3LS+3bzvak70zA9XA1vRVBBszyF33weBNlEYQkmgu
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-----END PGP PRIVATE KEY BLOCK-----

A.2.2. Transferable Public Key

Here is the corresponding Transferable Public Key for Appendix A.2.1 consisting of:

  • A v6 ML-DSA-65+Ed25519 Public-Key packet

  • A v6 direct key self-signature

  • A User ID packet

  • A v6 positive certification self-signature

  • A v6 ML-KEM-768+X25519 Public-Subkey packet

  • A v6 subkey binding signature

-----BEGIN PGP PUBLIC KEY BLOCK-----

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FbWhELPs9gRZXaqrwMXI3RM5W19sgZjzDS48cJKeodj/AA4/Tmxupq3uAAAAAAAA
AAAAAAAAAAAAAAQNFRseJw==
-----END PGP PUBLIC KEY BLOCK-----

A.2.3. Encrypted and Signed Message

Here is a signed message "Testing\n" encrypted to the certificate Appendix A.2.2 and signed by the secret key Appendix A.2.1:

  • A v6 PKESK

  • A v2 SEIPD

The hex-encoded mlkemKeyShare input to multiKeyCombine is 69d5a76ba5c48cac521607a37d3501c6427a410162b3da81bcce912302f33680.

The hex-encoded ecdhKeyShare input to multiKeyCombine is 3b193f5868838192f7728ec59a4d4719a01c0984881ad9377cb1ce57d692ca06.

The hex-encoded output of multiKeyCombine is fd86a366e4e5acfbb759aedc34b3777ab98a7a8aa4750516c2f9cbd858d37950.

The hex-encoded session key is ce374c24da35bfe1b351593d139f89f0c50805382ccc3d724bac721bdafc4e14.

-----BEGIN PGP MESSAGE-----

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po6qyVOnmxEPGzaZOgvV1BbNiD4kPyhcFMLM
-----END PGP MESSAGE-----

A.3. Sample ML-DSA-87+Ed448 with ML-KEM-1024+X448 Data

A.3.1. Transferable Secret Key

Here is a Transferable Secret Key consisting of:

  • A v6 ML-DSA-87+Ed448 Private-Key packet

  • A v6 direct key self-signature

  • A User ID packet

  • A v6 positive certification self-signature

  • A v6 ML-KEM-1024+X448 Private-Subkey packet

  • A v6 subkey binding signature

The primary key has the fingerprint ead878caeab3ae40d724cbc913777028e5f0809d393f796f710b7331c49a8ab1.

The subkey has the fingerprint d1caef1274b00ede8ce21575250621f96152d4a9aa68b400579be98b4fa0ca68.

-----BEGIN PGP PRIVATE KEY BLOCK-----

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FOYkks7QbMBJpFIWHwxu1sqxvghYAB6GoU+90hVE5k6rjR/rAVl6n3gmgZBiM7WH
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-----END PGP PRIVATE KEY BLOCK-----

A.3.2. Transferable Public Key

Here is the corresponding Transferable Public Key for Appendix A.3.1 consisting of:

  • A v6 ML-DSA-87+Ed448 Public-Key packet

  • A v6 direct key self-signature

  • A User ID packet

  • A v6 positive certification self-signature

  • A v6 ML-KEM-1024+X448 Public-Subkey packet

  • A v6 subkey binding signature

-----BEGIN PGP PUBLIC KEY BLOCK-----

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-----END PGP PUBLIC KEY BLOCK-----

A.3.3. Encrypted and Signed Message

Here is a signed message "Testing\n" encrypted to the certificate Appendix A.3.2 and signed by the secret key Appendix A.3.1:

  • A v6 PKESK

  • A v2 SEIPD

The hex-encoded mlkemKeyShare input to multiKeyCombine is d45ee2034337bf424e3541f06d480e7d3adf27732ca0e39a4469b4420fac20d6.

The hex-encoded ecdhKeyShare input to multiKeyCombine is c38db9ecccc983a69978deb54668634d1d5f86ba326de34fbdbbc76fe5d0b442fbbbe952dbe86ddce23cdf2c2acd57802421eb3fb27239b6.

The hex-encoded output of multiKeyCombine is d9bc00d8604364aba52cb46bdd30a99f36878c847694f9b87a03ae901fa7abde.

The hex-encoded session key is 670c31af0c5224a9d590584c23679cb643860716225e4802fba5db93785a66d8.

-----BEGIN PGP MESSAGE-----

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tjRfiOLyEbBRP5Y=
-----END PGP MESSAGE-----

A.4. Sample SLH-DSA-128s+Ed448 with ML-KEM-768+X25519 Data

A.4.1. Transferable Secret Key

Here is a Transferable Secret Key consisting of:

  • A v6 SLH-DSA-128s Private-Key packet

  • A v6 direct key self-signature

  • A User ID packet

  • A v6 positive certification self-signature

  • A v6 ML-KEM-768+X25519 Private-Subkey packet

  • A v6 subkey binding signature

The primary key has the fingerprint 2e7216dacc6d1c0896901f50eff94d6c071ed7fa246f0cb547f10e22f21896b1.

The subkey has the fingerprint 1adc9f55f5223a78948522a0f4d1b29aff2ed651d3fa56e234249402000ace41.

-----BEGIN PGP PRIVATE KEY BLOCK-----

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-----END PGP PRIVATE KEY BLOCK-----

A.4.2. Transferable Public Key

Here is the corresponding Transferable Public Key for Appendix A.4.1 consisting of:

  • A v6 SLH-DSA-128s Public-Key packet

  • A v6 direct key self-signature

  • A User ID packet

  • A v6 positive certification self-signature

  • A v6 ML-KEM-768+X25519 Public-Subkey packet

  • A v6 subkey binding signature

-----BEGIN PGP PUBLIC KEY BLOCK-----

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-----END PGP PUBLIC KEY BLOCK-----

A.4.3. Encrypted and Signed Message

Here is a signed message "Testing\n" encrypted to the certificate Appendix A.4.2 and signed by the secret key Appendix A.4.1:

  • A v6 PKESK

  • A v2 SEIPD

The hex-encoded mlkemKeyShare input to multiKeyCombine is dc96c3899e9bb3394e360f3f0587576f411c1fe20d536921a208c46121ed709d.

The hex-encoded ecdhKeyShare input to multiKeyCombine is 16dab4605b17b8096b7c601164fdd1bdc173e5f396dce29e61a994ad61199848.

The hex-encoded output of multiKeyCombine is baae7950649bcf6df658aae624066da1cb06f06a0b312037abf0b610eee4f8cc.

The hex-encoded session key is 348581a5a5fea23586dfb428c1911ed903fc4affaacca42b50f5a4c165fa8a98.

-----BEGIN PGP MESSAGE-----

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-----END PGP MESSAGE-----

Acknowledgments

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

Authors' Addresses

Stavros Kousidis
BSI
Germany
Johannes Roth
MTG AG
Germany
Falko Strenzke
MTG AG
Germany
Aron Wussler
Proton AG
Switzerland