]> 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 as a Key Encapsulation Mechanism (KEM), a KEM being a modern building block for public-key encryption, and ML-DSA as well as SLH-DSA 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 ECDH 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 EdDSA 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 ECDH encryption is defined here as a KEM via X25519 and X448 which are defined in . EdDSA as defined in is used as the elliptic curve-based digital signature scheme.

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 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.

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 parallel encryption to different keys by using multiple PKESK packets, thus realizing non-composite multi-algorithm public-key encryption.

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.

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

ID	Algorithm	Requirement	Definition
TBD (105 for testing)	ML-KEM-768+X25519	MUST
TBD (106 for testing)	ML-KEM-1024+X448	SHOULD

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

ID	Algorithm	Requirement	Definition
TBD (107 for testing)	ML-DSA-65+Ed25519	MUST
TBD (108 for testing)	ML-DSA-87+Ed448	SHOULD
TBD	SLH-DSA-SHAKE-128s	MAY
TBD	SLH-DSA-SHAKE-128f	MAY
TBD	SLH-DSA-SHAKE-256s	MAY

Experimental Codepoints for Interop Testing [ Note: this section to be removed before publication ] Algorithms indicated as MAY are not assigned a codepoint in the current state of the draft in order to leave enough private/experimental code points available for other drafts. 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.

Algorithm Combinations

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 , 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 it is explained how to deal with multiple key scenarios.

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.

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].]

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

Composite KEM schemes

Building Blocks

ECDH KEMs In this section we define the encryption, decryption, and data formats for the ECDH component of the composite algorithms. describes the ECDH-KEM parameters and artifact lengths. The artifacts in follow the encodings described in . 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 ()	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

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: and To instantiate ECDH-KEM, one must select a parameter set from .

X25519-KEM The encapsulation and decapsulation operations of x25519kem are described using the function X25519() and encodings defined in . 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 SHA3-256(X || ecdhCipherText || ecdhPublicKey)

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 SHA3-256(X || ecdhCipherText || ecdhPublicKey)

X448-KEM The encapsulation and decapsulation operations of x448kem are described using the function X448() and encodings defined in . 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 SHA3-512(X || ecdhCipherText || ecdhPublicKey)

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 SHA3-512(X || ecdhCipherText || ecdhPublicKey)

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 parametrization 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
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 . 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

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

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 key derivation function compliant to , Section 4.4, based on KMAC256. 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. Here, the parameters to KMAC256 appear in the order as specified in , Section 4, i.e., the key K, main input data X, requested output length in bits L, and optional customization string S. Note that the values ecdhKeyShare defined in and mlkemKeyShare defined in already use the relative ciphertext in the derivation. The ciphertext and public keys are by design included again in the key combiner to provide a robust security proof.

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

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 .
4. Instantiate the ECDH-KEM and the ML-KEM depending on the algorithm ID according to
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
8. Compute C := AESKeyWrap(KEK, sessionKey) with AES-256 as per 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.

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
5. Instantiate the ECDH-KEM and the ML-KEM depending on the algorithm ID according to
6. Parse ecdhCipherText, mlkemCipherText, and C from encryptedKey encoded as ecdhCipherText || mlkemCipherText || len(C,symAlgId) (|| symAlgId) || C as specified in , 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
10. Compute sessionKey := AESKeyUnwrap(KEK, C) with AES-256 as per , aborting if the 64 bit integrity check fails
11. Output sessionKey

Packet specifications

Public-Key Encrypted Session Key Packets (Tag 1) The algorithm-specific fields consists of the output of the encryption procedure described in :

• A fixed-length octet string representing an ECDH 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 .
• 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 , 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.

Key Material Packets The composite ML-KEM + ECDH schemes MUST be used only with v6 keys, as defined in . 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 in seed format, whose length is 64 octets (compare ). The seed format is defined in accordance with , 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 , 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 has to be invoked with the parsed values of d and z as input.

Composite Signature Schemes

Building blocks

EdDSA-Based signatures Throughout this specification EdDSA refers to the PureEdDSA variant defined in . 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
TBD (107 for testing)	Ed25519	32	32	32	64
TBD (108 for testing)	Ed448	57	57	57	114

ML-DSA signatures Throughout this specification ML-DSA refers to the pure version ML-DSA, i.e., in contrast to the pre-hash variant, defined in . 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 parametrization 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
TBD (107 for testing)	ML-DSA-65	1952	32	3309
TBD (108 for testing)	ML-DSA-87	2592	32	4627

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 [RFC9580, Section 5.2.4]. Composite ML-DSA + EdDSA 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 + EdDSA algorithm MUST also support the matching hash algorithm. Binding between ML-DSA + EdDSA and signature data digest

Algorithm ID reference	Hash function	Hash function ID reference
TBD (107 for testing)	SHA3-256	12
TBD (108 for testing)	SHA3-512	14

Key generation procedure The implementation MUST generate the ML-DSA and the EdDSA component keys independently. ML-DSA key generation follows the specification and the artifacts are encoded as fixed-length octet strings as defined in . For EdDSA this is done following the relative specification in , and encoding the artifacts as specified in 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 [RFC9580, 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 .

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

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

Packet Specifications

Signature Packet (Tag 2) The composite ML-DSA + EdDSA schemes MUST be used only with v6 signatures, as defined in . 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 .
• 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 + EdDSA 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 in seed format, whose length is 32 octets (compare ). The seed format is defined in accordance with , Section 3.6.3. Namely, the secret key is given by the value xi generated in step 1 of ML-DSA.KeyGen . Upon parsing the private key format, or before using the secret key, for the expansion of the key, the function ML-DSA.KeyGen_internal has to be invoked with the parsed value of xi as input.

SLH-DSA Throughout this specification SLH-DSA refers to the pure SLH-DSA version defined in .

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". 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
TBD (SLH-DSA-SHAKE-128s)	32	64	7856
TBD (SLH-DSA-SHAKE-128f)	32	64	17088
TBD (SLH-DSA-SHAKE-256s)	64	128	29792

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 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. Binding between SLH-DSA algorithm code points and signature data hash algorithms

Algorithm ID reference	Hash function	Hash function ID reference
TBD (SLH-DSA-SHAKE-128s)	SHA3-256	12
TBD (SLH-DSA-SHAKE-128f)	SHA3-256	12
TBD (SLH-DSA-SHAKE-256s)	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 .

Signature Verification SLH-DSA signature verification is performed via the algorithm SLH-DSA.Verify as specified in .

Packet specifications

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 .

Key Material Packets The SLH-DSA algorithms code points MUST be used only with v6 keys, as defined in . 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 .

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 .

Notes on Algorithms

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.

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.

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. 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 , 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 . Signing only with PQ(/T) key material is not backwards compatible.

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.

Security Considerations

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.

Hashing in ECDH-KEM Our construction of the ECDH-KEMs, in particular the inclusion of ecdhCipherText in the final hashing step in encapsulation and decapsulation that produces the ecdhKeyShare, 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 ecdhPublicKey follows the security advice in [RFC7748, Section 6.1].

Key combiner For the key combination in this specification limits itself to the use of KMAC256 in a construction following . The sponge construction used by KMAC256 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. 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 KMAC256. 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 KMAC256 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 (with ciphertexts C1 and C2 and public keys P1 and P2) 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 algorithm ID, passed as the algID paramter to multiKeyCombine, binds the derived KEK to the chosen algorithm. The input of the public keys into multiKeyCombine binds the KEK to the communication parties. The algorithm ID identifies unequivocally 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 unequivocally defined by the algorithm ID.

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 + EdDSA 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 ID, see .

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.

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.

Additional considerations

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).

IANA Considerations IANA is requested to add the algorithm IDs defined in 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. 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 (), 1184 octets ML-KEM-768 public key ()	32 octets X25519 secret key (), 2400 octets ML-KEM-768 secret-key ()	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 ()
TBD	ML-KEM-1024+X448	56 octets X448 public key (), 1568 octets ML-KEM-1024 public key ()	56 octets X448 secret key (), 3168 octets ML-KEM-1024 secret-key ()	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 ()
TBD	ML-DSA-65+Ed25519	32 octets Ed25519 public key (), 1952 octets ML-DSA-65 public key ()	32 octets Ed25519 secret key (), 4032 octets ML-DSA-65 secret ()	64 octets Ed25519 signature (), 3293 octets ML-DSA-65 signature ()	N/A
TBD	ML-DSA-87+Ed448	57 octets Ed448 public key (), 2592 octets ML-DSA-87 public key ()	57 octets Ed448 secret key (), 4896 octets ML-DSA-87 secret ()	114 octets Ed448 signature (), 4595 octets ML-DSA-87 signature ()	N/A
TBD	SLH-DSA-SHAKE-128s	32 octets public key ()	64 octets secret key ()	7856 octets signature ()	N/A
TBD	SLH-DSA-SHAKE-128f	32 octets public key ()	64 octets secret key ()	17088 octets signature ()	N/A
TBD	SLH-DSA-SHAKE-256s	64 octets public key ()	128 octets secret key ()	29792 octets signature ()	N/A

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.

draft-wussler-openpgp-pqc-04

• Added Johannes Roth as author

draft-ietf-openpgp-pqc-00

• Renamed draft

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.

draft-ietf-openpgp-pqc-02

• Removed git rebase artifact.

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.

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.

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.

draft-ietf-openpgp-pqc-06

• Fixed and improved test vectors.

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

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. 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 RFCs 4880 ("OpenPGP Message Format"), 5581 ("The Camellia Cipher in OpenPGP"), and 6637 ("Elliptic Curve Cryptography (ECC) in OpenPGP"). Informative References National Institute of Standards and Technology National Institute of Standards and Technology National Institute of Standards and Technology UK National Cyber Security Centre UK National Cyber Security Centre Naval Postgraduate School One aspect of the transition to post-quantum algorithms in cryptographic protocols is the development of hybrid schemes that incorporate both post-quantum and traditional asymmetric algorithms. This document defines terminology for such schemes. It is intended to be used as a reference and, hopefully, to ensure consistency and clarity across different protocols, standards, and organisations.

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

Sample Ed25519 with ML-KEM-768+X25519 Data

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

The primary key has the fingerprint 4a6722225bcd7cb077936b6e1bf7e7b3d8e8f5f49d61257bf79d572faaa792ce. The subkey has the fingerprint 9521f34e730a005fc5f912b088da710ff2f340c82ce3a5526833bfd7a0050006.

Transferable Public Key Here is the corresponding Transferable Public Key for 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 ML-KEM-768+X25519 Public-Subkey packet
• A v6 subkey binding signature

Encrypted and Signed Message Here is a signed message "Testing\n" encrypted to the certificate and signed by the secret key :

• A v6 PKESK
• A v2 SEIPD

The hex-encoded mlkemKeyShare input to multiKeyCombine is eb7fcf5ddbc127bc80d83dcb1bb43a1c6b9a1fa67b31752564d9f5fa18d80c64. The hex-encoded ecdhKeyShare input to multiKeyCombine is e5564bc3d80ed72c63e5eb940b47314ec68227aafba571f011399a2b7733545f. The hex-encoded output of multiKeyCombine is 4fa8f45b53b408b284bbcd13019a15f049c920306cfe8354fa3c5931894d6b92. The hex-encoded session key is 873b2a8218a75cf3d570729ba48b88acbeb2d7ce9f993f4228ff37faf785fee5.

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

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 bf262b24177002ac8ae5dc6da47c056d22ab9906d47d07952b75c358021901ca. The subkey has the fingerprint 48b94bce2f9771788f5feb74122d599989c400cc0f49108bc98e0ea7945e4838.

Transferable Public Key Here is the corresponding Transferable Public Key for 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

Encrypted and Signed Message Here is a signed message "Testing\n" encrypted to the certificate and signed by the secret key :

• A v6 PKESK
• A v2 SEIPD

The hex-encoded mlkemKeyShare input to multiKeyCombine is b755f49eb910e4e9e5c87eda9d5676a88918f063012f0bf0cc61a70f83232f0c. The hex-encoded ecdhKeyShare input to multiKeyCombine is 219a49490e65f96c87b7ade46bd65db9fcb96308e217acc5b421accf39217901. The hex-encoded output of multiKeyCombine is e00d037481ade01f4b061d2c81aec8e60072d24fc2bb5806b3358926bb03c7d8. The hex-encoded session key is 0e210c4027fa4f0be5a4d856cb6a6785b2e8cb48f5a12577f1621c8f8e4452a2.

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

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 275c8bea833c5deab538269381b120ebc002b8bca9c19df88740c942343f1462. The subkey has the fingerprint 9e5f6087500c4a72b96ad343745360c99a0126dd43545e7e882ca4cdfe107fef.

Transferable Public Key Here is the corresponding Transferable Public Key for 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

Encrypted and Signed Message Here is a signed message "Testing\n" encrypted to the certificate and signed by the secret key :

• A v6 PKESK
• A v2 SEIPD

The hex-encoded mlkemKeyShare input to multiKeyCombine is 98d3b185ced0cb4fbdb26e1d1a19a79c98afb1586d72947b5877162b89f6af3f. The hex-encoded ecdhKeyShare input to multiKeyCombine is a09c74f0d55eefbecdbc8a7cdf5a645d6bd1f6630f75ddd9958c25a6bc9d5bd8b9d2f393e98468ff9c267033f14034137ddf07a6fcf49824f3b9d1b97907d77a. The hex-encoded output of multiKeyCombine is 3bee730ccdc5ab30c1eef9c77c9d1ccd1b2489e3a23ac2b341f7283c5d27b673. The hex-encoded session key is 3d14b7f9140091c17ff30c3215284a9dbb7e699633f5d3edf02dba4dcdbd5c6e.

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