PQ/T Composite Schemes for OpenPGP using NIST and Brainpool Elliptic Curve Domain Parameters

1.1.1. Terminology for Multi-Algorithm Schemes

The terminology in this document is oriented towards the definitions in [draft-driscoll-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.¶

1.2.1. 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 ECC-based 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 ECC-based signature schemes.¶

2.1.1. SEC1 EC Point Wire Format

Elliptic curve points of the generic prime curves are encoded using the SEC1 (uncompressed) format as the following octet string:¶

B = 04 || X || Y

where X and Y are coordinates of the elliptic curve point P = (X, Y), and each coordinate is encoded in the big-endian format and zero-padded to the adjusted underlying field size. The adjusted underlying field size is the underlying field size rounded up to the nearest 8-bit boundary, as noted in the "Field size" column in Table 3, Table 4, or Table 7. This encoding is compatible with the definition given in [SEC1].¶

2.1.2. Measures to Ensure Secure Implementations

In the following measures are described that ensure secure implementations according to existing best practices and standards defining the operations of Elliptic Curve Cryptography.¶

Even though the zero point, also called the point at infinity, may occur as a result of arithmetic operations on points of an elliptic curve, it MUST NOT appear in any ECC data structure defined in this document.¶

Furthermore, when performing the explicitly listed operations in Section 5.1.1.1 it is REQUIRED to follow the specification and security advisory mandated from the respective elliptic curve specification.¶

3.1.1. 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 since there are not enough private/experimental code points available to cover all newly introduced public-key algorithm identifiers.¶

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.¶

5.1.1. ECC-Based KEMs

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

Table 3 and Table 4 describe the ECC-KEM parameters and artifact lengths.¶

The SEC1 format for point encoding is defined in Section 2.1.1.¶

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

(eccCipherText, eccKeyShare) <- ECC-KEM.Encaps(eccPublicKey)

and¶

(eccKeyShare) <- ECC-KEM.Decaps(eccSecretKey, eccCipherText, eccPublicKey)

To instantiate ECC-KEM, one must select a parameter set from Table 3 or Table 4.¶

5.1.2. 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 5. All artifacts are encoded as defined in [FIPS-203].¶

To instantiate ML-KEM, one must select a parameter set from the column "ML-KEM" of Table 5.¶

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¶

5.2.1. Fixed information

For the composite KEM schemes defined in Table 1 the following fixed information, which is identical to one specified in [draft-ietf-openpgp-pqc-03], MUST be used in the subsequently described key combiner Section 5.2.2.¶

//   Input:
//   algID - the algorithm ID encoded as octet
//
//   Constants:
//   domSeparation - the UTF-8 encoding of the string
//                   "OpenPGPCompositeKDFv1"

fixedInfo = algID || domSeparation

The value of domSeparation is the UTF-8 encoding of the string "OpenPGPCompositeKDFv1" and MUST be the following octet sequence:¶

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

5.2.2. Key combiner

For the composite KEM schemes defined in Table 1 the following procedure, which is identical to one described in [draft-ietf-openpgp-pqc-03], MUST be used to compute the KEK that wraps a session key. The construction is a one-step 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.¶

[Note to the reader: the key combiner defined in the current version of this draft is not actually compliant to [SP800-56C], since the NIST standard requires that the shared secret is fed to the KDF first whereas the combiner defined here feeds the key shares of the two component schemes, which together form the shared secret, in two parts with public information in between. The combiner will be reworked to fix this defect in conformance to the combiner defined in draft-ietf-openpgp-pqc. The change is planned to be integrated into both drafts prior to IETF 121.]¶

//   multiKeyCombine(ecdhKeyShare, ecdhCipherText, ecdhPublicKey, mlkemKeyShare,
//                   mlkemCipherText, mlkemPublicKey, fixedInfo)
//
//   Input:
//   ecdhKeyShare    - the ECDH key share encoded as an octet string
//   ecdhCipherText  - the ECDH ciphertext encoded as an octet string
//   mlkemKeyShare   - the ML-KEM key share encoded as an octet string
//   mlkemCipherText - the ML-KEM ciphertext encoded as an octet string
//   ecdhPublicKey   - The ECDH public key of the recipient as an octet string
//   mlkemPublicKey  - The ML-KEM public key of the recipient as an octet string
//   fixedInfo       - the fixed information octet string
//
//   Constants:
//   counter - the 4 byte value 00 00 00 01

ecdhData = ecdhKeyShare || ecdhCipherText || ecdhPublicKey
mlkemData = mlkemKeyShare || mlkemCipherText || mlkemPublicKey

KEK = SHA3-256(counter || ecdhData || mlkemData || fixedInfo)
return KEK

The value of counter MUST be set to the following octet sequence:¶

counter :=  00 00 00 01

The value of fixedInfo MUST be set according to Section 5.2.1.¶

5.2.3. Key generation procedure

The implementation MUST independently generate the ML-KEM and the ECC component keys. ML-KEM key generation follows the specification [FIPS-203] and the artifacts are encoded as fixed-length octet strings as defined in Section 5.1.2. For ECC this is done following the relative specification in [SP800-186] or [RFC5639], and encoding the outputs as fixed-length octet strings in the format specified in Table 3 or Table 4.¶

5.2.4. Encryption procedure

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

1. Take the recipient's authenticated public-key packet pkComposite and sessionKey as input¶

2. Parse the algorithm ID from pkComposite¶

3. Extract the eccPublicKey and mlkemPublicKey component from the algorithm specific data encoded in pkComposite with the format specified in Section 5.3.2.¶

4. Instantiate the ECC-KEM and the ML-KEM depending on the algorithm ID according to Table 6¶

5. Compute (eccCipherText, eccKeyShare) := ECC-KEM.Encaps(eccPublicKey)¶

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

7. Compute fixedInfo as specified in Section 5.2.1¶

8. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText, eccPublicKey, mlkemKeyShare, mlkemCipherText, mlkemPublicKey, fixedInfo) as defined in Section 5.2.2¶

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

10. Output the algorithm specific part of the PKESK as eccCipherText || mlkemCipherText len(symAlgId, C) || (|| 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.¶

5.2.5. Decryption procedure

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

1. Take the matching PKESK and own secret key packet as input¶

2. From the PKESK extract the algorithm ID and the encryptedKey, i.e., the wrapped session key¶

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

4. Parse the eccSecretKey and mlkemSecretKey from the algorithm specific data of the own secret key encoded in the format specified in Section 5.3.2¶

5. Instantiate the ECC-KEM and the ML-KEM depending on the algorithm ID according to Table 6¶

6. Parse eccCipherText, mlkemCipherText, and C from encryptedKey encoded as eccCipherText || mlkemCipherText || len(symAlgId, C) (|| symAlgId) || C as specified in Section 5.3.1, where symAlgId is present only in the case of a v3 PKESK.¶

7. Compute (eccKeyShare) := ECC-KEM.Decaps(eccCipherText, eccSecretKey, eccPublicKey)¶

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

9. Compute fixedInfo as specified in Section 5.2.1¶

10. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText, eccPublicKey, mlkemKeyShare, mlkemCipherText, mlkemPublicKey, fixedInfo) as defined in Section 5.2.2¶

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

12. Output sessionKey¶

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

The algorithm-specific fields consists of the output of the encryption procedure described in Section 5.2.4:¶

• A fixed-length octet string representing an ECC ephemeral public key in the format associated with the curve as specified in Section 5.1.1.¶

• A fixed-length octet string of the ML-KEM ciphertext, whose length depends on the algorithm ID as specified in Table 5.¶

• 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 [I-D.ietf-openpgp-crypto-refresh], for the ML-KEM+ECC 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.¶

5.3.2. Key Material Packets

The algorithm-specific public key is this series of values:¶

• A fixed-length octet string representing an EC point public key, in the point format associated with the curve specified in Section 5.1.1.¶

• A fixed-length octet string containing the ML-KEM public key, whose length depends on the algorithm ID as specified in Table 5.¶

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 5.1.1.¶

• A fixed-length octet string containing the ML-KEM secret key, whose length depends on the algorithm ID as specified in Table 5.¶

6.1.1. ECDSA-Based signatures

To sign and verify with ECDSA the following operations are defined:¶

(ecdsaSignatureR, ecdsaSignatureS) <- ECDSA.Sign(ecdsaSecretKey,
                                                 dataDigest)

and¶

(verified) <- ECDSA.Verify(ecdsaPublicKey, ecdsaSignatureR,
                           ecdsaSignatureS, dataDigest)

Here, the operation ECDSA.Sign() is defined as the algorithm in Section "6.4.1 ECDSA Signature Generation Algorithm" of [SP800-186-5], however, excluding Step 1: H = Hash(M) in that algorithm specification, as in this specification the message digest H is a direct input to the operation ECDSA.Sign(). Equivalently, the operation ECDSA.Sign() can be understood as representing the algorithm under Section "4.2.1.1. Signature Algorithm" in [TR-03111], again with the difference that in this specification the message digest H_Tau(M) appearing in Step 5 of the algorithm specification is the direct input to the operation ECDSA.Sign() and thus the hash computation is not carried out. The same statement holds for the definition of the verification operation ECDSA.Verify(): it is given either through the algorithm defined in Section "6.4.2 ECDSA Signature Verification Algorithm" of [SP800-186-5] omitting the message digest computation in Step 2 or by the algorithm in Section "4.2.1.2. Verification Algorithm" of [TR-03111] omitting the message digest computation in Step 3.¶

The public keys MUST be encoded in SEC1 format as defined in section Section 2.1.1. The secret key, as well as both values R and S of the signature MUST each be encoded as a big-endian integer in a fixed-length octet string of the specified size.¶

The following table describes the ECDSA parameters and artifact lengths:¶

6.1.2. ML-DSA signatures

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 8. All artifacts are encoded as defined in [FIPS-204].¶

6.2.1. Signature data digest

Signature data (i.e. the data to be signed) is digested prior to signing operations, see [I-D.ietf-openpgp-crypto-refresh], Section 5.2.4. Composite ML-DSA + ECC signatures MUST use the associated hash algorithm as specified in Table 9 for the signature data digest. Signatures using other hash algorithms MUST be considered invalid.¶

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

6.2.2. Key generation procedure

The implementation MUST independently generate the ML-DSA and the ECC component keys. ML-DSA key generation follows the specification [FIPS-204] and the artifacts are encoded as fixed-length octet strings as defined in Section 6.1.2. For ECC this is done following the relative specification in [SP800-186] or [RFC5639], and encoding the artifacts as specified in Section 6.1.1 as fixed-length octet strings.¶

6.2.3. Signature Generation

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

1. Generate dataDigest according to [I-D.ietf-openpgp-crypto-refresh], Section 5.2.4¶

2. Create the ECDSA signature over dataDigest with ECDSA.Sign() from Section 6.1.1¶

3. Create the ML-DSA signature over dataDigest with ML-DSA.Sign() from Section 6.1.2¶

4. Encode the ECDSA and ML-DSA signatures according to the packet structure given in Section 6.3.1.¶

6.2.4. Signature Verification

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

1. Verify the ECDSA signature with ECDSA.Verify() from Section 6.1.1¶

2. Verify the ML-DSA signature with ML-DSA.Verify() from Section 6.1.2¶

As specified in Section 4.2 an implementation MUST validate both signatures, i.e. ECDSA and ML-DSA, successfully to state that a composite ML-DSA + ECC signature is valid.¶

6.3.1. Signature Packet (Tag 2)

The composite ML-DSA + ECC schemes MUST be used only with v6 signatures, as defined in [I-D.ietf-openpgp-crypto-refresh].¶

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

• A fixed-length octet string of the big-endian encoded ECDSA value R, whose length depends on the algorithm ID as specified in Table 7.¶

• A fixed-length octet string of the big-endian encoded ECDSA value S, whose length depends on the algorithm ID as specified in Table 7.¶

• A fixed-length octet string of the ML-DSA signature value, whose length depends on the algorithm ID as specified in Table 8.¶

6.3.2. Key Material Packets

The composite ML-DSA + ECC schemes MUST be used only with v6 keys, as defined in [I-D.ietf-openpgp-crypto-refresh].¶

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

• A fixed-length octet string representing the ECDSA public key in SEC1 format, as specified in section Section 2.1.1 and with length specified in Table 7.¶

• A fixed-length octet string containing the ML-DSA public key, whose length depends on the algorithm ID as specified in Table 8.¶

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

• A fixed-length octet string representing the ECDSA secret key as a big-endian encoded integer, whose length depends on the algorithm used as specified in Table 7.¶

• A fixed-length octet string containing the ML-DSA secret key, whose length depends on the algorithm ID as specified in Table 8.¶