OpenSSH

djm@openssh.com https://www.openssh.com/

Security Secure Shell (SSHM) ssh mldsa ed25519 hybrid post-quantum This document specifies the integration of two composite post-quantum signature schemes into the Secure Shell (SSH) protocol. These schemes combine the post-quantum Module-Lattice Digital Signature Algorithm (ML-DSA) with Elliptic Curve signature algorithms (Ed25519 and ECDSA, respectively) to provide security against both quantum and classical adversaries.

Introduction The Secure Shell (SSH) protocol is a protocol for secure remote login and other secure network services over an untrusted network. The expected arrival of quantum computing poses a threat to traditional asymmetric cryptography. Post-quantum algorithms such as ML-DSA have been developed to remain secure against a quantum computer-equipped adversary. However, given the relative novelty of the post-quantum algorithms, it is desirable to use composite schemes that combine post-quantum and classical algorithms to protect against quantum attacks while ensuring the composite scheme remains at least as secure as the chosen classical algorithm alone, should a vulnerability be discovered in the post-quantum algorithm or its implementation. This document specifies two composite signature schemes for SSH, mapping the COMPSIG-MLDSA44-Ed25519-SHA512 and COMPSIG-MLDSA87-ECDSA-P384-SHA512 schemes defined in to the SSH protocol using the SSH algorithm identifiers ssh-mldsa44-ed25519 and ssh-mldsa87-p384 respectively.

Requirements Language The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here.

Terminology All encoding data types ("byte", "string", etc.) are as specified in . All length units are given in bytes unless otherwise specified.

Algorithm specifications For both the ssh-mldsa44-ed25519 and ssh-mldsa87-p384 algorithms, the underlying key generation, signing and verification primitives are as specified in , but are also described briefly below.

Key generation Keys are generated using the process specified in . ML-DSA and Elliptic Curve keys are generated separately and the results from each are combined to form the composite key. Public key concatenation follows . The private keys are also concatenated together, where the ML-DSA and EdDSA private keys are represented by their seeds, but the ECDSA private key is the private key integer. Private key concatenation follows . ML-DSA key generation uses the ML-DSA.KeyGen_internal algorithm defined in section 6.1 and not the ML-DSA.KeyGen algorithm, as only the former allows the private key seed to be emitted.

ssh-mldsa44-ed25519 For the ssh-mldsa44-ed25519 algorithm, Ed25519 key generation is described in .

Composite raw public key The public keys from the ML-DSA and Ed25519 key generation algorithms are combined by simple concatenation to form the composite public key. The composite public key consists of the raw ML-DSA-44 public key (1312 bytes) and the Ed25519 public key (32 bytes): byte[1312] mldsa_pk byte[32] ed25519_pk This 1344-byte combination is referred to as "composite_mldsa44_ed25519_public_key" henceforth in this document.

Composite raw private key The composite private key is a concatenation of the private key seeds from the respective key generation algorithms. Each seed is 32 bytes: byte[32] mldsa_seed byte[32] ed25519_seed This 64-byte combination is referred to as "composite_mldsa44_ed25519_private_key" henceforth in this document.

ssh-mldsa87-p384 For the ssh-mldsa87-p384 algorithm, ECDSA key generation is described in Appendix A.2 using the Curve P-384 domain parameters from section G.1.3.

Composite raw public key The public keys from the ML-DSA and ECDSA key generation algorithms are combined by simple concatenation to form the composite public key. It consists of the raw ML-DSA-87 public key (2592 bytes) and the uncompressed ECDSA public key "Q": byte[2592] mldsa_pk string Q This combination is referred to as "composite_mldsa87_p384_public_key" henceforth in this document.

Composite raw private key The composite private key is a concatenation of the ML-DSA seed (32 bytes) and the ECDSA private key "d". byte[32] mldsa_seed mpint d This combination is referred to as "composite_mldsa87_p384_private_key" henceforth in this document.

SSH Public Key Format In the SSH protocol, both the "ssh-mldsa44-ed25519" and "ssh-mldsa87-p384" public key types share the following wire format: string key_type_name string composite_public_key Where "key_type_name" is either "ssh-mldsa44-ed25519" or "ssh-mldsa87-p384" and "composite_public_key" is the corresponding "composite_mldsa44_ed25519_public_key" () or "composite_mldsa87_p384_public_key" ().

SSH Private Key Format When adding a key to an agent using the SSH_AGENTC_ADD_IDENTITY or SSH_AGENTC_ADD_ID_CONSTRAINED messages, the key data MUST have the following format: string key_type_name string composite_public_key string composite_private_key Where "key_type_name" is either "ssh-mldsa44-ed25519" or "ssh-mldsa87-p384". The "composite_public_key" is the corresponding "composite_mldsa44_ed25519_public_key" () or "composite_mldsa87_p384_public_key" (). The "composite_private_key" is the corresponding "composite_mldsa44_ed25519_private_key" () or "composite_mldsa87_p384_private_key" (). This private key serialisation may also be used as the basis of on-disk key formats, though these are beyond the scope of this document.

Signatures

Signature contexts The composite signature scheme used here, like its underlying ML-DSA component, accepts a Context parameter that is used to domain separate signatures. In all cases in the SSH protocol, this context value MUST be the empty string.

Signature Generation To sign a message M, the signer first constructs a message representative M' as follows: M' = Prefix || Label || len(ctx) || ctx || SHA512(M) Where:

• Prefix: The ASCII string "CompositeAlgorithmSignatures2025" [43 6F 6D 70 6F 73 69 74 65 41 6C 67 6F 72 69 74 68 6D 53 69 67 6E 61 74 75 72 65 73 32 30 32 35].
• Label: The ASCII algorithm label specific to the signature algorithm.
• len(ctx): A single unsigned byte representing the length of the context string.
• ctx: The context string.
• SHA512(M): The SHA-512 hash of the original message M.

The signer computes and combines the ML-DSA and Elliptic Curve signatures. Below, mldsa_sk, ed25519_sk, and ecdsa_sk are the private signing keys derived from or represented by mldsa_seed, ed25519_seed, and d, respectively.

ssh-mldsa44-ed25519 This algorithm uses the ASCII string "COMPSIG-MLDSA44-Ed25519-SHA512" [43 4F 4D 50 53 49 47 2D 4D 4C 44 53 41 34 34 2D 45 64 32 35 35 31 39 2D 53 48 41 35 31 32] as the Label when creating the M' message to be signed. The ML-DSA and Ed25519 signatures are calculated as:

• mldsa_sig = ML-DSA-44.Sign(mldsa_sk, M', ctx=Label)
• ed25519_sig = Ed25519.Sign(ed25519_sk, M')

The final composite signature is the concatenation of mldsa_sig and ed25519_sig in this order. byte[2420] mldsa_sig byte[64] ed25519_sig This 2484-byte combination is henceforth referred to as "composite_mldsa44_ed25519_signature".

ssh-mldsa87-p384 This algorithm uses the ASCII string "COMPSIG-MLDSA87-ECDSA-P384-SHA512" [43 4F 4D 50 53 49 47 2D 4D 4C 44 53 41 38 37 2D 45 43 44 53 41 2D 50 33 38 34 2D 53 48 41 35 31 32] as the Label when creating the M' message to be signed. The ML-DSA and ECDSA signatures are calculated as:

• mldsa_sig = ML-DSA-87.Sign(mldsa_sk, M', ctx=Label)
• r, s = ECDSA-P384.Sign(ecdsa_sk, M')

The final composite signature is the concatenation of mldsa_sig, r, and s in this order. byte[4896] mldsa_sig mpint r mpint s This combination is henceforth referred to as "composite_mldsa87_p384_signature".

SSH Signature Format Signatures are represented in SSH using the following format: string signature_type_name string composite_signature Where "signature_type_name" is either "ssh-mldsa44-ed25519" or "ssh-mldsa87-p384" and "composite_signature" is the corresponding "composite_mldsa44_ed25519_signature" () or "composite_mldsa87_p384_signature" ().

Signature Verification To verify a signature, the verifier reconstructs M' using the same process as defined for signature generation and verifies the ML-DSA and Elliptic Curve signatures. Both ML-DSA and Elliptic Curve verification operations MUST return success for the composite signature to verify successfully. Failure of either verification operation MUST cause the composite signature verification to fail.

ssh-mldsa44-ed25519 To verify an ssh-mldsa44-ed25519 signature, the verifier performs:

• ML-DSA-44.Verify(mldsa_pk, M', mldsa_sig, ctx=Label)
• Ed25519.Verify(ed25519_pk, M', ed25519_sig)

Both signatures must verify for the composite signature to verify.

ssh-mldsa87-p384 To verify an ssh-mldsa87-p384 signature, the verifier performs:

• ML-DSA-87.Verify(mldsa_pk, M', mldsa_sig, ctx=Label)
• ECDSA-P384.Verify(Q, M', r, s)

Both signatures must verify for the composite signature to verify.

Security Considerations The security considerations of apply here. The security of this composite scheme depends on the security of both component algorithms. An adversary must forge both ML-DSA and Elliptic Curve signatures in order to forge a composite signature. Implementations MUST NOT reuse component key material between composite and non-composite keys, or between multiple composite keys. See section 9.3. If neither of the component algorithms are broken, both ssh-mldsa44-ed25519 and ssh-mldsa87-p384 are Existentially Unforgeable under Chosen-Message Attack (EUF-CMA), since ML-DSA, Ed25519, and ECDSA are all EUF-CMA and SHA-512 is collision-resistant. This property will be degraded against particular adversary classes if either of of the constituent signature algorithms is broken. If ML-DSA is broken then the composite will not be EUF-CMA against quantum adversaries. Similarly, if the classical signature scheme is broken then the composite will not be EUF-CMA against classical adversaries. See section 9.2.1. This composite scheme is not Strongly Unforgeable under Chosen-Message Attack (SUF-CMA). Systems that rely on this property SHOULD NOT use this scheme. This composite scheme provides Weak Non-Separability (WNS) for both components due to evidence of the composite in the Prefix in `M'`. See section 9.2.3.

IANA Considerations IANA is requested to register the algorithm names "ssh-mldsa44-ed25519" and "ssh-mldsa87-p384" in the "Public Key Algorithm Names" registry ().

References Normative References National Institute of Standards and Technology (U.S.) National Institute of Standards and Technology FIPS PUB 186-5 National Institute of Standards and Technology SP 800-186 Informative References IANA

Acknowledgements Cindy Lin offered valuable feedback on this document.