Internet-Draft Composite ML-DSA June 2025
Ounsworth, et al. Expires 5 December 2025 [Page]
Workgroup:
LAMPS
Internet-Draft:
draft-ietf-lamps-pq-composite-sigs-latest
Published:
Intended Status:
Standards Track
Expires:
Authors:
M. Ounsworth
Entrust
J. Gray
Entrust
M. Pala
OpenCA Labs
J. Klaussner
Bundesdruckerei GmbH
S. Fluhrer
Cisco Systems

Composite ML-DSA for use in X.509 Public Key Infrastructure and CMS

Abstract

This document defines combinations of ML-DSA [FIPS.204] in hybrid with traditional algorithms RSASSA-PKCS1-v1_5, RSASSA-PSS, ECDSA, Ed25519, and Ed448. These combinations are tailored to meet security best practices and regulatory requirements. Composite ML-DSA is applicable in any application that uses X.509 or PKIX data structures that accept ML-DSA, but where the operator wants extra protection against breaks or catastrophic bugs in ML-DSA.

About This Document

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

The latest revision of this draft can be found at https://lamps-wg.github.io/draft-composite-sigs/draft-ietf-lamps-pq-composite-sigs.html. Status information for this document may be found at https://datatracker.ietf.org/doc/draft-ietf-lamps-pq-composite-sigs/.

Discussion of this document takes place on the LAMPS Working Group mailing list (mailto:spams@ietf.org), which is archived at https://datatracker.ietf.org/wg/lamps/about/. Subscribe at https://www.ietf.org/mailman/listinfo/spams/.

Source for this draft and an issue tracker can be found at https://github.com/lamps-wg/draft-composite-sigs.

Status of This Memo

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

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This Internet-Draft will expire on 5 December 2025.

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Table of Contents

1. Changes in -05

Interop-affecting changes:

Editorial changes:

Still to do in a future version:

2. Introduction

The advent of quantum computing poses a significant threat to current cryptographic systems. Traditional cryptographic algorithms such as RSA, Diffie-Hellman, DSA, and their elliptic curve variants are vulnerable to quantum attacks. During the transition to post-quantum cryptography (PQC), there is considerable uncertainty regarding the robustness of both existing and new cryptographic algorithms. While we can no longer fully trust traditional cryptography, we also cannot immediately place complete trust in post-quantum replacements until they have undergone extensive scrutiny and real-world testing to uncover and rectify potential implementation flaws.

Unlike previous migrations between cryptographic algorithms, the decision of when to migrate and which algorithms to adopt is far from straightforward. Even after the migration period, it may be advantageous for an entity's cryptographic identity to incorporate multiple public-key algorithms to enhance security.

Cautious implementers may opt to combine cryptographic algorithms in such a way that an attacker would need to break all of them simultaneously to compromise the protected data. These mechanisms are referred to as Post-Quantum/Traditional (PQ/T) Hybrids [I-D.ietf-pquip-pqt-hybrid-terminology]. Combining multiple algorithms can help to eliminate single points of failure, where a component algorithm is a technology that may fail in the future.

Certain jurisdictions are already recommending or mandating that PQC lattice schemes be used exclusively within a PQ/T hybrid framework. The use of Composite scheme provides a straightforward implementation of hybrid solutions compatible with (and advocated by) some governments and cybersecurity agencies [BSI2021].

Composite ML-DSA is applicable in any application that would otherwise use ML-DSA, but wants the protection against breaks or catastrophic bugs in ML-DSA.

2.1. Conventions and Terminology

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 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here. These words may also appear in this document in lower case as plain English words, absent their normative meanings.

This document is consistent with the terminology defined in [I-D.ietf-pquip-pqt-hybrid-terminology]. In addition, the following terminology is used throughout this document:

ALGORITHM: The usage of the term "algorithm" within this document generally refers to any function which has a registered Object Identifier (OID) for use within an ASN.1 AlgorithmIdentifier. This loosely, but not precisely, aligns with the definitions of "cryptographic algorithm" and "cryptographic scheme" given in [I-D.ietf-pquip-pqt-hybrid-terminology].

BER: Basic Encoding Rules (BER) as defined in [X.690].

CLIENT: Any software that is making use of a cryptographic key. This includes a signer, verifier, encrypter, decrypter. This is not meant to imply any sort of client-server relationship between the communicating parties.

DER: Distinguished Encoding Rules as defined in [X.690].

PKI: Public Key Infrastructure, as defined in [RFC5280].

PUBLIC / PRIVATE KEY: The public and private portion of an asymmetric cryptographic key, making no assumptions about which algorithm.

SIGNATURE: A digital cryptographic signature, making no assumptions about which algorithm.

Notation: The algorithm descriptions use python-like syntax. The following symbols deserve special mention:

  • || represents concatenation of two byte arrays.

  • [:] represents byte array slicing.

  • (a, b) represents a pair of values a and b. Typically this indicates that a function returns multiple values; the exact conveyance mechanism -- tuple, struct, output parameters, etc -- is left to the implementer.

  • (a, _): represents a pair of values where one -- the second one in this case -- is ignored.

2.2. Composite Design Philosophy

[I-D.ietf-pquip-pqt-hybrid-terminology] defines composites as:

  • Composite Cryptographic Element: A cryptographic element that incorporates multiple component cryptographic elements of the same type in a multi-algorithm scheme.

Composite keys, as defined here, follow this definition and should be regarded as a single key that performs a single cryptographic operation such as key generation, signing, verifying, encapsulating, or decapsulating -- using its internal sequence of component keys as if they form a single key. This generally means that the complexity of combining algorithms can and should be handled by the cryptographic library or cryptographic module, and the single composite public key, private key, ciphertext and signature can be carried in existing fields in protocols such as PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], CMS [RFC5652], and the Trust Anchor Format [RFC5914]. In this way, composites achieve "protocol backwards-compatibility" in that they will drop cleanly into any protocol that accepts an analogous single-algorithm cryptographic scheme without requiring any modification of the protocol to handle multiple algorithms.

3. Overview of the Composite ML-DSA Signature Scheme

Composite schemes are defined as cryptographic primitives that consist of three algorithms:

We define the following algorithms which we use to serialize and deserialize the public and private keys

We define the following algorithms which are used to serialize and deseralize the composite signature value

A composite signature allows the security properties of the two underlying algorithms to be combined via standard signature operations Sign() and Verify().

This specification uses the Post-Quantum signature scheme ML-DSA as specified in [FIPS.204] and [I-D.ietf-lamps-dilithium-certificates]. For Traditional signature schemes, this document uses the RSASSA-PKCS1-v1_5 and RSASSA-PSS algorithms defined in [RFC8017], the Elliptic Curve Digital Signature Algorithm ECDSA scheme defined in section 6 of [FIPS.186-5], and Ed25519 / Ed448 which are defined in [RFC8410]. A simple "signature combiner" function which prepends a domain separator value specific to the composite algorithm is used to bind the two component signatures to the composite algorithm and achieve weak non-separability.

3.1. Pre-hashing and Randomizer

In [FIPS.204] NIST defines separate algorithms for "pure" ML-DSA and "pre-hashed" signing modes, referred to as "ML-DSA" and "HashML-DSA" respectively. This document takes a middle-ground approach which borrows some design elements from each of ML-DSA and HashML-DSA and introduces a new design element -- the pre-hash randomizer inspired by [BonehShoup] -- which together provides a compromised balance between performance and security.

Composite-ML-DSA offers improved performance by pre-hashing the potentially large message only once and then passing the shorter digest into the component algorithms. The actual length of the to-be-signed message M' depends on the application context ctx provided at runtime but since ctx has a maximum length of 255 bytes, M' has a fixed maximum length which depends on the length of HashOID and the output size of the hash function chosen as PH, but can be computed per composite algorithm.

See Section 10.5 for a discussion of security implications of the randomized pre-hash.

This simplification into a single strongly-pre-hashed algorithm avoids the need for duplicate sets of "Composite-ML-DSA" and "Hash-Composite-ML-DSA" algorithms.

3.2. Prefix, Domain Separators and CTX

When constructing the message representative M', first a fixed prefix string is pre-pended which is the byte encoding of the ASCII string "CompositeAlgorithmSignatures2025" which in hex is:

 436F6D706F73697465416C676F726974686D5369676E61747572657332303235

This allows for cautious implementers to wrap their existing Traditional Verify() implementations with a guard that looks for messages starting with this string and fail with an error -- i.e. this can act as an extra protection against taking a composite signature and splitting it back into components. However, an implementation that does this will be unable to perform a Traditional signature and verification on a message which happens to start with this string. The designers accepted this trade-off.

The Domain separator defined in Section 7.2 is concatenated with the length of the context in bytes, the context, an additional DER encoded value that represents the OID of the Hash function and finally the hash of the message to be signed. After that, the signature process for each component algorithm is invoked and the values are serialized into a composite signature value as per Section 5.3.

A composite signature's value MUST include two signature components and MUST be in the same order as the components from the corresponding signing key.

Note that there are two different context strings ctx here: the first is the application context that is passed in to Composite-ML-DSA.Sign and bound to the composite signature combiner. The second is the ctx that is passed down into the underlying ML-DSA.Sign and here Composite-ML-DSA itself is the application that we wish to bind, and outer ctx is already contained within the M' message.

4. Composite ML-DSA Functions

This section describes the composite ML-DSA functions needed to instantiate the public signature API in Section 3.

4.1. Key Generation

In order to maintain security properties of the composite, applications that use composite keys MUST always perform fresh key generations of both component keys and MUST NOT reuse existing key material. See Section 10.3 for a discussion.

To generate a new keypair for Composite schemes, the KeyGen() -> (pk, sk) function is used. The KeyGen() function calls the two key generation functions of the component algorithms independently. Multi-process or multi-threaded applications might choose to execute the key generation functions in parallel for better key generation performance.

The following describes how to instantiate a KeyGen() function for a given composite algorithm reperesented by <OID>.

Composite-ML-DSA<OID>.KeyGen() -> (pk, sk)

Explicit inputs:

  None

Implicit inputs mapped from <OID>:

  ML-DSA     The underlying ML-DSA algorithm and
             parameter set, for example, could be "ML-DSA-65".

  Trad       The underlying traditional algorithm and
             parameter set, for example "RSASSA-PSS"
             or "Ed25519".

Output:

  (pk, sk)   The composite keypair.


Key Generation Process:

  1. Generate component keys

      mldsaSeed = Random(32)
      (mldsaPK, _) = ML-DSA.KeyGen(mldsaSeed)
      (tradPK, tradSK) = Trad.KeyGen()

      Note: Step 1 shows an example of an ML-DSA seed being generated
      externally (outside the ML-DSA.KeyGen()) routine. The seed may also
      be generated inside the ML-DSA.KeyGen() routine depending on the
      implementation and cryptographic library API.

  2. Check for component key gen failure

      if NOT (mldsaPK, mldsaSK) or NOT (tradPK, tradSK):
        output "Key generation error"

  3. Output the composite public and private keys

    pk = SerializePublicKey(mldsaPK, tradPK)
    sk = SerializePrivateKey(mldsaSeed, tradSK)
    return (pk, sk)
Figure 1: Composite KeyGen(pk, sk)

In order to ensure fresh keys, the key generation functions MUST be executed for both component algorithms. Compliant parties MUST NOT use, import or export component keys that are used in other contexts, combinations, or by themselves as keys for standalone algorithm use. For more details on the security considerations around key reuse, see section Section 10.3.

Note that in step 2 above, both component key generation processes are invoked, and no indication is given about which one failed. This SHOULD be done in a timing-invariant way to prevent side-channel attackers from learning which component algorithm failed.

Variations in the keygen process above and signature processes below to accommodate particular private key storage mechanisms or alternate interfaces to the underlying cryptographic modules are considered to be conformant to this specification so long as they produce the same output and error handling. For example, it is possible to use component private keys stored in separate software or hardware modules where it is not possible to do a joint keygen. It is also possible that the underlying cryptographic module does not expose a "ML-DSA.KeyGen(seed)` that accepts an externally-generated seed.

4.2. Sign

This mode mirrors HashML-DSA.Sign(sk, M, ctx, PH) defined in Algorithm 4 Section 5.4.1 of [FIPS.204]. Note that while the external behaviour of Composite-ML-DSA mirrors that of HashML-DSA, internally it uses pure ML-DSA as the component algorithm because there is no reason to pre-hash twice.

See Section 3.1 for a discussion of the pre-hashed design and randomizer r.

See Section 3.2 for a discussion on the domain separator and context values.

The following describes how to instantiate a Sign(..) function for a given composite algorithm reperesented by <OID>.

Composite-ML-DSA<OID>.Sign (sk, M, ctx, PH) -> (signature)

Explicit inputs:

  sk    Composite private key consisting of signing private keys for
        each component.

  M     The Message to be signed, an octet string.

  ctx   The Message context string used in the composite signature
        combiner, which defaults to the empty string.

  PH    The Message Digest Algorithm for pre-hashing.
        See section on pre-hashing the message below.

Implicit inputs mapped from <OID>:

  ML-DSA    The underlying ML-DSA algorithm and
            parameter set, for example, could be "ML-DSA-65".

  Trad      The underlying traditional algorithm and
            parameter set, for example "RSASSA-PSS with id-sha256"
            or "Ed25519".

  Prefix    The prefix String which is the byte encoding of the String
            "CompositeAlgorithmSignatures2025" which in hex is
            436F6D706F73697465416C676F726974686D5369676E61747572657332303235

  Domain    Domain separator value for binding the signature to the
            Composite OID. Additionally, the composite Domain is passed into
            the underlying ML-DSA primitive as the ctx.
            Domain values are defined in the "Domain Separators" section below.

  HashOID   The DER Encoding of the Object Identifier of the
            PreHash algorithm (PH) which is passed into the function.

Output:
  signature   The composite signature, a CompositeSignatureValue.


Signature Generation Process:

  1. If len(ctx) > 255:
      return error

  2. Compute the Message format M'.
     As in FIPS 204, len(ctx) is encoded as a single unsigned byte.
     Randomize the pre-hash.

        r = Random(32)
        M' :=  Prefix || Domain || len(ctx) || ctx || r
                                || HashOID || PH( r || M )

  3. Separate the private key into component keys
     and re-generate the ML-DSA key from seed.

       (mldsaSeed, tradSK) = DeserializePrivateKey(sk)
       (_, mldsaSK) = ML-DSA.KeyGen(mldsaSeed)

  4. Generate the 2 component signatures independently, by calculating
     the signature over M' according to their algorithm specifications.

       mldsaSig = ML-DSA.Sign( mldsaSK, M', ctx=Domain )
       tradSig = Trad.Sign( tradSK, M' )

  5. If either ML-DSA.Sign() or Trad.Sign() return an error, then this
     process must return an error.

      if NOT mldsaSig or NOT tradSig:
        output "Signature generation error"

  6. Output the encoded composite signature.

      signature = SerializeSignatureValue(r, mldsaSig, tradSig)
      return signature
Figure 2: Composite-ML-DSA.Sign(sk, M, ctx, PH)

Note that in step 5 above, both component signature processes are invoked, and no indication is given about which one failed. This SHOULD be done in a timing-invariant way to prevent side-channel attackers from learning which component algorithm failed.

4.3. Verify

This mode mirrors HashML-DSA.Verify(pk, M, signature, ctx, PH) defined in Algorithm 5 Section 5.4.1 of [FIPS.204].

Compliant applications MUST output "Valid signature" (true) if and only if all component signatures were successfully validated, and "Invalid signature" (false) otherwise.

The following describes how to instantiate a Verify(..) function for a given composite algorithm reperesented by <OID>.

Composite-ML-DSA.Verify(pk, M, signature, ctx, PH)

Explicit inputs:

  pk          Composite public key consisting of verification public
              keys for each component.

  M           Message whose signature is to be verified, an octet
              string.

  signature   CompositeSignatureValue containing the component
              signature values (mldsaSig and tradSig) to be verified.

  ctx         The Message context string used in the composite signature
              combiner, which defaults to the empty string.

  PH          The Message Digest Algorithm for pre-hashing. See
              section on pre-hashing the message below.

Implicit inputs mapped from <OID>:

  ML-DSA    The underlying ML-DSA algorithm and
            parameter set, for example, could be "ML-DSA-65".

  Trad      The underlying traditional algorithm and
            parameter set, for example "RSASSA-PSS with id-sha256"
            or "Ed25519".

  Prefix    The prefix String which is the byte encoding of the String
            "CompositeAlgorithmSignatures2025" which in hex is
            436F6D706F73697465416C676F726974686D5369676E61747572657332303235

 Domain     Domain separator value for binding the signature to the
            Composite OID. Additionally, the composite Domain is passed into
            the underlying ML-DSA primitive as the ctx.
            Domain values are defined in the "Domain Separators" section below.

 HashOID    The DER Encoding of the Object Identifier of the
            PreHash algorithm (PH) which is passed into the function.

Output:

  Validity (bool)   "Valid signature" (true) if the composite
                    signature is valid, "Invalid signature"
                    (false) otherwise.

Signature Verification Process:

  1. If len(ctx) > 255
       return error

  2. Separate the keys and signatures

     (mldsaPK, tradPK)       = DeserializePublicKey(pk)
     (r, mldsaSig, tradSig)  = DeserializeSignatureValue(signature)

   If Error during Desequencing, or if any of the component
   keys or signature values are not of the correct key type or
   length for the given component algorithm then output
   "Invalid signature" and stop.

  3. Check the length of r
     if len(r) != 32
       return error

  3. Compute a Hash of the Message.
     As in FIPS 204, len(ctx) is encoded as a single unsigned byte.

      M' = Prefix || Domain || len(ctx) || ctx || r
                            || HashOID || PH( r || M )

  4. Check each component signature individually, according to its
     algorithm specification.
     If any fail, then the entire signature validation fails.

      if not ML-DSA.Verify( mldsaPK, M', mldsaSig, ctx=Domain ) then
          output "Invalid signature"

      if not Trad.Verify( tradPK, M', tradPK ) then
          output "Invalid signature"

      if all succeeded, then
         output "Valid signature"
Figure 3: Composite-ML-DSA.Verify(pk, M, signature, ctx, PH)

Note that in step 4 above, the function fails early if the first component fails to verify. Since no private keys are involved in a signature verification, there are no timing attacks to consider, so this is ok.

5. Serialization

This section presents routines for serializing and deserializing composite public keys, private keys (seeds), and signature values to bytes via simple concatenation of the underlying encodings of the component algorithms. The functions defined in this section are considered internal implementation detail and are referenced from within the public API definitions in Section 4.

Deserialization is possible because ML-DSA has fixed-length public keys, private keys (seeds), and signature values as shown in the following table.

Table 1: ML-DSA Key and Signature Sizes in bytes
Algorithm Public key Private key Signature
ML-DSA-44 1312 32 2420
ML-DSA-65 1952 32 3309
ML-DSA-87 2592 32 4627

When these values are required to be carried in an ASN.1 structure, they are wrapped as described in Section 6.1.

While ML-DSA has a single fixed-size representation for each of public key, private key (seed), and signature, the traditional component might allow multiple valid encodings; for example an elliptic curve public key might be validly encoded as either compressed or uncompressed [SEC1], or an RSA private key could be encoded in Chinese Remainder Theorem form [RFC8017]. In order to obtain interoperability, composite algorithms MUST use the following encodings of the underlying components:

In the event that a composite implementation uses an underlying implementation of the traditional component that requires a different encoding, it is the responsibility of the composite implementation to perform the necessary transcoding. Even with fixed encodings for the traditional component, there may be slight differences in encoded size of the traditional component due to, for example, encoding rules that drop leading zeroes. See Appendix A for further discussion of encoded size of each composite algorithm.

5.1. SerializePublicKey and DeserializePublicKey

The serialization routine for keys simply concatenates the fixed-length public keys of the component signature algorithms, as defined below:

Composite-ML-DSA.SerializePublicKey(mldsaPK, tradPK) -> bytes

Explicit Input:

  mldsaPK  The ML-DSA public key, which is bytes.

  tradPK   The traditional public key in the appropriate
           bytes-like encoding for the underlying component algorithm.

Implicit inputs:

  None

Output:

  bytes   The encoded composite public key


Serialization Process:

  1. Combine and output the encoded public key

     output mldsaPK || tradPK
Figure 4: SerializePublicKey(mldsaPK, tradPK) -> bytes

Deserialization reverses this process, raising an error in the event that the input is malformed. Each component key is deserialized according to their respective standard as shown in Appendix C.

The following describes how to instantiate a DeserializePublicKey(bytes) function for a given composite algorithm reperesented by <OID>.

Composite-ML-DSA.DeserializePublicKey(bytes) -> (mldsaPK, tradPK)

Explicit Input:

  bytes   An encoded composite public key

Implicit inputs mapped from <OID>:

  ML-DSA   The underlying ML-DSA algorithm and
           parameter set to use, for example, could be "ML-DSA-65".

Output:

  mldsaPK  The ML-DSA public key, which is bytes.

  tradPK   The traditional public key in the appropriate
           bytes-like encoding for the underlying component algorithm.

Deserialization Process:

  1. Parse each constituent encoded public key.
       The length of the mldsaKey is known based on the size of
       the ML-DSA component key length specified by the Object ID

     switch ML-DSA do
        case ML-DSA-44:
          mldsaPK = bytes[:1312]
          tradPK  = bytes[1312:]
        case ML-DSA-65:
          mldsaPK = bytes[:1952]
          tradPK  = bytes[1952:]
        case ML-DSA-87:
          mldsaPK = bytes[:2592]
          tradPK  = bytes[2592:]

     Note that while ML-DSA has fixed-length keys, RSA and ECDH
     may not, depending on encoding, so rigorous length-checking
     of the overall composite key is not always possible.

  2. Output the component public keys

     output (mldsaPK, tradPK)
Figure 5: DeserializePublicKey(bytes) -> (mldsaPK, tradPK)

5.2. SerializePrivateKey and DeserializePrivateKey

The serialization routine for keys simply concatenates the fixed-length private keys of the component signature algorithms, as defined below:

Composite-ML-DSA.SerializePrivateKey(mldsaSeed, tradSK) -> bytes

Explicit Input:

  mldsaSeed  The ML-DSA private key, which is the bytes of the seed.

  tradSK     The traditional private key in the appropriate
             encoding for the underlying component algorithm.

Implicit inputs:

  None

Output:

  bytes   The encoded composite private key

Serialization Process:

  1. Combine and output the encoded private key

     output mldsaSeed || tradSK
Figure 6: SerializePrivateKey(mldsaSeed, tradSK) -> bytes

Deserialization reverses this process, raising an error in the event that the input is malformed.

Composite-ML-DSA.DeserializePrivateKey(bytes) -> (mldsaSeed, tradSK)

Explicit Input:

  bytes   An encoded composite private key

Implicit inputs:

  That an ML-DSA private key is 32 bytes for all parameter sets.

Output:

  mldsaSeed  The ML-DSA private key, which is the bytes of the seed.

  tradSK     The traditional private key in the appropriate
             encoding for the underlying component algorithm.

Deserialization Process:

  1. Parse each constituent encoded key.
       The length of an ML-DSA private key is always a 32 byte seed
       for all parameter sets.

      mldsaSeed = bytes[:32]
      tradSK  = bytes[32:]

     Note that while ML-KEM has fixed-length keys (seeds), RSA and ECDH
     may not, depending on encoding, so rigorous length-checking
     of the overall composite key is not always possible.

  2. Output the component private keys

     output (mldsaSeed, tradSK)
Figure 7: DeserializeKey(bytes) -> (mldsaSeed, tradSK)

5.3. SerializeSignatureValue and DeserializeSignatureValue

The serialization routine for the CompositeSignatureValue simply concatenates the fixed-length ML-DSA signature value with the signature value from the traditional algorithm, as defined below:

Composite-ML-DSA.SerializeSignatureValue(r, mldsaSig, tradSig) -> bytes

Explicit Inputs:

  r         The 32 byte signature randomizer.

  mldsaSig  The ML-DSA signature value, which is bytes.

  tradSig   The traditional signature value in the appropriate
            encoding for the underlying component algorithm.

Implicit inputs:

  None

Output:

  bytes   The encoded CompositeSignatureValue

Serialization Process:

  1. Combine and output the encoded composite signature

     output r || mldsaSig || tradSig
Figure 8: SerializeSignatureValue(r, mldsaSig, tradSig) -> bytes

Deserialization reverses this process, raising an error in the event that the input is malformed. Each component signature is deserialized according to their respective standard as shown in Appendix C.

The following describes how to instantiate a DeserializeSignatureValue(bytes) function for a given composite algorithm reperesented by <OID>.

Composite-ML-DSA<OID>.DeserializeSignatureValue(bytes) -> (r, mldsaSig, tradSig)

Explicit Input:

  bytes   An encoded CompositeSignatureValue

Implicit inputs:

  ML-DSA   The underlying ML-DSA algorithm and
           parameter set to use, for example, could be "ML-DSA-65".

Output:

  r         The 32 byte signature randomizer.

  mldsaSig  The ML-DSA signature value, which is bytes.

  tradSig   The traditional signature value in the appropriate
            encoding for the underlying component algorithm.

Deserialization Process:

  1. Parse the randomizer r.

     r = bytes[:32]
     sigs = bytes[32:]  # truncate off the randomizer

  2. Parse each constituent encoded signature.
       The length of the mldsaSig is known based on the size of
       the ML-DSA component signature length specified by the Object ID.

     switch ML-DSA do
        case ML-DSA-44:
          mldsaSig = sigs[:2420]
          tradSig  = sigs[2420:]
        case ML-DSA-65:
          mldsaSig = sigs[:3309]
          tradSig  = sigs[3309:]
        case ML-DSA-87:
          mldsaSig = sigs[:4627]
          tradSig  = sigs[4627:]

     Note that while ML-DSA has fixed-length signatures, RSA and ECDSA
     may not, depending on encoding, so rigorous length-checking is
     not always possible here.

  2. Output the component signature values

     output (r, mldsaSig, tradSig)
Figure 9: DeserializeSignatureValue(bytes) -> (r, mldsaSig, tradSig)

6. Use within X.509 and PKIX

The following sections provide processing logic and the necessary ASN.1 modules necessary to use composite ML-DSA within X.509 and PKIX protocols.

While composite ML-DSA keys and signature values MAY be used raw, the following sections provide conventions for using them within X.509 and other PKIX protocols, including defining ASN.1-based wrappers for the binary composite values such that these structures can be used as a drop-in replacement for existing public key and ciphertext fields such as those found in PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], CMS [RFC5652].

6.1. Encoding to DER

The serialization routines presented in Section 5 produce raw binary values. When these values are required to be carried within a DER-endeded message format such as an X.509's subjectPublicKey BIT STRING and signatureValue [RFC5280] or a CMS SignerInfo.signature OCTET STRING [RFC5652], then the composite value MUST be wrapped into a DER BIT STRING or OCTET STRING in the obvious ways:

When a BIT STRING is required, the octets of the composite data value SHALL be used as the bits of the bit string, with the most significant bit of the first octet becoming the first bit, and so on, ending with the least significant bit of the last octet becoming the last bit of the bit string.

When an OCTET STRING is required, the DER encoding of the composite data value SHALL be used directly.

6.2. Key Usage Bits

When any of the Composite ML-DSA AlgorithmIdentifier appears in the SubjectPublicKeyInfo field of an X.509 certificate [RFC5280], the key usage certificate extension MUST only contain only signing-type key usages.

The normal keyUsage rules for signing-type keys from [RFC5280] apply, and are reproduced here for completeness.

For Certification Authority (CA) certificates that carry a composite public key, any combination of the following values MAY be present and any other values MUST NOT be present:

digitalSignature;
nonRepudiation;
keyCertSign; and
cRLSign.

For End Entity certificates, any combination of the following values MAY be present and any other values MUST NOT be present:

digitalSignature; and
nonRepudiation;

Composite ML-DSA keys MUST NOT be used in a "dual usage" mode because even if the traditional component key supports both signing and encryption, the post-quantum algorithms do not and therefore the overall composite algorithm does not.

6.3. ASN.1 Definitions

The wire encoding of a Composite ML-DSA public key is:

The following ASN.1 Information Object Class is defined to allow for compact definitions of each composite algorithm, leading to a smaller overall ASN.1 module.

pk-CompositeSignature {OBJECT IDENTIFIER:id, PublicKeyType}
    PUBLIC-KEY ::= {
      IDENTIFIER id
      KEY BIT STRING
      PARAMS ARE absent
      CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign}
    }

As an example, the public key type id-MLDSA44-ECDSA-P256-SHA256 is defined as:

id-MLDSA44-ECDSA-P256-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{
    id-MLDSA44-ECDSA-P256,
    CompositeMLDSAPublicKey }

The full set of key types defined by this specification can be found in the ASN.1 Module in Section 8.

The ASN.1 algorithm object for a composite signature is:

sa-CompositeSignature{OBJECT IDENTIFIER:id,
   PUBLIC-KEY:publicKeyType }
      SIGNATURE-ALGORITHM ::=  {
         IDENTIFIER id
         VALUE BIT STRING
         PARAMS ARE absent
         PUBLIC-KEYS {publicKeyType}
      }

Use cases that require an interoperable encoding for composite private keys will often need to place a composite private key inside a OneAsymmetricKey structure defined in [RFC5958], such as when private keys are carried in PKCS #12 [RFC7292], CMP [RFC4210] or CRMF [RFC4211]. The definition of OneAsymmetricKey is copied here for convenience:

 OneAsymmetricKey ::= SEQUENCE {
       version                   Version,
       privateKeyAlgorithm       PrivateKeyAlgorithmIdentifier,
       privateKey                PrivateKey,
       attributes            [0] Attributes OPTIONAL,
       ...,
       [[2: publicKey        [1] PublicKey OPTIONAL ]],
       ...
     }
  ...
  PrivateKey ::= OCTET STRING
                        -- Content varies based on type of key.  The
                        -- algorithm identifier dictates the format of
                        -- the key.

When a composite private key is conveyed inside a OneAsymmetricKey structure (version 1 of which is also known as PrivateKeyInfo) [RFC5958], the privateKeyAlgorithm field SHALL be set to the corresponding composite algorithm identifier defined according to Section 7 and its parameters field MUST be absent. The privateKey field SHALL contain the OCTET STRING reperesentation of the serialized composite private key as per Section 5.2. The publicKey field remains OPTIONAL. If the publicKey field is present, it MUST be a composite public key as per Section 5.1.

Some applications may need to reconstruct the OneAsymmetricKey objects corresponding to each component private key. Section 7 provides the necessary mapping between composite and their component algorithms for doing this reconstruction.

Component keys of a composite MUST NOT be used in any other type of key or as a standalone key. For more details on the security considerations around key reuse, see section Section 10.3.

7. Algorithm Identifiers

This table summarizes the list of Composite ML-DSA algorithms and lists the OID and the two component algorithms. Domain separator values are defined below in Section 7.2.

EDNOTE: these are prototyping OIDs to be replaced by IANA.

<CompSig> is equal to 2.16.840.1.114027.80.8.1

7.1. Composite-ML-DSA Algorithm Identifiers

Composite-ML-DSA Signature public key types:

Table 2: Hash ML-DSA Composite Signature Algorithms
Composite Signature Algorithm OID First Algorithm Second Algorithm Pre-Hash
id-MLDSA44-RSA2048-PSS-SHA256 <CompSig>.100 id-ML-DSA-44 id-RSASSA-PSS with id-sha256 id-sha256
id-MLDSA44-RSA2048-PKCS15-SHA256 <CompSig>.101 id-ML-DSA-44 sha256WithRSAEncryption id-sha256
id-MLDSA44-Ed25519-SHA512 <CompSig>.102 id-ML-DSA-44 id-Ed25519 id-sha512
id-MLDSA44-ECDSA-P256-SHA256 <CompSig>.103 id-ML-DSA-44 ecdsa-with-SHA256 with secp256r1 id-sha256
id-MLDSA65-RSA3072-PSS-SHA512 <CompSig>.104 id-ML-DSA-65 id-RSASSA-PSS with id-sha256 id-sha512
id-MLDSA65-RSA3072-PKCS15-SHA512 <CompSig>.105 id-ML-DSA-65 sha256WithRSAEncryption id-sha512
id-MLDSA65-RSA4096-PSS-SHA512 <CompSig>.106 id-ML-DSA-65 id-RSASSA-PSS with id-sha384 id-sha512
id-MLDSA65-RSA4096-PKCS15-SHA512 <CompSig>.107 id-ML-DSA-65 sha384WithRSAEncryption id-sha512
id-MLDSA65-ECDSA-P256-SHA512 <CompSig>.108 id-ML-DSA-65 ecdsa-with-SHA256 with secp256r1 id-sha512
id-MLDSA65-ECDSA-P384-SHA512 <CompSig>.109 id-ML-DSA-65 ecdsa-with-SHA384 with secp384r1 id-sha512
id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 <CompSig>.110 id-ML-DSA-65 ecdsa-with-SHA256 with brainpoolP256r1 id-sha512
id-MLDSA65-Ed25519-SHA512 <CompSig>.111 id-ML-DSA-65 id-Ed25519 id-sha512
id-MLDSA87-ECDSA-P384-SHA512 <CompSig>.112 id-ML-DSA-87 ecdsa-with-SHA384 with secp384r1 id-sha512
id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 <CompSig>.113 id-ML-DSA-87 ecdsa-with-SHA384 with brainpoolP384r1 id-sha512
id-MLDSA87-Ed448-SHAKE256 <CompSig>.114 id-ML-DSA-87 id-Ed448 id-shake256/64
id-MLDSA87-RSA4096-PSS-SHA512 <CompSig>.115 id-ML-DSA-87 id-RSASSA-PSS with id-sha384 id-sha512
id-MLDSA87-ECDSA-P521-SHA512 <CompSig>.116 id-ML-DSA-87 ecdsa-with-SHA512 with secp521r1 id-sha512

Note that pre-hash functions were chosen to roughly match the security level of the stronger component. In the case of Ed25519 and Ed448 they match the hash function defined in [RFC8032]; SHA512 for Ed25519ph and SHAKE256(x, 64) (that is, 64 bytes of SHAKE256 output) for Ed448

See the ASN.1 module in Section 8 for the explicit definitions of the above Composite ML-DSA algorithms.

The Pre-Hash algorithm is used as the PH algorithm and the DER Encoded OID value of this Hash is used as HashOID for the Message format in step 2 of Composite-ML-DSA.Sign in section Section 4.2 and Composite-ML-DSA.Verify in Section 4.3.

As the number of algorithms can be daunting to implementers, see Appendix E.3 for a discussion of choosing a subset to support.

Full specifications for the referenced algorithms can be found in Appendix C.

7.2. Domain Separators

As mentioned above, the OID input value is used as a domain separator for the Composite Signature Generation and verification process and is the DER encoding of the OID. The following table shows the HEX encoding for each Signature Algorithm.

Table 3: Pure ML-DSA Composite Signature Domain Separators
Composite Signature Algorithm Domain Separator (in Hex encoding)
id-MLDSA44-RSA2048-PSS-SHA256 060B6086480186FA6B50080164
id-MLDSA44-RSA2048-PKCS15-SHA256 060B6086480186FA6B50080165
id-MLDSA44-Ed25519-SHA512 060B6086480186FA6B50080166
id-MLDSA44-ECDSA-P256-SHA256 060B6086480186FA6B50080167
id-MLDSA65-RSA3072-PSS-SHA512 060B6086480186FA6B50080169
id-MLDSA65-RSA4096-PSS-SHA512 060B6086480186FA6B5008016A
id-MLDSA65-RSA4096-PKCS15-SHA512 060B6086480186FA6B5008016B
id-MLDSA65-ECDSA-P256-SHA512 060B6086480186FA6B5008016C
id-MLDSA65-ECDSA-P384-SHA512 060B6086480186FA6B5008016D
id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 060B6086480186FA6B5008016E
id-MLDSA65-Ed25519-SHA512 060B6086480186FA6B5008016F
id-MLDSA87-ECDSA-P384-SHA512 060B6086480186FA6B50080170
id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 060B6086480186FA6B50080171
id-MLDSA87-Ed448-SHAKE256 060B6086480186FA6B50080172
id-MLDSA87-RSA4096-PSS-SHA512 060B6086480186FA6B50080173
id-MLDSA87-ECDSA-P521-SHA512 060B6086480186FA6B50080174

EDNOTE: these domain separators are based on the prototyping OIDs assigned on the Entrust arc. We will need to ask for IANA early allocation of these OIDs so that we can re-compute the domain separators over the final OIDs.

7.3. Rationale for choices

In generating the list of Composite algorithms, the idea was to provide composite algorithms at various security levels. Rather than trying for exact security level matching, the choice of traditional algorithm pairing prioritizes choosing commonly-deployed algorithms since there is no academic consensus on how to directly compare pre-quantum and post-quantum security levels.

SHA2 is used throughout in order to facilitate implementations that do not have easy access to SHA3 outside of the ML-DSA function.

At the higher security levels of pre-hashed Composite ML-DSA, for example id-MLDSA87-ECDSA-brainpoolP384r1-SHA512, the 384-bit elliptic curve component is used with SHA2-384 which is its pre-hash (ie the pre-hash that is considered to be internal to the ECDSA component), yet SHA2-512 is used as the pre-hash for the overall composite because in this case the pre-hash must not weaken the ML-DSA-87 component against a collision attack.

7.4. RSASSA-PSS

Use of RSASSA-PSS [RFC8017] requires extra parameters to be specified, which differ for each security level.

Also note that this specification fixes the Public Key OID of RSASSA-PSS to id-RSASSA-PSS (1.2.840.113549.1.1.10), although most implementations also would accept rsaEncryption (1.2.840.113549.1.1.1).

7.4.1. RSA2048-PSS

The RSA component keys MUST be generated at the 2048-bit security level in order to match that of ML-DSA-44.

As with the other composite signature algorithms, when id-MLDSA44-RSA2048-PSS and id-HashMLDSA44-RSA2048-PSS-SHA256 is used in an AlgorithmIdentifier, the parameters MUST be absent. id-MLDSA44-RSA2048-PSS and id-HashMLDSA44-RSA2048-PSS-SHA256 SHALL instantiate RSASSA-PSS with the following parameters:

Table 4: RSASSA-PSS 2048 Parameters
RSASSA-PSS Parameter Value
Mask Generation Function mgf1
Mask Generation params SHA-256
Message Digest Algorithm SHA-256
Salt Length in bits 256

where:

  • Mask Generation Function (mgf1) is defined in [RFC8017]

  • SHA-256 is defined in [RFC6234].

7.4.2. RSA3072-PSS

The RSA component keys MUST be generated at the 3072-bit security level in order to match that of ML-DSA-65.

As with the other composite signature algorithms, when id-MLDSA65-RSA3072-PSS or id-HashMLDSA65-RSA3072-PSS-SHA512 is used in an AlgorithmIdentifier, the parameters MUST be absent. id-MLDSA65-RSA3072-PSS or id-HashMLDSA65-RSA3072-PSS-SHA512 SHALL instantiate RSASSA-PSS with the following parameters:

Table 5: RSASSA-PSS 3072 Parameters
RSASSA-PSS Parameter Value
Mask Generation Function mgf1
Mask Generation params SHA-256
Message Digest Algorithm SHA-256
Salt Length in bits 256

where:

  • Mask Generation Function (mgf1) is defined in [RFC8017]

  • SHA-256 is defined in [RFC6234].

7.4.3. RSA4096-PSS

The RSA component keys MUST be generated at the 4096-bit security level in order to match that of ML-DSA-65 or ML-DSA-87.

When * id-MLDSA65-RSA4096-PSS, * id-HashMLDSA65-RSA4096-PSS-SHA512, * id-MLDSA87-RSA4096-PSS or * id-HashMLDSA87-RSA4096-PSS-SHA512 is used in an AlgorithmIdentifier, the parameters MUST be absent and RSASSA-PSS SHALL be instantiated with the following parameters:

Table 6: RSASSA-PSS 4096 Parameters
RSASSA-PSS Parameter Value
Mask Generation Function mgf1
Mask Generation params SHA-384
Message Digest Algorithm SHA-384
Salt Length in bits 384

where:

  • Mask Generation Function (mgf1) is defined in [RFC8017]

  • SHA-384 is defined in [RFC6234].

8. ASN.1 Module 

<CODE STARTS>

Composite-MLDSA-2025
  { iso(1) identified-organization(3) dod(6) internet(1)
        security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-composite-mldsa-2025(TBDMOD) }


DEFINITIONS IMPLICIT TAGS ::= BEGIN

EXPORTS ALL;

IMPORTS
  PUBLIC-KEY, SIGNATURE-ALGORITHM, SMIME-CAPS, AlgorithmIdentifier{}
    FROM AlgorithmInformation-2009  -- RFC 5912 [X509ASN1]
      { iso(1) identified-organization(3) dod(6) internet(1)
        security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-algorithmInformation-02(58) }
;

--
-- Object Identifiers
--

-- Defined in ITU-T X.690
der OBJECT IDENTIFIER ::=
  {joint-iso-itu-t asn1(1) ber-derived(2) distinguished-encoding(1)}

--
-- Information Object Classes
--

pk-CompositeSignature {OBJECT IDENTIFIER:id}
    PUBLIC-KEY ::= {
      IDENTIFIER id
      KEY BIT STRING
      PARAMS ARE absent
      CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign}
    }

sa-CompositeSignature{OBJECT IDENTIFIER:id,
   PUBLIC-KEY:publicKeyType }
      SIGNATURE-ALGORITHM ::=  {
         IDENTIFIER id
         VALUE OCTET STRING
         PARAMS ARE absent
         PUBLIC-KEYS {publicKeyType}
      }


-- Composite ML-DSA which uses a PreHash Message

-- TODO: OID to be replaced by IANA
id-MLDSA44-RSA2048-PSS-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 100 }

pk-MLDSA44-RSA2048-PSS-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-RSA2048-PSS-SHA256}

sa-MLDSA44-RSA2048-PSS-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-RSA2048-PSS-SHA256,
       pk-MLDSA44-RSA2048-PSS-SHA256 }

-- TODO: OID to be replaced by IANA
id-MLDSA44-RSA2048-PKCS15-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 101 }

pk-MLDSA44-RSA2048-PKCS15-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-RSA2048-PKCS15-SHA256}

sa-MLDSA44-RSA2048-PKCS15-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-RSA2048-PKCS15-SHA256,
       pk-MLDSA44-RSA2048-PKCS15-SHA256 }


-- TODO: OID to be replaced by IANA
id-MLDSA44-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 102 }

pk-MLDSA44-Ed25519-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-Ed25519-SHA512}

sa-MLDSA44-Ed25519-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-Ed25519-SHA512,
       pk-MLDSA44-Ed25519-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA44-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 103 }

pk-MLDSA44-ECDSA-P256-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-ECDSA-P256-SHA256}

sa-MLDSA44-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-ECDSA-P256-SHA256,
       pk-MLDSA44-ECDSA-P256-SHA256 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA3072-PSS-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 104 }

pk-MLDSA65-RSA3072-PSS-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA3072-PSS-SHA512}

sa-MLDSA65-RSA3072-PSS-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA3072-PSS-SHA512,
       pk-MLDSA65-RSA3072-PSS-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA3072-PKCS15-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 105 }

pk-MLDSA65-RSA3072-PKCS15-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA3072-PKCS15-SHA512}

sa-MLDSA65-RSA3072-PKCS15-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA3072-PKCS15-SHA512,
       pk-MLDSA65-RSA3072-PKCS15-SHA512 }

-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA4096-PSS-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 106 }

pk-MLDSA65-RSA4096-PSS-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA4096-PSS-SHA512}

sa-MLDSA65-RSA4096-PSS-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA4096-PSS-SHA512,
       pk-MLDSA65-RSA4096-PSS-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA4096-PKCS15-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 107 }

pk-MLDSA65-RSA4096-PKCS15-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA4096-PKCS15-SHA512}

sa-MLDSA65-RSA4096-PKCS15-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA4096-PKCS15-SHA512,
       pk-MLDSA65-RSA4096-PKCS15-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-ECDSA-P256-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 108 }

pk-MLDSA65-ECDSA-P256-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-P256-SHA512}

sa-MLDSA65-ECDSA-P256-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-ECDSA-P256-SHA512,
       pk-MLDSA65-ECDSA-P256-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-ECDSA-P384-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 109 }

pk-MLDSA65-ECDSA-P384-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-P384-SHA512}

sa-MLDSA65-ECDSA-P384-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-ECDSA-P384-SHA512,
       pk-MLDSA65-ECDSA-P384-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 110 }

pk-MLDSA65-ECDSA-brainpoolP256r1-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-brainpoolP256r1-SHA512}

sa-MLDSA65-ECDSA-brainpoolP256r1-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-ECDSA-brainpoolP256r1-SHA512,
       pk-MLDSA65-ECDSA-brainpoolP256r1-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 111 }

pk-MLDSA65-Ed25519-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-Ed25519-SHA512}

sa-MLDSA65-Ed25519-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-Ed25519-SHA512,
       pk-MLDSA65-Ed25519-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA87-ECDSA-P384-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 112 }

pk-MLDSA87-ECDSA-P384-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-ECDSA-P384-SHA512}

sa-MLDSA87-ECDSA-P384-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-ECDSA-P384-SHA512,
       pk-MLDSA87-ECDSA-P384-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 113 }

pk-MLDSA87-ECDSA-brainpoolP384r1-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-ECDSA-brainpoolP384r1-SHA512}

sa-MLDSA87-ECDSA-brainpoolP384r1-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-ECDSA-brainpoolP384r1-SHA512,
       pk-MLDSA87-ECDSA-brainpoolP384r1-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA87-Ed448-SHAKE256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 114 }

pk-MLDSA87-Ed448-SHAKE256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-Ed448-SHAKE256}

sa-MLDSA87-Ed448-SHAKE256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-Ed448-SHAKE256,
       pk-MLDSA87-Ed448-SHAKE256 }


-- TODO: OID to be replaced by IANA
id-MLDSA87-RSA4096-PSS-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 115 }

pk-MLDSA87-RSA4096-PSS-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-RSA4096-PSS-SHA512}

sa-MLDSA87-RSA4096-PSS-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-RSA4096-PSS-SHA512,
       pk-MLDSA87-RSA4096-PSS-SHA512 }


-- TODO: OID to be replaced by IANA
id-MLDSA87-ECDSA-P521-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(8) signature(1) 116 }

pk-MLDSA87-ECDSA-P521-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-ECDSA-P521-SHA512}

sa-MLDSA87-ECDSA-P521-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-ECDSA-P521-SHA512,
       pk-MLDSA87-ECDSA-P521-SHA512 }


SignatureAlgorithmSet SIGNATURE-ALGORITHM ::= {
  sa-MLDSA44-RSA2048-PSS-SHA256 |
  sa-MLDSA44-RSA2048-PKCS15-SHA256 |
  sa-MLDSA44-Ed25519-SHA512 |
  sa-MLDSA44-ECDSA-P256-SHA256 |
  sa-MLDSA65-RSA3072-PSS-SHA512 |
  sa-MLDSA65-RSA3072-PKCS15-SHA512 |
  sa-MLDSA65-RSA4096-PSS-SHA512 |
  sa-MLDSA65-RSA4096-PKCS15-SHA512 |
  sa-MLDSA65-ECDSA-P256-SHA512 |
  sa-MLDSA65-ECDSA-P384-SHA512 |
  sa-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |
  sa-MLDSA65-Ed25519-SHA512 |
  sa-MLDSA87-ECDSA-P384-SHA512 |
  sa-MLDSA87-ECDSA-brainpoolP384r1-SHA512 |
  sa-MLDSA87-Ed448-SHA512 |
  sa-MLDSA87-RSA4096-PSS-SHA512,
  ... }

END

<CODE ENDS>

9. IANA Considerations

IANA is requested to allocate a value from the "SMI Security for PKIX Module Identifier" registry [RFC7299] for the included ASN.1 module, and allocate values from "SMI Security for PKIX Algorithms" to identify the fourteen Algorithms defined within.

9.1. Object Identifier Allocations

EDNOTE to IANA: OIDs will need to be replaced in both the ASN.1 module and in Table 2.

9.1.1. Module Registration - SMI Security for PKIX Module Identifier

  • Decimal: IANA Assigned - Replace TBDMOD

  • Description: Composite-Signatures-2025 - id-mod-composite-signatures

  • References: This Document

9.1.2. Object Identifier Registrations - SMI Security for PKIX Algorithms

  • id-MLDSA44-RSA2048-PSS-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLDSA44-RSA2048-PSS-SHA256

    • References: This Document

  • id-MLDSA44-RSA2048-PKCS15-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLDSA44-RSA2048-PKCS15-SHA256

    • References: This Document

  • id-MLDSA44-Ed25519-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA44-Ed25519-SHA512

    • References: This Document

  • id-MLDSA44-ECDSA-P256-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLDSA44-ECDSA-P256-SHA256

    • References: This Document

  • id-MLDSA65-RSA3072-PSS-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-RSA3072-PSS-SHA512

    • References: This Document

  • id-MLDSA65-RSA3072-PKCS15-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-RSA3072-PKCS15-SHA512

    • References: This Document

  • id-MLDSA65-RSA4096-PSS-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-RSA4096-PSS-SHA512

    • References: This Document

  • id-MLDSA65-RSA4096-PKCS15-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-RSA4096-PKCS15-SHA512

    • References: This Document

  • id-MLDSA65-ECDSA-P256-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-ECDSA-P256-SHA512

    • References: This Document

  • id-MLDSA65-ECDSA-P384-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-ECDSA-P384-SHA512

    • References: This Document

  • id-MLDSA65-ECDSA-brainpoolP256r1-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-ECDSA-brainpoolP256r1-SHA512

    • References: This Document

  • id-MLDSA65-Ed25519-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-Ed25519-SHA512

    • References: This Document

  • id-MLDSA87-ECDSA-P384-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-ECDSA-P384-SHA512

    • References: This Document

  • id-MLDSA87-ECDSA-brainpoolP384r1-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-ECDSA-brainpoolP384r1-SHA512

    • References: This Document

  • id-MLDSA87-Ed448-SHAKE256

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-Ed448-SHAKE256

    • References: This Document

  • id-MLDSA87-RSA4096-PSS-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-RSA4096-PSS-SHA512

    • References: This Document

  • id-MLDSA87-ECDSA-P521-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-ECDSA-P521-SHA512

    • References: This Document

10. Security Considerations

10.1. Why Hybrids?

In broad terms, a PQ/T Hybrid can be used either to provide dual-algorithm security or to provide migration flexibility. Let's quickly explore both.

Dual-algorithm security. The general idea is that the data is protected by two algorithms such that an attacker would need to break both in order to compromise the data. As with most of cryptography, this property is easy to state in general terms, but becomes more complicated when expressed in formalisms. Section 10.2 goes into more detail here. One common counter-argument against PQ/T hybrid signatures is that if an attacker can forge one of the component algorithms, then why attack the hybrid-signed message at all when they could simply forge a completely new message? The answer to this question must be found outside the cryptographic primitives themselves, and instead in policy; once an algorithm is known to be broken it ought to be disallowed for single-algorithm use by cryptographic policy, while hybrids involving that algorithm may continue to be used and to provide value.

Migration flexibility. Some PQ/T hybrids exist to provide a sort of "OR" mode where the client can choose to use one algorithm or the other or both. The intention is that the PQ/T hybrid mechanism builds in backwards compatibility to allow legacy and upgraded clients to co-exist and communicate. The Composites presented in this specification do not provide this since they operate in a strict "AND" mode, but they do provide codebase migration flexibility. Consider that an organization has today a mature, validated, certified, hardened implementation of RSA or ECC. Composites allow them to add to this an ML-DSA implementation which immediately starts providing benefits against long-term document integrity attacks even if that ML-DSA implementation is still experimental, non-validated, non-certified, non-hardened implementation. More details of obtaining FIPS certification of a composite algorithm can be found in Appendix E.1.

10.2. Non-separability, EUF-CMA and SUF

The signature combiner defined in this document is Weakly Non-Separable (WNS), as defined in [I-D.ietf-pquip-hybrid-signature-spectrums], since the forged message M’ will include the composite domain separator as evidence. The prohibition on key reuse between composite and single-algorithm contexts discussed in Section 10.3 further strengthens the non-separability in practice, but does not achieve Strong Non-Separability (SNS) since policy mechanisms such as this are outside the definition of SNS.

Unforgeability properties are somewhat more nuanced. We recall first the definitions of Existential Unforgeability under Chosen Message Attack (EUF-CMA) and Strong Unforgeability (SUF).The classic EUF-CMA game is in reference to a pair of algorithms ( Sign(), Verify() ) where the attacker has access to a signing oracle using the Sign() and must produce a message-signature pair (m', s') that is accepted by the verifier using Verify() and where m was never signed by the oracle. SUF requires that the attacker cannot construct a new signature to an already-signed message.

The pair ( CompositeML-DSA.Sign(), CompositeML-DSA.Verify() ) is EUF-CMA secure so long as at least one component algorithm is EUF-CMA secure since any attempt to modify the message would cause the EUF-CMA secure component to fail its Verify() which in turn will cause CompositeML-DSA.Verify() to fail.

CompositeML-DSA only achieves SUF security if both components are SUF secure, which is not a useful property; the argument is that if the first component algorithm is not SUF secure then by definition it admits at least one (m, s1*) pair where s1* was not produced by the honest signer and it then can be combined with an honestly-signed (m, s2) signature over the same message m to create (m, (s1*, s2)) which violates SUF for the composite algorithm. Of the traditional signature component algorithms used in this specification, only Ed25519 and Ed448 are SUF secure and therefore applications that require SUF security to be maintained even in the event that ML-DSA is broken SHOULD use it in composite with Ed25519 or Ed448.

In addition to the classic EUF-CMA game, we should also consider a “cross-protocol” version of the EUF-CMA game that is relevant to hybrids. Specifically, we want to consider a modified version of the EUF-CMA game where the attacker has access to either a signing oracle over the two component algorithms in isolation, Trad.Sign() and ML-DSA.Sign(), and attempts to fraudulently present them as a composite, or where the attacker has access to a composite oracle for signing and then attempts to split the signature back into components and present them to either ML-DSA.Verify() or Trad.Verify().

In the case of CompositeML-DSA, a specific message forgery exists for a cross-protocol EUF-CMA attack, namely introduced by the prefix construction added to M. This applies to use of individual component signing oracles with fraudulent presentation of the signature to a composite verification oracle, and use of a composite signing oracle with fraudulent splitting of the signature for presentation to component verification oracle(s) of either ML-DSA.Verify() or Trad.Verify(). In the first case, an attacker with access to signing oracles for the two component algorithms can sign M’ and then trivially assemble a composite. In the second case, the message M’ (containing the composite domain separator) can be presented as having been signed by a standalone component algorithm. However, use of the context string for domain separation enables Weak Non-Separability and auditable checks on hybrid use, which is deemed a reasonable trade-off. Moreover and very importantly, the cross-protocol EUF-CMA attack in either direction is foiled if implementors strictly follow the prohibition on key reuse presented in Section 10.3 since there cannot exist simultaneously composite and non-composite signers and verifiers for the same keys.

10.2.1. Implications of mupliple encodings

As noted in Section 5, this specification leaves open the choice of encoding of the traditional component. As such it is possible for the same composite public key to carry multiple valid representations (mldsaPK, tradPK1) and (mldsaPK, tradPK2) where tradPK1 and tradPK2 are alternate encodings of the same key, for example compressed vs uncompressed EC points. In theory alternate encodings of the traditional signature value are also possible, although the authors are not aware of any.

In theory this introduces complications for EUF-CMA and SUF-CMA security proofs. Implementors who are concerned with this SHOULD choose implementations of the traditional component that only accept a single encoding and performs appropriate length-checking, and reject composites which contain any other encodings. This is permitted by this specification.

10.3. Key Reuse

When using single-algorithm cryptography, the best practice is to always generate fresh key material for each purpose, for example when renewing a certificate, or obtaining both a TLS and S/MIME certificate for the same device, however in practice key reuse in such scenarios is not always catastrophic to security and therefore often tolerated, despite cross-protocol attacks having been shown. (TODO citation needed here)

In the event that an application wishes to use two separate keys (for example from two single-algorithm certificates) and use them to construct a single Composite Signature, then it is RECOMMENDED to provide a composite ctx to prevent this signature from being validated under a composite key made up of the same two component keys. For example, an application or protocol called Foobar that wishes to do this could invoke the Composite algorithm as: Composite-ML-DSA.Sign( (sk1, sk2), M', ctx="Foobar-dual-cert-sig", PH).

Within the broader context of PQ / Traditional hybrids, we need to consider new attack surfaces that arise due to the hybrid constructions that did not exist in single-algorithm contexts. One of these is key reuse where the component keys within a hybrid are also used by themselves within a single-algorithm context. For example, it might be tempting for an operator to take an already-deployed RSA key pair and combine it with an ML-DSA key pair to form a hybrid key pair for use in a hybrid algorithm. Within a hybrid signature context this leads to a class of attacks referred to as "stripping attacks" discussed in Section 10.2 and may also open up risks from further cross-protocol attacks. Despite the weak non-separability property offered by the composite signature combiner, key reuse MUST be avoided to prevent the introduction of EUF-CMA vulnerabilities.

In addition, there is a further implication to key reuse regarding certificate revocation. Upon receiving a new certificate enrolment request, many certification authorities will check if the requested public key has been previously revoked due to key compromise. Often a CA will perform this check by using the public key hash. Therefore, even if both components of a composite have been previously revoked, the CA may only check the hash of the combined composite key and not find the revocations. Therefore, because the possibility of key reuse exists even though forbidden in this specification, CAs performing revocation checks on a composite key SHOULD also check both component keys independently to verify that the component keys have not been revoked.

10.4. Use of Prefix to for attack mitigation

The Prefix value specified in the message format calculated in Section 4 can be used by a traditional verifier to detect if the composite signature has been stripped apart. An attacker would need to compute M' := Prefix || Domain || len(ctx) || ctx || HashOID || PH(r || M). Since the Prefix is the constant String "CompositeAlgorithmSignatures2025" (Byte encoding 436F6D706F73697465416C676F726974686D5369676E61747572657332303235 ) a traditional verifier can check if the Message starts with this prefix and reject the message.

10.5. Implications of pre-hash randomizer

The primary design motivation behind pre-hashing is to perform only a single pass over the potentially large input message M and to allow for optimizations in cases such as signing the same message digest with multiple different keys.

To combat collision and second pre-image weaknesses introduced by the pre-hash, Composite-ML-DSA introduces a 32-byte randomizer into the pre-hash:

PH( r || M )

as part of the overall construction of the to-be-signed message:

r = Random(32)
M' :=  Prefix || Domain || len(ctx) || ctx || r
                        || HashOID || PH( r || M )
...
output (r, mldsaSig, tradSig)

This follows closely the construction given in section 13.2.1 of [BonehShoup] which is given as:

This construction's security hinges on the assumption that H(r, m) is "Target Collision Resistant" -- a weaker version of second pre-image resistance which applies to keyed hash functions.

Randomizing the pre-hash strongly protects against pre-computed collision attacks where an attacker pre-computes a message pair M1, M2 such that PH(M1) = PH(M2) and submits one to the signing oracle, thus obtaining a valid signature for both. However, collision-finding pre-computation cannot be performed against PH(r || M1) = PH(r || M2) when r is unknown to the attacker in advance. We also consider signature collision forgeries via finding a second pre-image after the signature has been created. In this case, the attack is only possible only if the attacker can perform what [BonehShoup] calls a Target Collision attack where the attacker can take the honestly-produced signature s = (r, mldsaSig, tradSig) over the message M and find a second message M2 such that PH( r || M) = PH( r || M2) for the same randomizer r. [BonehShoup] defines Target Collision Resistance (TCR) as a security notion that applies to keyed hash functions and is weaker requirement of the hash function compared second pre-image resistance.

[BonehShoup] notes:

  • The benefit of the TCR construction is that security only relies on H being TCR, which is a much weaker property than collision resistance and hence more likely to hold for H. For example, the function SHA256 may eventually be broken as a collision-resistant hash, but the function H(r, m) := SHA256(r ‖ m) may still be secure as a TCR.

To this goal, it is sufficient that the randomizer be un-predictable from outside the signing oracle -- i.e. the caller of Composite-ML-DSA.Sign (sk, M, ctx, PH) cannot predict randomizer value that will be used. In some contexts it MAY be acceptable to use a randomizer which is not truly random without compromising the stated security properties; for example if performing batch signatures where the same message is signed with multiple keys, it MAY be acceptable to pre-hash the message once and then sign that digest multiple times -- i.e. using the same randomizer across multiple signatures. Provided that the batch signature is performed as an atomic signing oracle and an attacker is never able to see the randomizer that will be used in a future signature then this ought to satisfy the stated security requirements, but detailed security analysis of such a modification of the Composite-ML-DSA signing routine MUST be perfermed on a per-application basis.

Further, since introduction of the randomizer is a net-gain over both the ML-DSA and Traditional components, a failure of randomness reverts the overall collision resistance of Composite-ML-DSA to the collision resistance of the hash function used as PH, which is no worse than the security properties that Composite-ML-DSA would have had without a randomizer, which is the same collision resistance property that RSA, ECDSA, and HashML-DSA have.

Another benefit to the randomizer is to prevent a class of attacks unique to composites, which we define as a "mixed-key forgery attack": Take two composite keys (mldsaPK1, tradPK1) and (mldsaPK2, tradPK2) which do not share any key material and have them produce signatures (r1, mldsaSig1, tradSig1) and (r2, mldsaSig2, tradSig2) respectively over the same message M. Consider whether it is possible to construct a forgery by swapping components and presenting (r, mldsaSig1, tradSig2) that verifies under a forged public key (mldsaPK1, tradPK2). This forgery attack is blocked by the randomizer r so long as r1 != r2.

Introduction of the randomizer might introduce other benificial security properties, but these are outside the scope of design consideration.

10.6. Policy for Deprecated and Acceptable Algorithms

Traditionally, a public key, certificate, or signature contains a single cryptographic algorithm. If and when an algorithm becomes deprecated (for example, RSA-512, or SHA1), then clients performing signatures or verifications should be updated to adhere to appropriate policies.

In the composite model this is less obvious since implementers may decide that certain cryptographic algorithms have complementary security properties and are acceptable in combination even though one or both algorithms are deprecated for individual use. As such, a single composite public key or certificate may contain a mixture of deprecated and non-deprecated algorithms.

Since composite algorithms are registered independently of their component algorithms, their deprecation can be handled independently from that of their component algorithms. For example a cryptographic policy might continue to allow id-MLDSA65-ECDSA-P256-SHA512 even after ECDSA-P256 is deprecated.

When considering stripping attacks, one need consider the case where an attacker has fully compromised one of the component algorithms to the point that they can produce forged signatures that appear valid under one of the component public keys, and thus fool a victim verifier into accepting a forged signature. The protection against this attack relies on the victim verifier trusting the pair of public keys as a single composite key, and not trusting the individual component keys by themselves.

Specifically, in order to achieve this non-separability property, this specification makes two assumptions about how the verifier will establish trust in a composite public key:

  1. This specification assumes that all of the component keys within a composite key are freshly generated for the composite; i.e. a given public key MUST NOT appear as a component within a composite key and also within single-algorithm constructions.

  2. This specification assumes that composite public keys will be bound in a structure that contains a signature over the public key (for example, an X.509 Certificate [RFC5280]), which is chained back to a trust anchor, and where that signature algorithm is at least as strong as the composite public key that it is protecting.

There are mechanisms within Internet PKI where trusted public keys do not appear within signed structures -- such as the Trust Anchor format defined in [RFC5914]. In such cases, it is the responsibility of implementers to ensure that trusted composite keys are distributed in a way that is tamper-resistant and does not allow the component keys to be trusted independently.

11. References

11.1. Normative References

[FIPS.186-5]
National Institute of Standards and Technology (NIST), "Digital Signature Standard (DSS)", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-5.pdf>.
[FIPS.202]
National Institute of Standards and Technology (NIST), "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf>.
[FIPS.204]
National Institute of Standards and Technology (NIST), "Module-Lattice-Based Digital Signature Standard", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.204.pdf>.
[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/info/rfc2119>.
[RFC2986]
Nystrom, M. and B. Kaliski, "PKCS #10: Certification Request Syntax Specification Version 1.7", RFC 2986, DOI 10.17487/RFC2986, , <https://www.rfc-editor.org/info/rfc2986>.
[RFC4210]
Adams, C., Farrell, S., Kause, T., and T. Mononen, "Internet X.509 Public Key Infrastructure Certificate Management Protocol (CMP)", RFC 4210, DOI 10.17487/RFC4210, , <https://www.rfc-editor.org/info/rfc4210>.
[RFC4211]
Schaad, J., "Internet X.509 Public Key Infrastructure Certificate Request Message Format (CRMF)", RFC 4211, DOI 10.17487/RFC4211, , <https://www.rfc-editor.org/info/rfc4211>.
[RFC5280]
Cooper, D., Santesson, S., Farrell, S., Boeyen, S., Housley, R., and W. Polk, "Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, , <https://www.rfc-editor.org/info/rfc5280>.
[RFC5480]
Turner, S., Brown, D., Yiu, K., Housley, R., and T. Polk, "Elliptic Curve Cryptography Subject Public Key Information", RFC 5480, DOI 10.17487/RFC5480, , <https://www.rfc-editor.org/info/rfc5480>.
[RFC5639]
Lochter, M. and J. Merkle, "Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation", RFC 5639, DOI 10.17487/RFC5639, , <https://www.rfc-editor.org/info/rfc5639>.
[RFC5652]
Housley, R., "Cryptographic Message Syntax (CMS)", STD 70, RFC 5652, DOI 10.17487/RFC5652, , <https://www.rfc-editor.org/info/rfc5652>.
[RFC5758]
Dang, Q., Santesson, S., Moriarty, K., Brown, D., and T. Polk, "Internet X.509 Public Key Infrastructure: Additional Algorithms and Identifiers for DSA and ECDSA", RFC 5758, DOI 10.17487/RFC5758, , <https://www.rfc-editor.org/info/rfc5758>.
[RFC5958]
Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, , <https://www.rfc-editor.org/info/rfc5958>.
[RFC6090]
McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic Curve Cryptography Algorithms", RFC 6090, DOI 10.17487/RFC6090, , <https://www.rfc-editor.org/info/rfc6090>.
[RFC6234]
Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, DOI 10.17487/RFC6234, , <https://www.rfc-editor.org/info/rfc6234>.
[RFC7748]
Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, , <https://www.rfc-editor.org/info/rfc7748>.
[RFC8032]
Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital Signature Algorithm (EdDSA)", RFC 8032, DOI 10.17487/RFC8032, , <https://www.rfc-editor.org/info/rfc8032>.
[RFC8174]
Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, , <https://www.rfc-editor.org/info/rfc8174>.
[RFC8410]
Josefsson, S. and J. Schaad, "Algorithm Identifiers for Ed25519, Ed448, X25519, and X448 for Use in the Internet X.509 Public Key Infrastructure", RFC 8410, DOI 10.17487/RFC8410, , <https://www.rfc-editor.org/info/rfc8410>.
[RFC8411]
Schaad, J. and R. Andrews, "IANA Registration for the Cryptographic Algorithm Object Identifier Range", RFC 8411, DOI 10.17487/RFC8411, , <https://www.rfc-editor.org/info/rfc8411>.
[SEC1]
Certicom Research, "SEC 1: Elliptic Curve Cryptography", , <https://www.secg.org/sec1-v2.pdf>.
[SEC2]
Certicom Research, "SEC 2: Recommended Elliptic Curve Domain Parameters", , <https://www.secg.org/sec2-v2.pdf>.
[X.690]
ITU-T, "Information technology - ASN.1 encoding Rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)", ISO/IEC 8825-1:2015, .
[X9.62_2005]
American National Standards Institute, "Public Key Cryptography for the Financial Services Industry The Elliptic Curve Digital Signature Algorithm (ECDSA)", .

11.2. Informative References

[ANSSI2024]
French Cybersecurity Agency (ANSSI), Federal Office for Information Security (BSI), Netherlands National Communications Security Agency (NLNCSA), and Swedish National Communications Security Authority, Swedish Armed Forces, "Position Paper on Quantum Key Distribution", n.d., <https://cyber.gouv.fr/sites/default/files/document/Quantum_Key_Distribution_Position_Paper.pdf>.
[Bindel2017]
Bindel, N., Herath, U., McKague, M., and D. Stebila, "Transitioning to a quantum-resistant public key infrastructure", , <https://link.springer.com/chapter/10.1007/978-3-319-59879-6_22>.
[BonehShoup]
Boneh, D. and V. Shoup, "A Graduate Course in Applied Cryptography v0.6", , <https://crypto.stanford.edu/~dabo/cryptobook/BonehShoup_0_6.pdf>.
[BSI2021]
Federal Office for Information Security (BSI), "Quantum-safe cryptography - fundamentals, current developments and recommendations", , <https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/Publications/Brochure/quantum-safe-cryptography.pdf>.
[codesigningbrsv3.8]
"Baseline Requirements for the Issuance and Management of Publicly‐Trusted Code Signing Certificates Version 3.8.0", n.d., <https://cabforum.org/working-groups/code-signing/documents/>.
[eIDAS2014]
"Regulation (EU) No 910/2014 of the European Parliament and of the Council of 23 July 2014 on electronic identification and trust services for electronic transactions in the internal market and repealing Directive 1999/93/EC", n.d., <https://eur-lex.europa.eu/eli/reg/2014/910/oj/eng>.
[I-D.ietf-lamps-dilithium-certificates]
Massimo, J., Kampanakis, P., Turner, S., and B. Westerbaan, "Internet X.509 Public Key Infrastructure: Algorithm Identifiers for ML-DSA", Work in Progress, Internet-Draft, draft-ietf-lamps-dilithium-certificates-04, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-dilithium-certificates-04>.
[I-D.ietf-pquip-hybrid-signature-spectrums]
Bindel, N., Hale, B., Connolly, D., and F. D, "Hybrid signature spectrums", Work in Progress, Internet-Draft, draft-ietf-pquip-hybrid-signature-spectrums-00, , <https://datatracker.ietf.org/doc/html/draft-ietf-pquip-hybrid-signature-spectrums-00>.
[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-04, , <https://datatracker.ietf.org/doc/html/draft-ietf-pquip-pqt-hybrid-terminology-04>.
[RFC3279]
Bassham, L., Polk, W., and R. Housley, "Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 3279, DOI 10.17487/RFC3279, , <https://www.rfc-editor.org/info/rfc3279>.
[RFC5914]
Housley, R., Ashmore, S., and C. Wallace, "Trust Anchor Format", RFC 5914, DOI 10.17487/RFC5914, , <https://www.rfc-editor.org/info/rfc5914>.
[RFC7292]
Moriarty, K., Ed., Nystrom, M., Parkinson, S., Rusch, A., and M. Scott, "PKCS #12: Personal Information Exchange Syntax v1.1", RFC 7292, DOI 10.17487/RFC7292, , <https://www.rfc-editor.org/info/rfc7292>.
[RFC7296]
Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T. Kivinen, "Internet Key Exchange Protocol Version 2 (IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, , <https://www.rfc-editor.org/info/rfc7296>.
[RFC7299]
Housley, R., "Object Identifier Registry for the PKIX Working Group", RFC 7299, DOI 10.17487/RFC7299, , <https://www.rfc-editor.org/info/rfc7299>.
[RFC8017]
Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch, "PKCS #1: RSA Cryptography Specifications Version 2.2", RFC 8017, DOI 10.17487/RFC8017, , <https://www.rfc-editor.org/info/rfc8017>.
[RFC8446]
Rescorla, E., "The Transport Layer Security (TLS) Protocol Version 1.3", RFC 8446, DOI 10.17487/RFC8446, , <https://www.rfc-editor.org/info/rfc8446>.
[RFC8551]
Schaad, J., Ramsdell, B., and S. Turner, "Secure/Multipurpose Internet Mail Extensions (S/MIME) Version 4.0 Message Specification", RFC 8551, DOI 10.17487/RFC8551, , <https://www.rfc-editor.org/info/rfc8551>.

Appendix A. Approximate Key and Signature Sizes

Note that the sizes listed below are approximate: these values are measured from the test vectors, but other implementations could produce values where the traditional component has a different size. For example, this could be due to:

Note that by contrast, ML-DSA values are always fixed size, so composite values can always be correctly de-serialized based on the size of the ML-DSA component. It is expected for the size values of RSA and ECDSA variants to fluctuate by a few bytes even between subsequent runs of the same composite implementation signing the same message over different keys. EdDSA values are always fixed size, so the size values for ML-DSA + EdDSA variants can be treated as constants.

Implementations MUST NOT perform strict length checking based on the values in this table.

Non-hybrid ML-DSA is included for reference.

Table 7: Approximate size values of composite ML-DSA
Algorithm Public key Private key Signature
id-ML-DSA-44 1312 32 2420
id-ML-DSA-65 1952 32 3309
id-ML-DSA-87 2592 32 4627
id-MLDSA44-RSA2048-PSS-SHA256 1582 1249 2708
id-MLDSA44-RSA2048-PKCS15-SHA256 1582 1249 2708
id-MLDSA44-Ed25519-SHA512 1344 64 2516
id-MLDSA44-ECDSA-P256-SHA256 1377 170 2522
id-MLDSA65-RSA3072-PSS-SHA512 2350 1825 3725
id-MLDSA65-RSA4096-PSS-SHA512 2478 2407 3853
id-MLDSA65-RSA4096-PKCS15-SHA512 2478 2407 3853
id-MLDSA65-ECDSA-P256-SHA512 2017 170 3411
id-MLDSA65-ECDSA-P384-SHA512 2049 217 3444
id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 2017 171 3411
id-MLDSA65-Ed25519-SHA512 1984 64 3405
id-MLDSA87-ECDSA-P384-SHA512 2689 217 4761
id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 2689 221 4761
id-MLDSA87-RSA4096-PSS-SHA512 3118 2406 5171
id-MLDSA87-Ed448-SHAKE256 2649 89 4773
id-MLDSA87-ECDSA-P521-SHA512 2085 273 3479

Appendix B. Samples

B.1. Message Format Examples

B.1.1. Example of MLDSA44-ECDSA-P256-SHA256 with Context 

M' = Prefix || Domain || len(ctx) || ctx || HashOID || PH(M)

M = new byte[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
ctx = new byte[] { 8, 13, 6, 12, 5, 16, 25, 23 }

Encoded Message:
43:6F:6D:70:6F:73:69:74:65:41:6C:67:6F:72:69:74:68:6D:53:69:67:6E:61:74:75:72:65:73:32:30:32:35:06:0B:60:86:48:01:86:FA:6B:50:08:01:53:08:08:0D:06:0C:05:10:19:17:06:09:60:86:48:01:65:03:04:02:01:1F:82:5A:A2:F0:02:0E:F7:CF:91:DF:A3:0D:A4:66:8D:79:1C:5D:48:24:FC:8E:41:35:4B:89:EC:05:79:5A:B3

Prefix: 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:
Domain: :06:0B:60:86:48:01:86:FA:6B:50:08:01:53:
len(ctx): 08:
ctx: 08:0D:06:0C:05:10:19:17:
HashOID: 06:09:60:86:48:01:65:03:04:02:01:
PH(M): 1F:82:5A:A2:F0:02:0E:F7:CF:91:DF:A3:0D:A4:66:8D:79:1C:5D:48:24:FC:8E:41:35:4B:89:EC:05:79:5A:B3

B.1.2. Example of MLDSA44-ECDSA-P256-SHA256 without Context 

M' = Prefix || Domain || len(ctx) || ctx || HashOID || PH(M)

M = new byte[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
ctx = not used

Encoded Message:
43:6F:6D:70:6F:73:69:74:65:41:6C:67:6F:72:69:74:68:6D:53:69:67:6E:61:74:75:72:65:73:32:30:32:35:06:0B:60:86:48:01:86:FA:6B:50:08:01:53:00:06:09:60:86:48:01:65:03:04:02:01:1F:82:5A:A2:F0:02:0E:F7:CF:91:DF:A3:0D:A4:66:8D:79:1C:5D:48:24:FC:8E:41:35:4B:89:EC:05:79:5A:B3

Prefix: 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:
Domain: :06:0B:60:86:48:01:86:FA:6B:50:08:01:53
len(ctx): 00:
ctx: empty
HashOID: 06:09:60:86:48:01:65:03:04:02:01:
PH(M): 1F:82:5A:A2:F0:02:0E:F7:CF:91:DF:A3:0D:A4:66:8D:79:1C:5D:48:24:FC:8E:41:35:4B:89:EC:05:79:5A:B3

Appendix C. Component Algorithm Reference

This section provides references to the full specification of the algorithms used in the composite constructions.

Table 8: Component Signature Algorithms used in Composite Constructions
Component Signature Algorithm ID OID Specification
id-ML-DSA-44 2.16.840.1.101.3.4.3.17 [FIPS.204]
id-ML-DSA-65 2.16.840.1.101.3.4.3.18 [FIPS.204]
id-ML-DSA-87 2.16.840.1.101.3.4.3.19 [FIPS.204]
id-Ed25519 1.3.101.112 [RFC8032], [RFC8410]
id-Ed448 1.3.101.113 [RFC8032], [RFC8410]
ecdsa-with-SHA256 1.2.840.10045.4.3.2 [RFC5758], [RFC5480], [SEC1], [X9.62_2005]
ecdsa-with-SHA384 1.2.840.10045.4.3.3 [RFC5758], [RFC5480], [SEC1], [X9.62_2005]
ecdsa-with-SHA512 1.2.840.10045.4.3.4 [RFC5758], [RFC5480], [SEC1], [X9.62_2005]
sha256WithRSAEncryption 1.2.840.113549.1.1.11 [RFC8017]
sha384WithRSAEncryption 1.2.840.113549.1.1.12 [RFC8017]
id-RSASSA-PSS 1.2.840.113549.1.1.10 [RFC8017]
Table 9: Elliptic Curves used in Composite Constructions
Elliptic CurveID OID Specification
secp256r1 1.2.840.10045.3.1.7 [RFC6090], [SEC2]
secp384r1 1.3.132.0.34 [RFC5480], [RFC6090], [SEC2]
secp521r1 1.3.132.0.35 [RFC5480], [RFC6090], [SEC2]
brainpoolP256r1 1.3.36.3.3.2.8.1.1.7 [RFC5639]
brainpoolP384r1 1.3.36.3.3.2.8.1.1.11 [RFC5639]
Table 10: Hash algorithms used in pre-hashed Composite Constructions to build PH element
HashID OID Specification
id-sha256 2.16.840.1.101.3.4.2.1 [RFC6234]
id-sha512 2.16.840.1.101.3.4.2.3 [RFC6234]
id-shake256 2.16.840.1.101.3.4.2.18 [FIPS 202]

Appendix D. Component AlgorithmIdentifiers for Public Keys and Signatures

To ease implementing Composite Signatures this section specifies the Algorithms Identifiers for each component algorithm. They are provided as ASN.1 value notation and copy and paste DER encoding to avoid any ambiguity. Developers may use this information to reconstruct non hybrid public keys and signatures from each component that can be fed to crypto APIs to create or verify a single component signature.

For newer Algorithms like Ed25519 or ML-DSA the AlgorithmIdentifiers are the same for Public Key and Signature. Older Algorithms have different AlgorithmIdentifiers for keys and signatures and are specified separately here for each component.

ML-DSA-44 -- AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ML-DSA-44   -- (2 16 840 1 101 3 4 3 17)
   }

DER:
  30 0B 06 09 60 86 48 01 65 03 04 03 11

ML-DSA-65 -- AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ML-DSA-65   -- (2 16 840 1 101 3 4 3 18)
   }

DER:
  30 0B 06 09 60 86 48 01 65 03 04 03 12

ML-DSA-87 -- AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ML-DSA-87   -- (2 16 840 1 101 3 4 3 19)
   }

DER:
  30 0B 06 09 60 86 48 01 65 03 04 03 13

RSASSA-PSS 2048 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-RSASSA-PSS   -- (1.2.840.113549.1.1.10)
    }

DER:
  30 0B 06 09 2A 86 48 86 F7 0D 01 01 0A

RSASSA-PSS 2048 -- AlgorithmIdentifier of Signature

ASN.1:
  signatureAlgorithm AlgorithmIdentifier ::= {
    algorithm id-RSASSA-PSS,   -- (1.2.840.113549.1.1.10)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm id-sha256,   -- (2.16.840.1.101.3.4.2.1)
        parameters NULL
        },
      AlgorithmIdentifier ::= {
        algorithm id-mgf1,       -- (1.2.840.113549.1.1.8)
        parameters AlgorithmIdentifier ::= {
          algorithm id-sha256,   -- (2.16.840.1.101.3.4.2.1)
          parameters NULL
          }
        },
      saltLength 32
      }
    }

DER:
  30 41 06 09 2A 86 48 86 F7 0D 01 01 0A 30 34 A0 0F 30 0D 06 09 60 86
  48 01 65 03 04 02 01 05 00 A1 1C 30 1A 06 09 2A 86 48 86 F7 0D 01 01
  08 30 0D 06 09 60 86 48 01 65 03 04 02 01 05 00 A2 03 02 01 20

RSASSA-PSS 3072 & 4096 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-RSASSA-PSS   -- (1.2.840.113549.1.1.10)
    }

DER:
  30 0B 06 09 2A 86 48 86 F7 0D 01 01 0A

RSASSA-PSS 3072 & 4096 -- AlgorithmIdentifier of Signature

ASN.1:
  signatureAlgorithm AlgorithmIdentifier ::= {
    algorithm id-RSASSA-PSS,   -- (1.2.840.113549.1.1.10)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm id-sha512,   -- (2.16.840.1.101.3.4.2.3)
        parameters NULL
        },
      AlgorithmIdentifier ::= {
        algorithm id-mgf1,       -- (1.2.840.113549.1.1.8)
        parameters AlgorithmIdentifier ::= {
          algorithm id-sha512,   -- (2.16.840.1.101.3.4.2.3)
          parameters NULL
          }
        },
      saltLength 64
      }
    }

DER:
  30 41 06 09 2A 86 48 86 F7 0D 01 01 0A 30 34 A0 0F 30 0D 06 09 60 86
  48 01 65 03 04 02 03 05 00 A1 1C 30 1A 06 09 2A 86 48 86 F7 0D 01 01
  08 30 0D 06 09 60 86 48 01 65 03 04 02 03 05 00 A2 03 02 01 40

RSASSA-PKCS1-v1_5 2048 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm rsaEncryption,   -- (1.2.840.113549.1.1.1)
    parameters NULL
    }

DER:
  30 0D 06 09 2A 86 48 86 F7 0D 01 01 01 05 00

RSASSA-PKCS1-v1_5 2048 -- AlgorithmIdentifier of Signature

ASN.1:
  signatureAlgorithm AlgorithmIdentifier ::= {
    algorithm sha256WithRSAEncryption,   -- (1.2.840.113549.1.1.11)
    parameters NULL
    }

DER:
  30 0D 06 09 2A 86 48 86 F7 0D 01 01 0D 05 00

RSASSA-PKCS1-v1_5 3072 & 4096 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm rsaEncryption,   -- (1.2.840.113549.1.1.1)
    parameters NULL
    }

DER:
  30 0D 06 09 2A 86 48 86 F7 0D 01 01 01 05 00

RSASSA-PKCS1-v1_5 3072 & 4096 -- AlgorithmIdentifier of Signature

ASN.1:
  signatureAlgorithm AlgorithmIdentifier ::= {
    algorithm sha512WithRSAEncryption,   -- (1.2.840.113549.1.1.13)
    parameters NULL
    }

DER:
  30 0D 06 09 2A 86 48 86 F7 0D 01 01 0D 05 00

ECDSA NIST 256 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm secp256r1   -- (1.2.840.10045.3.1.7)
        }
      }
    }

DER:
  30 13 06 07 2A 86 48 CE 3D 02 01 06 08 2A 86 48 CE 3D 03 01 07

ECDSA NIST 256 -- AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA256   -- (1.2.840.10045.4.3.2)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 02

ECDSA NIST-384 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm secp384r1   -- (1.3.132.0.34)
        }
      }
    }

DER:
  30 10 06 07 2A 86 48 CE 3D 02 01 06 05 2B 81 04 00 22

ECDSA NIST-384 -- AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA384   -- (1.2.840.10045.4.3.3)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 03

ECDSA NIST-521 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm secp521r1   -- (1.3.132.0.35)
        }
      }
    }

DER:
  30 10 06 07 2A 86 48 CE 3D 02 01 06 05 2B 81 04 00 23

ECDSA NIST-521 -- AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA512   -- (1.2.840.10045.4.3.4)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 04

ECDSA Brainpool-256 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm brainpoolP256r1   -- (1.3.36.3.3.2.8.1.1.7)
        }
      }
    }

DER:
  30 14 06 07 2A 86 48 CE 3D 02 01 06 09 2B 24 03 03 02 08 01 01 07

ECDSA Brainpool-256 -- AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA256   -- (1.2.840.10045.4.3.2)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 02

ECDSA Brainpool-384 -- AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm brainpoolP384r1   -- (1.3.36.3.3.2.8.1.1.11)
        }
      }
    }

DER:
  30 14 06 07 2A 86 48 CE 3D 02 01 06 09 2B 24 03 03 02 08 01 01 0B

ECDSA Brainpool-384 -- AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA384   -- (1.2.840.10045.4.3.3)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 03

Ed25519 -- AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-Ed25519   -- (1.3.101.112)
    }

DER:
  30 05 06 03 2B 65 70

Ed448 -- AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-Ed448   -- (1.3.101.113)
    }

DER:
  30 05 06 03 2B 65 71

Appendix E. Implementation Considerations

E.1. FIPS certification

One of the primary design goals of this specification is for the overall composite algorithm to be able to be considered FIPS-approved even when one of the component algorithms is not.

Implementors seeking FIPS certification of a composite Signature algorithm where only one of the component algorithms has been FIPS-validated or FIPS-approved should credit the FIPS-validated component algorithm with full security strength, the non-FIPS-validated component algorithm with zero security, and the overall composite should be considered at least as strong and thus FIPS-approved.

The composite algorithm has been designed to treat the underlying primitives as "black-box implementations" and not impose any additional requirements on them that could require an existing implementation of an underlying primitive to run in a mode different from the one under which it was certified. For example, the KeyGen defined in Section 4.1 invokes ML-DSA.KeyGen(mldsaSeed), but this is only a suggested implementation and the composite KeyGen MAY be implemented using a different available interface for ML-DSA.KeyGen. Another example is pre-hashing; a pre-hash is inherent to RSA, ECDSA, and ML-DSA (mu), and composite makes no assumptions or requirements about whether component-specific pre-hashing is done locally as part of the composite, or remotely as part of the component primitive, although composite itself includes a pre-hash in order to ligthen the data transmission requirements in cases where, for example, FIPS compliance of the underlying primitive requires pre-hashing to be done remotely.

The pre-hash randomizer r requires the composite implementation to have access to a cryptographic random number generator; as noted in Section 10.5, this provides additional security properties on top of those provided by ML-DSA, RSA, ECDSA, and EdDSA, and failure of randomness does not compromise the Composite-ML-DSA algorithm or the underlying primitives, so it should be possible to exclude this RNG invocation from the FIPS boundary if an implementation is not able to guarantee use of a FIPS-approved RNG.

The authors wish to note that composite algorithms have great future utility both for future cryptographic migrations as well as bridging across jurisdictions, for example defining composite algorithms which combine FIPS cryptography with cryptography from a different national standards body.

E.2. Backwards Compatibility

The term "backwards compatibility" is used here to mean something more specific; that existing systems as they are deployed today can interoperate with the upgraded systems of the future. This draft explicitly does not provide backwards compatibility, only upgraded systems will understand the OIDs defined in this document.

If backwards compatibility is required, then additional mechanisms will be needed. Migration and interoperability concerns need to be thought about in the context of various types of protocols that make use of X.509 and PKIX with relation to digital signature objects, from online negotiated protocols such as TLS 1.3 [RFC8446] and IKEv2 [RFC7296], to non-negotiated asynchronous protocols such as S/MIME signed email [RFC8551], document signing such as in the context of the European eIDAS regulations [eIDAS2014], and publicly trusted code signing [codesigningbrsv3.8], as well as myriad other standardized and proprietary protocols and applications that leverage CMS [RFC5652] signed structures. Composite simplifies the protocol design work because it can be implemented as a signature algorithm that fits into existing systems.

E.2.1. Hybrid Extensions (Keys and Signatures)

The use of Composite Crypto provides the possibility to process multiple algorithms without changing the logic of applications but updating the cryptographic libraries: one-time change across the whole system. However, when it is not possible to upgrade the crypto engines/libraries, it is possible to leverage X.509 extensions to encode the additional keys and signatures. When the custom extensions are not marked critical, although this approach provides the most backward-compatible approach where clients can simply ignore the post-quantum (or extra) keys and signatures, it also requires all applications to be updated for correctly processing multiple algorithms together.

E.3. Profiling down the number of options

One immediately daunting aspect of this specification is the number of composite algorithm combinations. Each option has been specified because there is a community that has a direct application for it; typically because the traditional component is already deployed in a change-managed environment, or because that specific traditional component is required for regulatory reasons.

However, this large number of combinations leads either to fracturing of the ecosystem into non-interoperable sub-groups when different communities choose non-overlapping subsets to support, or on the other hand it leads to spreading development resources too thin when trying to support all options.

This specification does not list any particular composite algorithm as mandatory-to-implement, however organizations that operate within specific application domains are encouraged to define profiles that select a small number of composites appropriate for that application domain. For applications that do not have any regulatory requirements or legacy implementations to consider, it is RECOMMENDED to focus implemtation effort on:

id-MLDSA65-ECDSA-P256-SHA512

In applications that require RSA, it is RECOMMENDED to focus implementation effort on:

id-MLDSA65-RSA3072-PSS-SHA512

In applications that only allow NIST PQC Level 5, it is RECOMMENDED to focus implemtation effort on:

id-MLDSA87-ECDSA-P384-SHA512

Appendix F. Test Vectors

The following test vectors are provided in a format similar to the NIST ACVP Known-Answer-Tests (KATs).

The structure is that a global message m is signed over in all test cases. m is the ASCII string "The quick brown fox jumps over the lazy dog." Within each test case there are the following values:

Implementers should be able to perform the following tests using the test vectors below:

  1. Load the public key pk or certificate x5c and use it to verify the signature s over the message m.

  2. Validate the self-signed certificate x5c.

  3. Load the signing private key sk and use it to produce a new signature which can be verified using the provided pk or x5c.

Test vectors are provided for each underlying component in isolation for the purposes of debugging.

Due to the length of the test vectors, you may prefer to retrieve them from GitHub. The reference implementation that generated them is also available:

https://github.com/lamps-wg/draft-composite-sigs/tree/main/src

{
"m":
"VGhlIHF1aWNrIGJyb3duIGZveCBqdW1wcyBvdmVyIHRoZSBsYXp5IGRvZy4=",

"tests": [
{
"tcId": "id-ML-DSA-44",
"pk": "Vbn3715DarAARRLAeRbHhyQg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]
}

Appendix G. Intellectual Property Considerations

The following IPR Disclosure relates to this draft:

https://datatracker.ietf.org/ipr/3588/

Appendix H. Contributors and Acknowledgements

This document incorporates contributions and comments from a large group of experts. The Editors would especially like to acknowledge the expertise and tireless dedication of the following people, who attended many long meetings and generated millions of bytes of electronic mail and VOIP traffic over the past few years in pursuit of this document:

Serge Mister (Entrust), Felipe Ventura (Entrust), Richard Kettlewell (Entrust), Ali Noman (Entrust), Daniel Van Geest (CryptoNext), Dr. Britta Hale (Naval Postgraduade School), Tim Hollebeek (Digicert), Panos Kampanakis (Amazon), Richard Kisley (IBM), Piotr Popis, François Rousseau, Falko Strenzke, Alexander Ralien (Siemens), José Ignacio Escribano, Jan Oupický, 陳志華 (Abel C. H. Chen, Chunghwa Telecom), 林邦曄 (Austin Lin, Chunghwa Telecom), Zhao Peiduo (Seventh Sense AI), Phil Hallin (Microsoft), Samuel Lee (Microsoft), Alicja Kario (Red Hat), Jean-Pierre Fiset (Crypto4A), Varun Chatterji (Seventh Sense AI) and Mojtaba Bisheh-Niasar

We especially want to recognize the contributions of Dr. Britta Hale who has helped immensely with strengthening the signature combiner construction, and with analyzing the scheme with respect to EUF-CMA and Non-Separability properties.

We are grateful to all who have given feedback over the years, formally or informally, on mailing lists or in person, including any contributors who may have been inadvertently omitted from this list.

This document borrows text from similar documents, including those referenced below. Thanks go to the authors of those documents. "Copying always makes things easier and less error prone" - [RFC8411].

H.1. Making contributions

Additional contributions to this draft are welcome. Please see the working copy of this draft at, as well as open issues at:

https://github.com/lamps-wg/draft-composite-sigs

Authors' Addresses

Mike Ounsworth
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
John Gray
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
Massimiliano Pala
OpenCA Labs
New York City, New York,
United States of America
Jan Klaussner
Bundesdruckerei GmbH
Kommandantenstr. 18
10969 Berlin
Germany
Scott Fluhrer
Cisco Systems