Composite Signatures For Use In Internet PKI

Internet-Draft	PQ Composite Sigs	October 2023
Ounsworth, et al.	Expires 25 April 2024	[Page]

Abstract

The migration to post-quantum cryptography is unique in the history of modern digital cryptography in that neither the old outgoing nor the new incoming algorithms are fully trusted to protect data for the required data lifetimes. The outgoing algorithms, such as RSA and elliptic curve, may fall to quantum cryptanalysis, while the incoming post-quantum algorithms face uncertainty about both the underlying mathematics as well as hardware and software implementations that have not had sufficient maturing time to rule out classical cryptanalytic attacks and implementation bugs.¶

Cautious implementers may wish to layer cryptographic algorithms such that an attacker would need to break all of them in order to compromise the data being protected using either a Post-Quantum / Traditional Hybrid, Post-Quantum / Post-Quantum Hybrid, or combinations thereof. This document, and its companions, defines a specific instantiation of hybrid paradigm called "composite" where multiple cryptographic algorithms are combined to form a single key or signature such that they can be treated as a single atomic object at the protocol level.¶

This document defines the structures CompositeSignaturePublicKey, CompositeSignaturePrivateKey and CompositeSignatureValue, which are sequences of the respective structure for each component algorithm. Composite signature algorithm identifiers are specified in this document which represent the explicit combinations of the underlying component algorithms.¶

2. Introduction

During the transition to post-quantum cryptography, there will be uncertainty as to the strength of cryptographic algorithms; we will no longer fully trust traditional cryptography such as RSA, Diffie-Hellman, DSA and their elliptic curve variants, but we will also not fully trust their post-quantum replacements until they have had sufficient scrutiny and time to discover and fix implementation bugs. Unlike previous cryptographic algorithm migrations, the choice of when to migrate and which algorithms to migrate to, is not so clear. Even after the migration period, it may be advantageous for an entity's cryptographic identity to be composed of multiple public-key algorithms.¶

Cautious implementers may wish to combine cryptographic algorithms such that an attacker would need to break all of them in order to compromise the data being protected. Such mechanisms are referred to as Post-Quantum / Traditional Hybrids [I-D.driscoll-pqt-hybrid-terminology].¶

PQ/T Hybrid cryptography can, in general, provide solutions to two migration problems:¶

Algorithm strength uncertainty: During the transition period, some post-quantum signature and encryption algorithms will not be fully trusted, while also the trust in legacy public key algorithms will start to erode. A relying party may learn some time after deployment that a public key algorithm has become untrustworthy, but in the interim, they may not know which algorithm an adversary has compromised.¶
Ease-of-migration: During the transition period, systems will require mechanisms that allow for staged migrations from fully classical to fully post-quantum-aware cryptography.¶
Safeguard against faulty algorithm implementations and compromised keys: Even for long known algorithms there is a non-negligible risk of severe implementation faults. Latest examples are the ROCA attack and ECDSA psychic signatures. Using more than one algorithms will mitigate these risks.¶

This document defines a specific instantiation of the PQ/T Hybrid paradigm called "composite" where multiple cryptographic algorithms are combined to form a single signature such that it can be treated as a single atomic algorithm at the protocol level. Composite algorithms address algorithm strength uncertainty because the composite algorithm remains strong so long as one of its components remains strong. Concrete instantiations of composite signature algorithms are provided based on ML-DSA, Falcon, RSA and ECDSA. Backwards compatibility is not directly covered in this document, but is the subject of Appendix B.2.¶

This document is intended for general applicability anywhere that digital signatures are used within PKIX and CMS structures. For a more detailed use-case discussion for composite signatures, the reader is encouraged to look at [I-D.vaira-pquip-pqc-use-cases]¶

2.1. 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.¶

The following terms are used in this document:¶

ALGORITHM: A standardized cryptographic primitive, as well as any ASN.1 structures needed for encoding data and metadata needed to use the algorithm. This document is primarily concerned with algorithms for producing digital signatures.¶

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.¶

COMPONENT ALGORITHM: A single basic algorithm which is contained within a composite algorithm.¶

COMPOSITE ALGORITHM: An algorithm which is a sequence of two or more component algorithms, as defined in Section 3.¶

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

LEGACY: For the purposes of this document, a legacy algorithm is any cryptographic algorithm currently is use which is not believe to be resistant to quantum cryptanalysis.¶

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

POST-QUANTUM ALGORITHM: Any cryptographic algorithm which is believed to be resistant to classical and quantum cryptanalysis, such as the algorithms being considered for standardization by NIST.¶

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.¶

STRIPPING ATTACK: An attack in which the attacker is able to downgrade the cryptographic object to an attacker-chosen subset of original set of component algorithms in such a way that it is not detectable by the receiver. For example, substituting a composite public key or signature for a version with fewer components.¶

2.2. Composite Design Philosophy

[I-D.driscoll-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 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, and ciphertext 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 KEM algorithms without requiring any modification of the protocol to handle multiple keys.¶

2.3. Composite Signatures

Here we define the signature mechanism in which a signature is a cryptographic primitive that consists of three algorithms:¶

KeyGen() -> (pk, sk): A probabilistic key generation algorithm, which generates a public key pk and a secret key sk.¶
Sign(sk, Message) -> (signature): A signing algorithm which takes as input a secret key sk and a Message, and outputs a signature¶
Verify(pk, Message, signature) -> true or false: A verification algorithm which takes as input a public key, a Message and signature and outputs true if the signature and public key can be used to verify the message. Thus it proves the Message was signed with the secret key associated with the public key and verifies the integrity of the Message. If the signature and public key cannot verify the Message, it returns false.¶

A composite signature allows two or more underlying signature algorithms to be combined into a single cryptographic signature operation and can be used for applications that require signatures.¶

2.3.1. Composite KeyGen

The KeyGen() -> (pk, sk) of a composite signature algorithm will perform the KeyGen() of the respective component signature algorithms and it produces a composite public key pk as per Section 3.2 and a composite secret key sk is per Section 3.3.¶

2.3.2. Composite Sign

Generation of a composite signature involves applying each component algorithm's signature process to the input message according to its specification, and then placing each component signature value into the CompositeSignatureValue structure defined in Section 4.1.¶

The following process is used to generate composite signature values.¶

Sign (sk, Message) -> (signature)
Input:
     K1, K2             Signing private keys for each component. See note below on
                        composite inputs.

     A1, A2             Component signature algorithms. See note below on
                        composite inputs.

     Message            The Message to be signed, an octet string

     HASH               The Message Digest Algorithm used for pre-hashing.  See section
                        on pre-hashing below.

     OID                The Composite Signature String Algorithm Name converted
                        from ASCII to bytes.  See section on OID concatenation
                        below.

Output:
     signature          The composite signature, a CompositeSignatureValue

Signature Generation Process:

   1. Compute a Hash of the Message

         M' = HASH(Message)

   2. Generate the n component signatures independently,
      according to their algorithm specifications.

         S1 := Sign( K1, A1, OID || M' )
         S2 := Sign( K2, A2, OID || M' )

   3. Encode each component signature S1 and S2 into a BIT STRING
      according to its algorithm specification.

        signature ::= Sequence { S1, S2 }

   4. Output signature

Figure 1: Composite Sign(sk, Message)

Note on composite inputs: the method of providing the list of component keys and algorithms is flexible and beyond the scope of this pseudo-code. When passed to the Composite Sign(sk, Message) API the sk is a CompositePrivateKey. It is possible to construct a CompositePrivateKey from component keys stored in separate software or hardware keystores. Variations in the process to accommodate particular private key storage mechanisms are considered to be conformant to this document so long as it produces the same output as the process sketched above.¶

Since recursive composite public keys are disallowed, no component signature may itself be a composite; ie the signature generation process MUST fail if one of the private keys K1 or K2 is a composite.¶

A composite signature MUST produce, and include in the output, a signature value for every component key in the corresponding CompositePublicKey, and they MUST be in the same order; ie in the output, S1 MUST correspond to K1, S2 to K2.¶

2.3.3. Composite Verify

Verification of a composite signature involves applying each component algorithm's verification process according to its specification.¶

In the absence of an application profile specifying otherwise, compliant applications MUST output "Valid signature" (true) if and only if all component signatures were successfully validated, and "Invalid signature" (false) otherwise.¶

The following process is used to perform this verification.¶

Composite Verify(pk, Message, signature)
Input:
     P1, P2             Public verification keys. See note below on
                        composite inputs.

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

     signature          CompositeSignatureValue containing the component
                        signature values (S1 and S2) to be verified.

     A1, A2             Component signature algorithms. See note
                        below on composite inputs.

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

     OID                The Composite Signature String Algorithm Name converted
                        from ASCII to bytes.  See section on OID concatenation
                        below

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

Signature Verification Procedure::
   1. Check keys, signatures, and algorithms lists for consistency.

      If Error during Desequencing, or the sequences have
      different numbers of elements, or any of the public keys
      P1 or P2 and the algorithm identifiers A1 or A2 are
      composite then output "Invalid signature" and stop.

   2. Compute a Hash of the Message

         M' = HASH(Message)

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

       if not verify( P1, OID || M', S1, A1 ) then
            output "Invalid signature"
       if not verify( P2, OID || M', S2, A2 ) then
            output "Invalid signature"

       if all succeeded, then
        output "Valid signature"

Figure 2: Composite Verify(pk, Message, signature)

Note on composite inputs: the method of providing the list of component keys and algorithms is flexible and beyond the scope of this pseudo-code. When passed to the Composite Verify(pk, Message, signature) API the pk is a CompositePublicKey. It is possible to construct a CompositePublicKey from component keys stored in separate software or hardware keystores. Variations in the process to accommodate particular private key storage mechanisms are considered to be conformant to this document so long as it produces the same output as the process sketched above.¶

2.4. OID Concatenation

As mentioned above, the OID input value for the Composite Signature Generation and verification process is the String representation of the OID converted from ASCII to bytes. The following table shows the HEX encoding of the ASCII String representation for each Signature AlgorithmID¶

Table 1: Composite Signature OID Concatenations
Composite Signature AlgorithmID	HEX Encoding to be prepended to each Message
id-MLDSA44-RSA2048-PSS-SHA256	69642D4D4C44534134342D525341323034382D5053532D534841323536
id-MLDSA44-RSA2048-PKCS15-SHA256	69642D4D4C44534134342D525341323034382D504B435331352D534841323536
id-MLDSA44-Ed25519-SHA512	69642D4D4C44534134342D456432353531392D534841353132
id-MLDSA44-ECDSA-P256-SHA256	69642D4D4C44534134342D45434453412D503235362D534841323536
id-MLDSA44-ECDSA-brainpoolP256r1-SHA256	69642D4D4C44534134342D45434453412D627261696E706F6F6C5032353672312D534841323536
id-MLDSA65-RSA3072-PSS-SHA256	69642D4D4C44534136352D525341333037322D5053532D534841323536
id-MLDSA65-RSA3072-PKCS15-SHA256	69642D4D4C44534136352D525341333037322D504B435331352D534841323536
id-MLDSA65-ECDSA-P256-SHA256	69642D4D4C44534136352D45434453412D503235362D534841323536
id-MLDSA65-ECDSA-brainpoolP256r1-SHA256	69642D4D4C44534136352D45434453412D627261696E706F6F6C5032353672312D534841323536
id-MLDSA65-Ed25519-SHA512	69642D4D4C44534136352D456432353531392D534841353132
id-MLDSA87-ECDSA-P384-SHA384	69642D4D4C44534138372D45434453412D503338342D534841333834
id-MLDSA87-ECDSA-brainpoolP384r1-SHA384	69642D4D4C44534138372D45434453412D627261696E706F6F6C5033383472312D534841333834
id-MLDSA87-Ed448-SHAKE256	69642D4D4C44534138372D45643434382D5348414B45323536
id-Falon512-ECDSA-P256-SHA256	69642D46616C6F6E3531322D45434453412D503235362D534841323536
id-Falcon512-ECDSA-brainpoolP256r1-SHA256	69642D46616C636F6E3531322D45434453412D627261696E706F6F6C5032353672312D534841323536
id-Falcon512-Ed25519-SHA512	69642D46616C636F6E3531322D456432353531392D534841353132

2.5. PreHashing the Message

As noted in the composite signature generation process and composite signature verification process, the Message should be pre-hashed into M' with the digest algorithm specified in the composite signature algorithm identifier. The choice of the digest algorithm was chosen with the following criteria:¶

For composites paired with RSA or ECDSA, the hashing algorithm SHA256 or SHA384 is used as part of the RSA or ECDSA signature algorithm and is therefore also used as the composite prehashing algorithm.¶
For Dilithium signing a digest of the message is allowed as long as the hash function provides at least y bits of classical security strength against both collision and second preimage attacks. For MLDSA44 y is 128 bits, MLDSA65 y is 192 bits and for MLDSA87 y is 256 bits. Therefore SHA256 paired with RSA and SHA256 and SHA384 paired with ECDSA match the appropriate security strength.¶
Ed25519 [RFC8032] uses SHA512 internally, therefore SHA512 is used to pre-hash the message when Ed25519 is a component algorithm.¶
Ed448 [RFC8032] uses SHAKE256 internally, therefore SHA256 with an output length of 512 bits is used to pre-hash the message when Ed448 is a component algorithm. This is denoted in the table in Section 5 as SHAKE256/512.¶
TODO: For Falcon signing it is expected prehashing digest accomodations will be allowed.¶

2.6. Algorithm Selection Criteria

The composite algorithm combinations defined in this document were chosen according to the following guidelines:¶

A single RSA combination is provided at a key size of 3072 bits, matched with NIST PQC Level 3 algorithms.¶
Elliptic curve algorithms are provided with combinations on each of the NIST [RFC6090], Brainpool [RFC5639], and Edwards [RFC7748] curves. NIST PQC Levels 1 - 3 algorithms are matched with 256-bit curves, while NIST levels 4 - 5 are matched with 384-bit elliptic curves. This provides a balance between matching classical security levels of post-quantum and traditional algorithms, and also selecting elliptic curves which already have wide adoption.¶
NIST level 1 candidates are provided, matched with 256-bit elliptic curves, intended for constrained use cases.¶

If other combinations are needed, a separate specification should be submitted to the IETF LAMPS working group. To ease implementation, these specifications are encouraged to follow the construction pattern of the algorithms specified in this document.¶

The composite structures defined in this specification allow only for pairs of algorithms. This also does not preclude future specification from extending these structures to define combinations with three or more components.¶

3. Composite Signature Structures

In order for signatures to be composed of multiple algorithms, we define encodings consisting of a sequence of signature primitives (aka "component algorithms") such that these structures can be used as a drop-in replacement for existing signature fields such as those found in PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], CMS [RFC5652].¶

3.1. pk-CompositeSignature

The following ASN.1 Information Object Class is a template to be used in defining all composite Signature public key types.¶

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

As an example, the public key type pk-MLDSA65-ECDSA-P256-SHA256 is defined as:¶

pk-MLDSA65-ECDSA-P256-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-P256-SHA256,
  OCTET STRING, ECPoint}

The full set of key types defined by this specification can be found in the ASN.1 Module in Section 6.¶

3.2. CompositeSignaturePublicKey

Composite public key data is represented by the following structure:¶

CompositeSignaturePublicKey ::= SEQUENCE SIZE (2) OF BIT STRING

A composite key MUST contain two component public keys. The order of the component keys is determined by the definition of the corresponding algorithm identifier as defined in section Section 5.¶

Some applications may need to reconstruct the SubjectPublicKeyInfo objects corresponding to each component public key. Table 3 in Section 5 provides the necessary mapping between composite and their component algorithms for doing this reconstruction. This also motivates the design choice of SEQUENCE OF BIT STRING instead of SEQUENCE OF OCTET STRING; using BIT STRING allows for easier transcription between CompositeSignaturePublicKey and SubjectPublicKeyInfo.¶

When the CompositeSignaturePublicKey must be provided in octet string or bit string format, the data structure is encoded as specified in Section 3.4.¶

3.3. CompositeSignaturePrivateKey

Usecases that require an interoperable encoding for composite private keys, such as when private keys are carried in PKCS #12 [RFC7292], CMP [RFC4210] or CRMF [RFC4211] MUST use the following structure.¶

CompositeSignaturePrivateKey ::= SEQUENCE SIZE (2) OF OneAsymmetricKey

Each element is a OneAsymmetricKey` [RFC5958] object for a component private key.¶

The parameters field MUST be absent.¶

The order of the component keys is the same as the order defined in Section 3.2 for the components of CompositeSignaturePublicKey.¶

When a CompositePrivateKey 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 5, the privateKey field SHALL contain the CompositeSignaturePrivateKey, and the publicKey field MUST NOT be present. Associated public key material MAY be present in the CompositeSignaturePrivateKey.¶

In some usecases the private keys that comprise a composite key may not be represented in a single structure or even be contained in a single cryptographic module; for example if one component is within the FIPS boundary of a cryptographic module and the other is not; see {sec-fips} for more discussion. The establishment of correspondence between public keys in a CompositeSignaturePublicKey and private keys not represented in a single composite structure is beyond the scope of this document.¶

3.4. Encoding Rules

Many protocol specifications will require that the composite public key and composite private key data structures be represented by an octet string or bit string.¶

When an octet string is required, the DER encoding of the composite data structure SHALL be used directly.¶

CompositeSignaturePublicKeyOs ::= OCTET STRING (CONTAINING CompositeSignaturePublicKey ENCODED BY der)

When a bit string is required, the octets of the DER encoded composite data structure 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.¶

CompositeSignaturePublicKeyBs ::= BIT STRING (CONTAINING CompositeSignaturePublicKey ENCODED BY der)

In the interests of simplicity and avoiding compatibility issues, implementations that parse these structures MAY accept both BER and DER.¶

3.5. Key Usage Bits

For protocols such as X.509 [RFC5280] that specify key usage along with the public key, then the composite public key associated with a composite signature MUST have a signing-type key usage.¶

If the keyUsage extension is present in a Certification Authority (CA) certificate that indicates a composite key, then any combination of the following values MAY be present:¶

digitalSignature;
nonRepudiation;
keyCertSign; and
cRLSign.

If the keyUsage extension is present in an End Entity (EE) certificate that indicates a composite key, then any combination of the following values MAY be present:¶

digitalSignature; and
nonRepudiation;

Table 2
SIGNATURE-ALGORITHM element	Definition
IDENTIFIER	The Object ID used to identify the composite Signature Algorithm
VALUE	The Sequence of BIT STRINGS for each component signature value
PARAMS	Parameters are absent
PUBLIC-KEYS	The composite key required to produce the composite signature

5. Algorithm Identifiers

This section defines the algorithm identifiers for explicit combinations. For simplicity and prototyping purposes, the signature algorithm object identifiers specified in this document are the same as the composite key object Identifiers. A proper implementation should not presume that the object ID of a composite key will be the same as its composite signature algorithm.¶

This section is not intended to be exhaustive and other authors may define others composite signature algorithms so long as they are compatible with the structures and processes defined in this and companion public and private key documents.¶

Some use-cases desire the flexibility for clients to use any combination of supported algorithms, while others desire the rigidity of explicitly-specified combinations of algorithms.¶

The following table summarizes the details for each explicit composite signature algorithms:¶

The OID referenced are TBD for prototyping only, and the following prefix is used for each:¶

replace <CompSig> with the String "2.16.840.1.114027.80.7.1"¶

Therefore <CompSig>.1 is equal to 2.16.840.1.114027.80.7.1.1¶

Signature public key types:¶

Table 3: Composite Signature Algorithms
Composite Signature AlgorithmID	OID	First Algorithm	Second Algorithm	Pre-Hash
id-MLDSA44-RSA2048-PSS-SHA256	<CompSig>.1	MLDSA44	SHA256WithRSAEncryption	SHA256
id-MLDSA44-RSA2048-PKCS15-SHA256	<CompSig>.2	MLDSA44	SHA256WithRSAEncryption	SHA256
id-MLDSA44-Ed25519-SHA512	<CompSig>.3	MLDSA44	Ed25519	SHA512
id-MLDSA44-ECDSA-P256-SHA256	<CompSig>.4	MLDSA44	SHA256withECDSA	SHA256
id-MLDSA44-ECDSA-brainpoolP256r1-SHA256	<CompSig>.5	MLDSA44	SHA256withECDSA	SHA256
id-MLDSA65-RSA3072-PSS-SHA256	<CompSig>.6	MLDSA65	SHA256WithRSAPSS	SHA256
id-MLDSA65-RSA3072-PKCS15-SHA256	<CompSig>.7	MLDSA65	SHA256WithRSAEncryption	SHA256
id-MLDSA65-ECDSA-P256-SHA256	<CompSig>.8	MLDSA65	SHA256withECDSA	SHA256
id-MLDSA65-ECDSA-brainpoolP256r1-SHA256	<CompSig>.9	MLDSA65	SHA256withECDSA	SHA256
id-MLDSA65-Ed25519-SHA512	<CompSig>.10	MLDSA65	Ed25519	SHA512
id-MLDSA87-ECDSA-P384-SHA384	<CompSig>.11	MLDSA87	SHA384withECDSA	SHA384
id-MLDSA87-ECDSA-brainpoolP384r1-SHA384	<CompSig>.12	MLDSA87	SHA384withECDSA	SHA384
id-MLDSA87-Ed448-SHAKE256	<CompSig>.13	MLDSA87	Ed448	SHAKE256/512
id-Falon512-ECDSA-P256-SHA256	<CompSig>.14	Falcon512	SHA256withECDSA	SHA256
id-Falcon512-ECDSA-brainpoolP256r1-SHA256	<CompSig>.15	Falcon512	SHA256withECDSA	SHA256
id-Falcon512-Ed25519-SHA512	<CompSig>.16	Falcon512	Ed25519	SHA512

The table above contains everything needed to implement the listed explicit composite algorithms. See the ASN.1 module in section Section 6 for the explicit definitions of the above Composite signature algorithms.¶

Full specifications for the referenced algorithms can be found as follows:¶

MLDSA: [I-D.ietf-lamps-dilithium-certificates] and [FIPS.204-ipd]¶
ECDSA: [RFC5480]¶
Ed25519 / Ed448: [RFC8410]¶
Falcon: TBD¶
RSAES-PKCS-v1_5: [RFC8017]¶
RSASSA-PSS: [RFC8017]¶

5.1. Notes on id-MLDSA44-RSA2048-PSS-SHA256 and id-MLDSA65-RSA3072-PSS-SHA256

Use of RSA-PSS [RFC8017] deserves a special explanation.¶

The RSA component keys MUST be generated at the 2048-bit security level in order to match security level with ML-DSA-44 or at 3072-bits to match ML-DSA-65.¶

As with the other composite signature algorithms, when id-MLDSA44-RSA2048-PSS-SHA256 or id-MLDSA65-RSA3072-PSS-SHA256 is used in an AlgorithmIdentifier, the parameters MUST be absent. id-MLDSA44-RSA2048-PSS-SHA256 and id-MLDSA65-RSA3072-PSS-SHA256 SHALL instantiate RSA-PSS with the following parameters:¶

Table 4: RSA-PSS 2048 and 3072 Parameters
RSA-PSS Parameter	Value
Mask Generation Function	mgf1
Mask Generation params	SHA-256
Message Digest Algorithm	SHA-256

where:¶

Mask Generation Function (mgf1) is defined in [RFC8017]¶
SHA-256 is defined in [RFC6234].¶

6. ASN.1 Module

<CODE STARTS>


   Composite-Signatures-2023
     { joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
       algorithm(80) id-composite-signatures-2023 (TBDMOD) }

DEFINITIONS IMPLICIT TAGS ::= BEGIN

EXPORTS ALL;

IMPORTS
  PUBLIC-KEY, SIGNATURE-ALGORITHM, 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) }

  SubjectPublicKeyInfo
    FROM PKIX1Explicit-2009
      { iso(1) identified-organization(3) dod(6) internet(1)
        security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-pkix1-explicit-02(51) }

  OneAsymmetricKey
    FROM AsymmetricKeyPackageModuleV1
      { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
        pkcs-9(9) smime(16) modules(0)
        id-mod-asymmetricKeyPkgV1(50) }

  RSAPublicKey, ECPoint
    FROM PKIXAlgs-2009
      { iso(1) identified-organization(3) dod(6)
        internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-pkix1-algorithms2008-02(56) }

  sa-rsaSSA-PSS
    FROM PKIX1-PSS-OAEP-Algorithms-2009
       {iso(1) identified-organization(3) dod(6) internet(1) security(5)
       mechanisms(5) pkix(7) id-mod(0) id-mod-pkix1-rsa-pkalgs-02(54)}

;

--
-- Object Identifiers
--

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




--
-- Signature Algorithm
--


--
-- Composite Signature basic structures
--

CompositeSignaturePublicKey ::= SEQUENCE SIZE (2) OF BIT STRING

CompositeSignaturePublicKeyOs ::= OCTET STRING (CONTAINING
                                CompositeSignaturePublicKey ENCODED BY der)

CompositeSignaturePublicKeyBs ::= BIT STRING (CONTAINING
                                CompositeSignaturePublicKey ENCODED BY der)

CompositeSignaturePrivateKey ::= SEQUENCE SIZE (2) OF OneAsymmetricKey

CompositeSignatureValue ::= SEQUENCE SIZE (2) OF OCTET STRING

-- Composite Signature Value is just a sequence of OCTET STRINGS

--   CompositeSignaturePair{FirstSignatureValue, SecondSignatureValue} ::=
--     SEQUENCE {
--      signaturevalue1 FirstSignatureValue,
--      signaturevalue2 SecondSignatureValue }

   -- An Explicit Compsite Signature is a set of Signatures which
   -- are composed of OCTET STRINGS
--   ExplicitCompositeSignatureValue ::= CompositeSignaturePair {
--       OCTET STRING,OCTET STRING}


--
-- Information Object Classes
--

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


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

-- 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(7) signature(1) 1 }

pk-MLDSA44-RSA2048-PSS-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-RSA2048-PSS-SHA256,
  OCTET STRING, RSAPublicKey}

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(7) signature(1) 2 }

pk-MLDSA44-RSA2048-PKCS15-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-RSA2048-PKCS15-SHA256,
  OCTET STRING, RSAPublicKey}

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(7) signature(1) 3 }

pk-MLDSA44-Ed25519-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-Ed25519-SHA512,
  OCTET STRING, ECPoint}

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(7) signature(1) 4 }

pk-MLDSA44-ECDSA-P256-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-ECDSA-P256-SHA256,
  OCTET STRING, ECPoint}

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-MLDSA44-ECDSA-brainpoolP256r1-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 5 }

pk-MLDSA44-ECDSA-brainpoolP256r1-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-ECDSA-brainpoolP256r1-SHA256,
  OCTET STRING, ECPoint}

sa-MLDSA44-ECDSA-brainpoolP256r1-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-ECDSA-brainpoolP256r1-SHA256,
       pk-MLDSA44-ECDSA-brainpoolP256r1-SHA256 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA3072-PSS-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 6 }

pk-MLDSA65-RSA3072-PSS-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA3072-PSS-SHA256,
  OCTET STRING, RSAPublicKey}

sa-MLDSA65-RSA3072-PSS-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA3072-PSS-SHA256,
       pk-MLDSA65-RSA3072-PSS-SHA256 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA3072-PKCS15-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 7 }

pk-MLDSA65-RSA3072-PKCS15-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA3072-PKCS15-SHA256,
  OCTET STRING, RSAPublicKey}

sa-MLDSA65-RSA3072-PKCS15-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA3072-PKCS15-SHA256,
       pk-MLDSA65-RSA3072-PKCS15-SHA256 }


-- TODO: OID to be replaced by IANA
id-MLDSA65-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 8 }

pk-MLDSA65-ECDSA-P256-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-P256-SHA256,
  OCTET STRING, ECPoint}

sa-MLDSA65-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-ECDSA-P256-SHA256,
       pk-MLDSA65-ECDSA-P256-SHA256 }


-- TODO: OID to be replaced by IANA
id-id-MLDSA65-ECDSA-brainpoolP256r1-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 9 }

pk-id-MLDSA65-ECDSA-brainpoolP256r1-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-brainpoolP256r1-SHA256,
  OCTET STRING, ECPoint}

sa-id-MLDSA65-ECDSA-brainpoolP256r1-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-id-MLDSA65-ECDSA-brainpoolP256r1-SHA256,
       pk-id-MLDSA65-ECDSA-brainpoolP256r1-SHA256 }


-- 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(7) signature(1) 10 }

pk-MLDSA65-Ed25519-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-Ed25519-SHA512,
  OCTET STRING, ECPoint}

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-SHA384 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 11 }

pk-MLDSA87-ECDSA-P384-SHA384 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-ECDSA-P384-SHA384,
  OCTET STRING, ECPoint}

sa-MLDSA87-ECDSA-P384-SHA384 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-ECDSA-P384-SHA384,
       pk-MLDSA87-ECDSA-P384-SHA384 }


-- TODO: OID to be replaced by IANA
id-MLDSA87-ECDSA-brainpoolP384r1-SHA384 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 12 }

pk-MLDSA87-ECDSA-brainpoolP384r1-SHA384 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-ECDSA-brainpoolP384r1-SHA384,
  OCTET STRING, ECPoint}

sa-MLDSA87-ECDSA-brainpoolP384r1-SHA384 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-ECDSA-brainpoolP384r1-SHA384,
       pk-MLDSA87-ECDSA-brainpoolP384r1-SHA384 }


-- 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(7) signature(1) 13 }

pk-MLDSA87-Ed448-SHAKE256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-Ed448-SHAKE256,
  OCTET STRING, ECPoint}

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

-- TODO: OID to be replaced by IANA
id-Falon512-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 14 }

pk-Falon512-ECDSA-P256-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-Ed448-SHAKE256,
  OCTET STRING, ECPoint}

sa-Falon512-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-Falon512-ECDSA-P256-SHA256,
       pk-Falon512-ECDSA-P256-SHA256 }

-- TODO: OID to be replaced by IANA
id-Falcon512-ECDSA-brainpoolP256r1-SHA256 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 15 }

pk-Falcon512-ECDSA-brainpoolP256r1-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-Falcon512-ECDSA-brainpoolP256r1-SHA256,
  OCTET STRING, ECPoint}

sa-Falcon512-ECDSA-brainpoolP256r1-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-Falcon512-ECDSA-brainpoolP256r1-SHA256,
       pk-Falcon512-ECDSA-brainpoolP256r1-SHA256 }

-- TODO: OID to be replaced by IANA
id-Falcon512-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
   joint-iso-itu-t(2) country(16) us(840) organization(1)
   entrust(114027) algorithm(80) composite(7) signature(1) 16 }

pk-Falcon512-Ed25519-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-Falcon512-Ed25519-SHA512,
  OCTET STRING, ECPoint}

sa-Falcon512-Ed25519-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-Falcon512-Ed25519-SHA512,
       pk-Falcon512-Ed25519-SHA512 }


END

<CODE ENDS>

7. IANA Considerations

7.1. Object Identifier Allocations

EDNOTE to IANA: OIDs will need to be replaced in both the ASN.1 module and in Table 3.¶

7.1.1. Module Registration - SMI Security for PKIX Module Identifier

Decimal: IANA Assigned - Replace TBDMOD¶
Description: Composite-Signatures-2023 - id-mod-composite-signatures¶
References: This Document¶

7.1.2. 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-MLDSA44-ECDSA-brainpoolP256r1-SHA256¶
Decimal: IANA Assigned¶
Description: id-MLDSA44-ECDSA-brainpoolP256r1-SHA256¶
References: This Document¶
id-MLDSA65-RSA3072-PSS-SHA256¶
Decimal: IANA Assigned¶
Description: id-MLDSA65-RSA3072-PSS-SHA256¶
References: This Document¶
id-MLDSA65-RSA3072-PKCS15-SHA256¶
Decimal: IANA Assigned¶
Description: id-MLDSA65-RSA3072-PKCS15-SHA256¶
References: This Document¶
id-MLDSA65-ECDSA-P256-SHA256¶
Decimal: IANA Assigned¶
Description: id-MLDSA65-ECDSA-P256-SHA256¶
References: This Document¶
id-MLDSA65-ECDSA-brainpoolP256r1-SHA256¶
Decimal: IANA Assigned¶
Description: id-MLDSA65-ECDSA-brainpoolP256r1-SHA256¶
References: This Document¶
id-MLDSA65-Ed25519-SHA512¶
Decimal: IANA Assigned¶
Description: id-MLDSA65-Ed25519-SHA512¶
References: This Document¶
id-MLDSA87-ECDSA-P384-SHA384¶
Decimal: IANA Assigned¶
Description: id-MLDSA87-ECDSA-P384-SHA384¶
References: This Document¶
id-MLDSA87-ECDSA-brainpoolP384r1-SHA384¶
Decimal: IANA Assigned¶
Description: id-MLDSA87-ECDSA-brainpoolP384r1-SHA384¶
References: This Document¶
id-MLDSA87-Ed448-SHAKE256¶
Decimal: IANA Assigned¶
Description: id-MLDSA87-Ed448¶
References: This Document¶
id-Falon512-ECDSA-P256-SHA256¶
Decimal: IANA Assigned¶
Description: id-Falon512-ECDSA-P256-SHA256¶
References: This Document¶
id-Falcon512-ECDSA-brainpoolP256r1-SHA256¶
Decimal: IANA Assigned¶
Description: id-Falcon512-ECDSA-brainpoolP256r1-SHA256¶
References: This Document¶
id-Falcon512-Ed25519-SHA512¶
Decimal: IANA Assigned¶
Description: id-Falcon512-Ed25519¶
References: This Document¶

9. References

9.1. Normative References

[RFC2119]: Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, <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, November 2000, <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, September 2005, <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, September 2005, <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, May 2008, <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, March 2009, <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, March 2010, <https://www.rfc-editor.org/info/rfc5639>.
[RFC5652]: Housley, R., "Cryptographic Message Syntax (CMS)", STD 70, RFC 5652, DOI 10.17487/RFC5652, September 2009, <https://www.rfc-editor.org/info/rfc5652>.
[RFC5958]: Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, August 2010, <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, February 2011, <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, May 2011, <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, January 2016, <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, January 2017, <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, May 2017, <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, August 2018, <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, August 2018, <https://www.rfc-editor.org/info/rfc8411>.
[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, November 2015.

9.2. Informative References

[Bindel2017]: Bindel, N., Herath, U., McKague, M., and D. Stebila, "Transitioning to a quantum-resistant public key infrastructure", 2017, <https://link.springer.com/chapter/10.1007/978-3-319-59879-6_22>.
[I-D.becker-guthrie-noncomposite-hybrid-auth]: Becker, A., Guthrie, R., and M. J. Jenkins, "Non-Composite Hybrid Authentication in PKIX and Applications to Internet Protocols", Work in Progress, Internet-Draft, draft-becker-guthrie-noncomposite-hybrid-auth-00, 22 March 2022, <https://datatracker.ietf.org/doc/html/draft-becker-guthrie-noncomposite-hybrid-auth-00>.
[I-D.driscoll-pqt-hybrid-terminology]: D, F., "Terminology for Post-Quantum Traditional Hybrid Schemes", Work in Progress, Internet-Draft, draft-driscoll-pqt-hybrid-terminology-01, 20 October 2022, <https://datatracker.ietf.org/doc/html/draft-driscoll-pqt-hybrid-terminology-01>.
[I-D.guthrie-ipsecme-ikev2-hybrid-auth]: Guthrie, R., "Hybrid Non-Composite Authentication in IKEv2", Work in Progress, Internet-Draft, draft-guthrie-ipsecme-ikev2-hybrid-auth-00, 25 March 2022, <https://datatracker.ietf.org/doc/html/draft-guthrie-ipsecme-ikev2-hybrid-auth-00>.
[I-D.ietf-lamps-dilithium-certificates]: Massimo, J., Kampanakis, P., Turner, S., and B. Westerbaan, "Internet X.509 Public Key Infrastructure: Algorithm Identifiers for Dilithium", Work in Progress, Internet-Draft, draft-ietf-lamps-dilithium-certificates-01, 6 February 2023, <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-dilithium-certificates-01>.
[I-D.massimo-lamps-pq-sig-certificates]: Massimo, J., Kampanakis, P., Turner, S., and B. Westerbaan, "Algorithms and Identifiers for Post-Quantum Algorithms", Work in Progress, Internet-Draft, draft-massimo-lamps-pq-sig-certificates-00, 8 July 2022, <https://datatracker.ietf.org/doc/html/draft-massimo-lamps-pq-sig-certificates-00>.
[I-D.ounsworth-pq-composite-kem]: Ounsworth, M. and J. Gray, "Composite KEM For Use In Internet PKI", Work in Progress, Internet-Draft, draft-ounsworth-pq-composite-kem-01, 13 March 2023, <https://datatracker.ietf.org/doc/html/draft-ounsworth-pq-composite-kem-01>.
[I-D.pala-klaussner-composite-kofn]: Pala, M. and J. Klaußner, "K-threshold Composite Signatures for the Internet PKI", Work in Progress, Internet-Draft, draft-pala-klaussner-composite-kofn-00, 15 November 2022, <https://datatracker.ietf.org/doc/html/draft-pala-klaussner-composite-kofn-00>.
[I-D.vaira-pquip-pqc-use-cases]: Vaira, A., Brockhaus, H., Railean, A., Gray, J., and M. Ounsworth, "Post-quantum cryptography use cases", Work in Progress, Internet-Draft, draft-vaira-pquip-pqc-use-cases-00, 23 October 2023, <https://datatracker.ietf.org/api/v1/doc/document/draft-vaira-pquip-pqc-use-cases/>.
[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, April 2002, <https://www.rfc-editor.org/info/rfc3279>.
[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, July 2014, <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, October 2014, <https://www.rfc-editor.org/info/rfc7296>.
[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, November 2016, <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, August 2018, <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, April 2019, <https://www.rfc-editor.org/info/rfc8551>.

Appendix A. Samples

A.1. Explicit Composite Signature Examples

A.1.1. MLDSA44-ECDSA-P256-SHA256 Public Key

A.1.2. MLDSA44-ECDSA-P256 Private Key

A.1.3. MLDSA44-ECDSA-P256 Self-Signed X509 Certificate

Appendix B. Implementation Considerations

B.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 algorith with zero security, and the overall composite should be considered full strength and thus FIPS-approved.¶

The authors wish to note that this gives composite algorithms 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.¶

B.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 [codeSigningBRsv2.8], 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.¶

B.2.1. Parallel PKIs

We present the term "Parallel PKI" to refer to the setup where a PKI end entity possesses two or more distinct public keys or certificates for the same identity (name), but containing keys for different cryptographic algorithms. One could imagine a set of parallel PKIs where an existing PKI using legacy algorithms (RSA, ECC) is left operational during the post-quantum migration but is shadowed by one or more parallel PKIs using pure post quantum algorithms or composite algorithms (legacy and post-quantum).¶

Equipped with a set of parallel public keys in this way, a client would have the flexibility to choose which public key(s) or certificate(s) to use in a given signature operation.¶

For negotiated protocols, the client could choose which public key(s) or certificate(s) to use based on the negotiated algorithms, or could combine two of the public keys for example in a non-composite hybrid method such as [I-D.becker-guthrie-noncomposite-hybrid-auth] or [I-D.guthrie-ipsecme-ikev2-hybrid-auth]. Note that it is possible to use the signature algorithms defined in Section 5 as a way to carry the multiple signature values generated by one of the non-composite public mechanism in protocols where it is easier to support the composite signature algorithms than to implement such a mechanism in the protocol itself. There is also nothing precluding a composite public key from being one of the components used within a non-composite authentication operation; this may lead to greater convenience in setting up parallel PKI hierarchies that need to service a range of clients implementing different styles of post-quantum migration strategies.¶

For non-negotiated protocols, the details for obtaining backwards compatibility will vary by protocol, but for example in CMS [RFC5652], the inclusion of multiple SignerInfo objects is often already treated as an OR relationship, so including one for each of the signer's parallel PKI public keys would, in many cases, have the desired effect of allowing the receiver to choose one they are compatible with and ignore the others, thus achieving full backwards compatibility.¶

B.2.2. 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.¶