Composite Signatures For Use In Internet PKI

2.1. Algorithm Selection Criteria

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

1. A single RSA combination is provided (but RSA modulus size not mandated), matched with NIST PQC Level 3 algorithms.¶
2. 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.¶
3. NIST level 1 candidates (Falcon512 and Kyber512) are provided, matched with 256-bit elliptic curves, intended for constrained use cases.¶
4. A single SPHINCS+ combination is provided for use cases that wish to put hash-based signatures into hybrid combination.¶
5. A generic composite algorithm is provided for implementers who wish to use combinations not listed here, without the overhead of defining new OIDs. Caution should be exercised to avoid issues with compatibility and complex cryptographic policy mechanisms.¶

The authors wish to note that although all the composite structures defined in this and the companion composite keys [I-D.ounsworth-pq-composite-keys] and composite KEM [I-D.ounsworth-pq-composite-kem] specifications are defined in such a way as to easily allow 3 or more component algorithms, it was decided to only specify explicit pairs. The generic composite specified in this document allows for an arbitrary number of components. This also does not preclude future specification of explicit combinations with three or more components.¶

2.2. 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.¶

3.1. Composite Keys

A composite signature MAY be associated with a composite public key as defined in [I-D.ounsworth-pq-composite-keys], but MAY also be associated with multiple public keys from different sources, for example multiple X.509 certificates, or multiple cryptographic modules. In the latter case, composite signatures MAY be used as the mechanism for carrying multiple signatures in a non-composite hybrid authentication mechanism such as those described in [I-D.becker-guthrie-noncomposite-hybrid-auth].¶

digitalSignature;
nonRepudiation;
keyCertSign; and
cRLSign.

digitalSignature; and
nonRepudiation;

3.2. sa-CompositeSignature

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

sa-CompositeSignature SIGNATURE-ALGORITHM ::= {
    IDENTIFIER TYPE OBJECT IDENTIFIER
    VALUE CompositeSignatureValue
    PARAMS ANY DEFINED BY ALGORITHM
    PUBLIC-KEYS { pk-Composite }
    SMIME-CAPS ANY DEFINED BY ALGORITHM }

The following is an explanation how SIGNATURE-ALGORITHM elements are used to create Composite Signatures:¶

3.3. CompositeSignatureValue

The output of the composite signature algorithm is the DER encoding of the following structure:¶

CompositeSignatureValue ::= SEQUENCE SIZE (2..MAX) OF BIT STRING

Where each BIT STRING within the SEQUENCE is a signature value produced by one of the component keys. It MUST contain one signature value produced by each component algorithm, and in the same order as in the associated CompositeSignatureParams object.¶

A CompositeSignatureValue MUST contain the same number of component signatures as the corresponding public and private keys, and the order of component signature values MUST correspond to the component public keys.¶

The choice of SEQUENCE OF BIT STRING, rather than for example a single BIT STRING containing the concatenated signature values, is to gracefully handle variable-length signature values by taking advantage of ASN.1's built-in length fields.¶

3.4. CompositeSignatureParameters

Composite signature parameters are defined as follows and MAY be used when a composite signature is used with an AlgorithmIdentifier:¶

CompositeSignatureParams ::= SEQUENCE SIZE (2..MAX) OF
     AlgorithmIdentifier{SIGNATURE-ALGORITHM, {SignatureAlgSet}}

The signature's CompositeSignatureParams sequence MUST contain the same component algorithms listed in the same order as in the associated CompositePublicKey.¶

For explicit algorithms, it is not strictly necessary to carry a CompositeSignatureParams with the list of component algorithms in the signature algorithm parameters because clients can infer the expected component algorithms from the algorithm identifier. The PARAMS is left optional because some types of component algorithms will require parameters to be carried, such as RSASSA-PSS-params as defined in [RFC8017]. Section 3.2 defines PARAMS ANY DEFINED BY ALGORITHM so that explicit algorithms may define params as ABSENT, or use CompositeSignatureParams as defined in ASN.1 module. For generic compsite algorithms, CompositeSignatureParams MUST be included.¶

3.5. Encoding Rules

Many protocol specifications will require that composite signature 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.¶

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.¶

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

4.1. Notes on id-Dilithium3-RSA-PSS

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

When the id-Dilithium3-RSA-PSS object identifier is used with an AlgorithmIdentifier, the AlgorithmIdentifier.parameters MUST be of type `CompositeSignatureParams as follows:¶

SEQUENCE {
    AlgorithmIdentifier {
        id-Dilithium3TBD
    },
    AlgorithmIdentifier {
        id-RSASSA-PSS,
        RSASSA-PSS-params
    }
}

EDNOTE: We probably should pick concrete crypto for the RSASSA-PSS-params. Once the crypto is fixed, we could omit the parameters entirely and expect implementations to re-constitute the params structures as necessary in order to call into lower-level crypto libraries.¶

TODO: there must be a way to put all this the ASN.1 Module rather than just specifying it as text?¶

4.2. Notes on Generic Composite

This draft remains backwards compatible with the previous version of composite signatures. Explicit Composite keys are a rigid subset of generic composite keys. In previous versions, the composite signature algorihtm Identifier and the composite key identifier used different Object Identifiers. The generic composite signature algorithm identifier is:¶

id-alg-composite OBJECT IDENTIFIER ::= {
    iso(1)  identified-organization(3) dod(6) internet(1) private(4)
    enterprise(1) opencA(18227) algorithms(2) id-alg-composite(1) }

As defined in [I-D.ounsworth-pq-composite-keys], a generic composite key uses the following identifier:¶

id-composite-key OBJECT IDENTIFIER ::= {
    joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
    algorithm(80) composite(4) compositekey(1) }

See the ASN.1 module in section Section 6 for the definitions of Generic Composite algorithms¶

id-alg-composite-sha256 OBJECT IDENTIFIER ::= {
    iso(1)  identified-organization(3) dod(6) internet(1) private(4)
    enterprise(1) openCA(18227) algorithms(2) id-alg-composite(1)
    id-alg-composite-sha256(2) }

id-alg-composite-sha512 OBJECT IDENTIFIER ::= {
    iso(1)  identified-organization(3) dod(6) internet(1) private(4)
    enterprise(1) openCA(18227) algorithms(2) id-alg-composite(1)
    id-alg-composite-sha512(4) }

CompositeSignatureParams ::= SEQUENCE SIZE (2..MAX) OF
     AlgorithmIdentifier{SIGNATURE-ALGORITHM, {SignatureAlgSet}}

5.1. Composite Signature Generation Process

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 3.2.¶

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

Input:
     K1, K2, .., Kn     Signing private keys. See note below on
                        composite inputs.

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

     M                  Message to be signed, an octet string

Output:
     S                  The signatures, a CompositeSignatureValue

Signature Generation Process:
   1. Generate the n component signatures independently,
      according to their algorithm specifications.

        for i := 1 to n
            Si := Sign( Ki, Ai, M )

   2. Encode each component signature S1, S2, .., Sn into a BIT STRING
      according to its algorithm specification.

        S ::= Sequence { S1, S2, .., Sn }

   3. Output S

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, for example they may be carried in CompositePrivateKey and CompositeSignatureParams structures. It is also possible to generate a composite signature that combines signatures from distinct 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 in [I-D.ounsworth-pq-composite-keys], no component signature may itself be a composite; ie the signature generation process MUST fail if one of the private keys K1, K2, .., Kn is a composite with the OID id-alg-composite or an explicit composite OID.¶

A composite signature MUST produce, and include in the output, a signature value for every component key in 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, etc.¶

For security when using a generic composite signature algorithm, the list of component signature algorithms A1, A2, .., An, which may be carried in a CompositeSignatureParams object, SHOULD be included in the signed message M to prevent an attacker from substituting a weaker algorithm which is compatible with the same public key. This attack is not unique or new to the composite format.¶

5.2. Composite Signature Verification Process

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.¶

Input:
     P1, P2, .., Pn     Public verification keys. See note below on
                        composite inputs.

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

     S1, S2, .., Sn    Component signature values to be verified.
                       See note below on composite inputs.

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

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 three sequences have
      different numbers of elements, or any of the public keys
      P1, P2, .., Pn or algorithm identifiers A1, A2, .., An are
      composite with the OID id-alg-composite or an explicit composite
      OID then output "Invalid signature" and stop.

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

     for i := 1 to n
          if not verify( Pi, M, Si, Ai ), then
            output "Invalid signature"

      if all succeeded, then
        output "Valid signature"

Note on composite inputs: the method of providing the list of component keys, algorithms and signatures is flexible and beyond the scope of this pseudo-code, for example they may be carried in CompositePublicKey, CompositeSignatureParams, and compositesignaturevalue structures. It is also possible to verify a composite signature where the component public verification keys belong, for example, to separate X.509 certificates or cryptographic modules. Variations in the process to accommodate particular public verification 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 in [I-D.ounsworth-pq-composite-keys], no component signature may be composite; ie the signature verification procedure MUST fail if any of the public keys P1, P2, .., Pn or algorithm identifiers A1, A2, .., An are composite with OID id-alg-composite or an explicit composite OID.¶

Some verification clients may include a policy mechanism for specifying acceptable subsets of algorithms. In these cases, implementer MAY, in the interest of performance of compatibility, modify the above process to skip one or more signature validations as per their local client policy. See [I-D.pala-klaussner-composite-kofn] for a discussion of implementation and associated risks.¶

8.1. 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 a single public key, certificate, or signature may contain a mixture of deprecated and non-deprecated algorithms. Moreover, implementers may decide that certain cryptographic algorithms have complementary security properties and are acceptable in combination even though neither algorithm is acceptable by itself.¶

Specifying a modified verification algorithm to handle these situations is beyond the scope of this draft, but could be desirable as the subject of an application profile document, or to be up to the discretion of implementers.¶

2. Check policy to see whether A1, A2, ..., An constitutes a valid
   combination of algorithms.

   if not checkPolicy(A1, A2, ..., An), then
     output "Invalid signature"

8.2. K-of-N Validation Mode

This document defines a composite signature verification process in Section 5.2 where the verifier verifies all component signatures and fails if any component fails.¶

The authors recognize that there will be scenarios where the verifier considers a single component algorithm -- or subset of component algorithms -- to provide sufficient security, and therefore for performance, or other practical reasons, wishes to skip the verification of one or more component signatures. For example, it might be the case where the signer (whether it be a CA or an end entity) needs to be able to specify how its signatures are to be interpreted and verified. Another use-case is where one of the composite algorithms' implementation might not be stable yet, possibly causing signature validation or generation issues across different providers or vendors.¶

A detailed description of a K of N validation mode that address all these use-cases is described in [I-D.pala-klaussner-composite-kofn].¶

A.1. Combiner modes (KofN)

For content commitment use-cases, such as legally-binding non-repudiation, the signer (whether it be a CA or an end entity) needs to be able to specify how its signature is to be interpreted and verified.¶

For now we have removed combiner modes (AND, OR, KofN) from this draft, but we are still discussing how to incorporate this for the cases where it is needed (maybe a X.509 v3 extension, or a signature algorithm param).¶

B.1. Generic Composite Signature Examples

TODO¶

B.2. Explicit Composite Signature Examples

TODO¶

C.1. Backwards Compatibility

As noted in the introduction, the post-quantum cryptographic migration will face challenges in both ensuring cryptographic strength against adversaries of unknown capabilities, as well as providing ease of migration. The composite mechanisms defined in this document primarily address cryptographic strength, however this section contains notes on how backwards compatibility may be obtained.¶

The term "ease of migration" is used here to mean that existing systems can be gracefully transitioned to the new technology without requiring large service disruptions or expensive upgrades. 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.¶

These 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.¶

E.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/EntrustCorporation/draft-ounsworth-composite-sigs¶