PQ/T Hybrid Composite Signatures for JOSE and COSE

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Table of Contents

1. Introduction

The impact of a potential Cryptographically Relevant Quantum Computer (CRQC) on algorithms whose security is based on mathematical problems such as integer factorisation or discrete logarithms over finite fields or elliptic curves raises the need for new algorithms that are perceived to be secure against CRQC as well as classical computers. Such algorithms are called post-quantum, while algorithms based on integer factorisation or discrete logarithms are called traditional.¶

While switching from a traditional algorithm to a post-quantum one intends to strengthen the security against an adversary possessing a quantum computer, the lack of maturing time of post-quantum algorithms compared to traditional algorithms raises uncertainty about their security.¶

Thus, the joint use of a traditional algorithm and a post-quantum algorithm in protocols represents a solution to this problem by providing security as long as at least one of the traditional or post-quantum components remains secure.¶

This document describes JSON Object Signing and Encryption (JOSE) and CBOR Object Signing and Encryption (COSE) serializations for hybrid composite signatures. The composite algorithms described combine ML-DSA as the post-quantum component and ECDSA as the traditional component.¶

2. Conventions and Definitions

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.¶

This document follows the terminology for post-quantum hybrid schemes defined in [I-D.draft-ietf-pquip-pqt-hybrid-terminology-04].¶

This section recalls some of this terminology, but also adds other definitions used throughout the whole document:¶

"Asymmetric Traditional Cryptographic Algorithm": An asymmetric cryptographic algorithm based on integer factorisation, finite field discrete logarithms, elliptic curve discrete logarithms, or related mathematical problems. A related mathematical problem is one that can be solved by solving the integer factorisation, finite field discrete logarithm or elliptic curve discrete logarithm problem. Where there is little risk of confusion asymmetric traditional cryptographic algorithms can also be referred to as traditional algorithms for brevity.¶

"Post-Quantum Algorithm": An asymmetric cryptographic algorithm that is intended to be secure against attacks using quantum computers as well as classical computers. As with all cryptography, it always remains the case that attacks, either quantum or classical, may be found against post-quantum algorithms. Therefore it should not be assumed that just because an algorithm is designed to provide post-quantum security it will not be compromised.¶

"Component Algorithm": Each cryptographic algorithm that forms part of a cryptographic scheme.¶

"Post-Quantum Traditional (PQ/T) Hybrid Scheme": A multi-algorithm scheme where at least one component algorithm is a post-quantum algorithm and at least one is a traditional algorithm.¶

"PQ/T Hybrid Digital Signature": A multi-algorithm digital signature scheme made up of two or more component digital signature algorithms where at least one is a post-quantum algorithm and at least one is a traditional algorithm.¶

"Composite Algorithm": An algorithm which is a sequence of two component algorithms, as defined in [I-D.draft-ietf-lamps-pq-composite-sigs-02].¶

3. Composite Keys and Signatures Structures

The structures of the composite keys and composite signatures follow the approach of [I-D.draft-ietf-lamps-pq-composite-sigs-02]. This design was chosen so that composite keys and signatures can be used as a drop-in replacement in JOSE / COSE object formats. This section gives some details about their construction.¶

(pk_1, sk_1) <- MLDSA.KeyGen()
(pk_2 = (x,y), sk_2 = d) <- ECDSA.KeyGen()

Composite Public Key <- pk_1 || pk_2 = pk_1 || x || y
Composite Private Key <- sk_1 || sk_2 = sk_1 || d

M' <- Domain || HASH(M)
M' <- Encode(M')

sig_1 <- MLDSA.Sign(sk_1, M')
sig_2 <- ECDSA.Sign(sk_2, M')

Composite Signature <- (sig_1, sig_2)

4. Composite Signature Algorithms

The ML-DSA signature scheme supports three possible parameter sets, each of which corresponding to a specific security strength. See [FIPS.204] for more considerations on that matter.¶

The hybrid composite schemes are described in more detail in [I-D.draft-ietf-lamps-pq-composite-sigs-02].¶

The traditional signature algorithm for each combination in Table 2 and Table 3 was chosen to match the security level of the ML-DSA post-quantum component. More precisely, NIST security levels 1-3 are matched with 256-bit curves and NIST security levels 4-5 are matched with 384-bit elliptic curves.¶

5. Composite Signature Key Types

6. Composite Signature Web Key and Key Type Parameters

7. Security Considerations

The security considerations of [RFC7515], [RFC7517], [RFC9053] and [FIPS.204] also apply to this document.¶

All security issues that are pertinent to any cryptographic application must be addressed by JWS/JWK agents. Protecting the user's private key and employing countermeasures to various attacks constitute a priority.¶

For security properties and security issues related to the use of a hybrid signature scheme, the user can refer to [I-D.draft-ietf-pquip-hybrid-signature-spectrums-00]. For more information about hybrid composite signature schemes and the different hybrid combinations that appear in this document, the user can read [I-D.draft-ietf-lamps-pq-composite-sigs-02].¶

8. IANA Considerations

9. References

Appendix A. Examples

Will be added in later versions.¶

Authors' Addresses