Internet-Draft ML-DSA in Certificates February 2025
Massimo, et al. Expires 6 August 2025 [Page]
Workgroup:
LAMPS WG
Internet-Draft:
draft-ietf-lamps-dilithium-certificates-07
Published:
Intended Status:
Standards Track
Expires:
Authors:
J. Massimo
AWS
P. Kampanakis
AWS
S. Turner
sn3rd
B. E. Westerbaan
Cloudflare

Internet X.509 Public Key Infrastructure: Algorithm Identifiers for ML-DSA

Abstract

Digital signatures are used within X.509 certificates, Certificate Revocation Lists (CRLs), and to sign messages. This document describes the conventions for using FIPS 204, the Module-Lattice-Based Digital Signature Algorithm (ML-DSA) in Internet X.509 certificates and certificate revocation lists. The conventions for the associated signatures, subject public keys, and private key are also described.

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/dilithium-certificates/#go.draft-ietf-lamps-dilithium-certificates.html. Status information for this document may be found at https://datatracker.ietf.org/doc/draft-ietf-lamps-dilithium-certificates/.

Discussion of this document takes place on the Limited Additional Mechanisms for PKIX and SMIME (lamps) Working Group mailing list (mailto:spasm@ietf.org), which is archived at https://mailarchive.ietf.org/arch/browse/spasm/. Subscribe at https://www.ietf.org/mailman/listinfo/spasm/.

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

Status of This Memo

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

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.

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This Internet-Draft will expire on 6 August 2025.

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Table of Contents

1. Introduction

The Module-Lattice-Based Digital Signature Algorithm (ML-DSA) is a quantum-resistant digital signature scheme standardized by the US National Institute of Standards and Technology (NIST) PQC project [NIST-PQC] in [FIPS204]. This document specifies the use of the ML-DSA in Public Key Infrastructure X.509 (PKIX) certificates and Certificate Revocation Lists (CRLs) at three security levels: ML-DSA-44, ML-DSA-65, and ML-DSA-87.

[FIPS204] defines two variants of ML-DSA: a pure and a prehash variant. Only the former is specified in this document. See Section 8.1 for the rationale. The pure variant of ML-DSA supports the typical prehash flow, see Appendix D. In short: one cryptographic module can compute the hash mu on line 6 of algorithm 7 of [FIPS204] and pass it to a second module to finish the signature. The first module only needs access to the full message and the public key, whereas the second module only needs access to hash mu and the private key.

Prior to standardisation, ML-DSA was known as Dilithium. ML-DSA and Dilithium are not compatible.

1.1. Requirements Language

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.

2. Identifiers

The AlgorithmIdentifier type is defined in [RFC5912] as follows:

    AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::=
      SEQUENCE {
        algorithm   ALGORITHM-TYPE.id({AlgorithmSet}),
        parameters  ALGORITHM-TYPE.
                      Params({AlgorithmSet}{@algorithm}) OPTIONAL
     }

The fields in AlgorithmIdentifier have the following meanings:

The OIDs are:

   id-ml-dsa-44 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
            country(16) us(840) organization(1) gov(101) csor(3)
            nistAlgorithm(4) sigAlgs(3) id-ml-dsa-44(17) }

   id-ml-dsa-65 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
            country(16) us(840) organization(1) gov(101) csor(3)
            nistAlgorithm(4) sigAlgs(3) id-ml-dsa-65(18) }

   id-ml-dsa-87 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
            country(16) us(840) organization(1) gov(101) csor(3)
            nistAlgorithm(4) sigAlgs(3) id-ml-dsa-87(19) }

The contents of the parameters component for each algorithm MUST be absent. The ctx value used in the ML-DSA signing and verification [FIPS204] of ML-DSA signatures defined in this specification (X.509 certificates, CRLs) is the empty string.

3. ML-DSA Signatures in PKIX

ML-DSA is a digital signature scheme built upon the Fiat-Shamir-with-aborts framework [Fiat-Shamir]. The security is based upon the hardness of lattice problems over module lattices [Dilithium]. ML-DSA provides three parameter sets for the NIST PQC security categories 2, 3 and 5.

Signatures are used in a number of different ASN.1 structures. As shown in the ASN.1 representation from [RFC5280] below, in an X.509 certificate, a signature is encoded with an algorithm identifier in the signatureAlgorithm attribute and a signatureValue attribute that contains the actual signature.

  Certificate  ::=  SIGNED{ TBSCertificate }

  SIGNED{ToBeSigned} ::= SEQUENCE {
     toBeSigned           ToBeSigned,
     algorithmIdentifier  SEQUENCE {
         algorithm        SIGNATURE-ALGORITHM.
                            &id({SignatureAlgorithms}),
         parameters       SIGNATURE-ALGORITHM.
                            &Params({SignatureAlgorithms}
                              {@algorithmIdentifier.algorithm})
                                OPTIONAL
     },
     signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value(
                              {SignatureAlgorithms}
                              {@algorithmIdentifier.algorithm}))
  }

Signatures are also used in the CRL list ASN.1 representation from [RFC5280] below. In a X.509 CRL, a signature is encoded with an algorithm identifier in the signatureAlgorithm attribute and a signatureValue attribute that contains the actual signature.

   CertificateList  ::=  SIGNED{ TBSCertList }

The identifiers defined in Section 2 can be used as the AlgorithmIdentifier in the signatureAlgorithm field in the sequence Certificate/CertificateList and the signature field in the sequence TBSCertificate/TBSCertList in certificates and CRLs, respectively, [RFC5280]. The parameters of these signature algorithms MUST be absent, as explained in Section 2. That is, the AlgorithmIdentifier SHALL be a SEQUENCE of one component, the OID id-ml-dsa-*.

The signatureValue field contains the corresponding ML-DSA signature computed upon the ASN.1 DER encoded tbsCertificate/tbsCertList [RFC5280].

Conforming Certification Authority (CA) implementations MUST specify the algorithms explicitly by using the OIDs specified in Section 2 when encoding ML-DSA signatures in certificates and CRLs. Conforming client implementations that process certificates and CRLs using ML-DSA MUST recognize the corresponding OIDs. Encoding rules for ML-DSA signature values are specified Section 2.

4. ML-DSA Public Keys in PKIX

In the X.509 certificate, the subjectPublicKeyInfo field has the SubjectPublicKeyInfo type, which has the following ASN.1 syntax:

  SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE {
      algorithm        AlgorithmIdentifier {PUBLIC-KEY, {IOSet}},
      subjectPublicKey BIT STRING
  }

The fields in SubjectPublicKeyInfo have the following meaning:

The PUBLIC-KEY ASN.1 types for ML-DSA are defined here:

  pk-ml-dsa-44 PUBLIC-KEY ::= {
    IDENTIFIER id-ml-dsa-44
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

  pk-ml-dsa-65 PUBLIC-KEY ::= {
    IDENTIFIER id-ml-dsa-65
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

  pk-ml-dsa-87 PUBLIC-KEY ::= {
    IDENTIFIER id-ml-dsa-87
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

  ML-DSA-PublicKey ::= OCTET STRING (SIZE (1312 | 1952 | 2592))

  ML-DSA-PrivateKey ::= OCTET STRING (SIZE (32))

Algorithm 22 in Section 7.2 of [FIPS204] defines the raw byte string encoding of an ML-DSA public key. When used in a SubjectPublicKeyInfo type, the subjectPublicKey BIT STRING contains the raw byte string encoding of the public key.

When an ML-DSA public key appears outside of a SubjectPublicKeyInfo type in an environment that uses ASN.1 encoding, it can be encoded as an OCTET STRING by using the ML-DSA-PublicKey type.

[RFC5958] describes the Asymmetric Key Package's OneAsymmetricKey type for encoding asymmetric keypairs. When an ML-DSA private key or keypair is encoded as a OneAsymmetricKey, it follows the description in Section 6.

When the ML-DSA private key appears outside of an Asymmetric Key Package in an environment that uses ASN.1 encoding, it can be encoded as an OCTET STRING by using the ML-DSA-PrivateKey type.

Appendix C contains example ML-DSA public keys encoded using the textual encoding defined in [RFC7468].

5. Key Usage Bits

The intended application for the key is indicated in the keyUsage certificate extension; see Section 4.2.1.3 of [RFC5280]. If the keyUsage extension is present in a certificate that indicates id-ml-dsa-* in the SubjectPublicKeyInfo, then the at least one of following MUST be present:

  digitalSignature; or
  nonRepudiation; or
  keyCertSign; or
  cRLSign.

If the keyUsage extension is present in a certificate that indicates id-ml-dsa-* in the SubjectPublicKeyInfo, then the following MUST NOT be present:

   keyEncipherment; or
   dataEncipherment; or
   keyAgreement; or
   encipherOnly; or
   decipherOnly.

Requirements about the keyUsage extension bits defined in [RFC5280] still apply.

6. Private Key Format

An ML-DSA private key is encoded by storing its 32-octet seed in the privateKey field as follows.

[FIPS204] specifies two formats for an ML-DSA private key: a 32-octet seed (xi) and an (expanded) private key. The expanded private key (and public key) is computed from the seed using ML-DSA.KeyGen_internal(xi) (algorithm 6).

"Asymmetric Key Packages" [RFC5958] describes how to encode a private key in a structure that both identifies what algorithm the private key is for and allows for the public key and additional attributes about the key to be included as well. For illustration, the ASN.1 structure OneAsymmetricKey is replicated below.

  OneAsymmetricKey ::= SEQUENCE {
    version                  Version,
    privateKeyAlgorithm      SEQUENCE {
    algorithm                PUBLIC-KEY.&id({PublicKeySet}),
    parameters               PUBLIC-KEY.&Params({PublicKeySet}
                               {@privateKeyAlgorithm.algorithm})
                                  OPTIONAL}
    privateKey               OCTET STRING (CONTAINING
                               PUBLIC-KEY.&PrivateKey({PublicKeySet}
                                 {@privateKeyAlgorithm.algorithm})),
    attributes           [0] Attributes OPTIONAL,
    ...,
    [[2: publicKey       [1] BIT STRING (CONTAINING
                               PUBLIC-KEY.&Params({PublicKeySet}
                                 {@privateKeyAlgorithm.algorithm})
                                 OPTIONAL,
    ...
  }

When used in a OneAsymmetricKey type, the privateKey OCTET STRING contains the raw octet string encoding of the 32-octet seed. The publicKey field SHOULD be omitted because the public key can be computed as noted earlier in this section.

Appendix C contains example ML-DSA private keys encoded using the textual encoding defined in [RFC7468].

7. IANA Considerations

For the ASN.1 module in Appendix A, IANA is requested to assign an object identifier (OID) for the module identifier (TBD1) with a Description of "id-mod-x509-ml-dsa-2024". The OID for the module should be allocated in the "SMI Security for PKIX Module Identifier" registry (1.3.6.1.5.5.7.0).

8. Security Considerations

The Security Considerations section of [RFC5280] applies to this specification as well.

The digital signature scheme defined within this document are modeled under strongly existentially unforgeable under chosen message attack (SUF-CMA). For the purpose of estimating security strength, it has been assumed that the attacker has access to signatures for no more than 2^{64} chosen messages.

ML-DSA offers both deterministic and randomized signing. By default ML-DSA signatures are non-deterministic. The private random seed (rho') for the signature is pseudorandomly derived from the signer’s private key, the message, and a 256-bit string, rnd - where rnd should be generated by an approved RBG. In the deterministic version, rng is instead a 256-bit constant string. The source of randomness in the randomized mode has been "hedged" against sources of poor entropy, by including the signers private key and message into the derivation. The primary purpose of rnd is to facilitate countermeasures to side-channel attacks and fault attacks on deterministic signatures.

In the design of ML-DSA, care has been taken to make side-channel resilience easier to achieve. For instance, ML-DSA does not depend on Gaussian sampling. Implementations must still take great care not to leak information via various side channels. While deliberate design decisions such as these can help to deliver a greater ease of secure implementation - particularly against side-channel attacks - it does not necessarily provide resistance to more powerful attacks such as differential power analysis. Some amount of side-channel leakage has been demonstrated in parts of the signing algorithm (specifically the bit-unpacking function), from which a demonstration of key recovery has been made over a large sample of signatures. Masking countermeasures exist for ML-DSA, but come with a performance overhead.

A fundamental security property also associated with digital signatures is non-repudiation. Non-repudiation refers to the assurance that the owner of a signature key pair that was capable of generating an existing signature corresponding to certain data cannot convincingly deny having signed the data. The digital signature scheme ML-DSA possess three security properties beyond unforgeability, that are associated with non-repudiation. These are exclusive ownership, message-bound signatures, and non-resignability. These properties are based tightly on the assumed collision resistance of the hash function used (in this case SHAKE-256).

Exclusive ownership is a property in which a signature sigma uniquely determines the public key and message for which it is valid. Message-bound signatures is the property that a valid signature uniquely determines the message for which it is valid, but not necessarily the public key. Non-resignability is the property in which one cannot produce a valid signature under another key given a signature sigma for some unknown message m. These properties are not provided by classical signature schemes such as DSA or ECDSA, and have led to a variety of attacks such as Duplicate-Signature Key Selection (DSKS) attacks , and attacks on the protocols for secure routing. A full discussion of these properties in ML-DSA can be found at [CDFFJ21].

These properties are dependent, in part, on unambiguous public key serialization. It for this reason the public key structure defined in Section 4 is intentionally encoded as a single OCTET STRING.

8.1. Rationale for disallowing HashML-DSA

The HashML-DSA mode defined in Section 5.4 of [FIPS204] MUST NOT be used; in other words, public keys identified by id-hash-ml-dsa-44-with-sha512, id-hash-ml-dsa-65-with-sha512, and id-hash-ml-dsa-87-with-sha512 MUST NOT be in X.509 certificates used for CRLs, OCSP, certificate issuance and related PKIX protocols (e.g. TLS). The use of HashML-DSA public keys within end entity certificates is not prohibited, but conventions for doing so are outside the scope of this document.

This restriction is for both implementation and security reasons.

The implementation reason for disallowing HashML-DSA stems from the fact that ML-DSA and HashML-DSA are incompatible algorithms that require different Verify() routines. This forwards to the protocol the complexity of informing the client whether to use ML-DSA.Verify() or HashML-DSA.Verify() along with the hash algorithm to use. Additionally, since the same OIDs are used to identify the ML-DSA public keys and ML-DSA signature algorithms, an implementation would need to commit a given public key to be either of type ML-DSA or HashML-DSA at the time of certificate creation. This is anticipated to cause operational issues in contexts where the operator does not know at key generation time whether the key will need to produce pure or pre-hashed signatures. ExternalMu-ML-DSA avoids all of these operational concerns by virtue of having keys and signatures that are indistinguishable from ML-DSA (i.e., ML-DSA and ExternalMu-ML-DSA are mathematically equivalent algorithms). The difference between ML-DSA and ExternalMu-ML-DSA is merely an internal implementation detail of the signer and has no impact on the verifier or network protocol.

The security reason for disallowing HashML-DSA is that the design of the ML-DSA algorithm provides enhanced resistance against signature collision attacks, compared with conventional RSA or ECDSA signature algorithms. Specifically, ML-DSA binds the hash of the public key tr to the message to-be-signed prior to hashing, as described in line 6 of Algorithm 7 of [FIPS204]. In practice, this provides binding to the indended verification public key, preventing some attacks that would otherwise allow a signature to be successfully verified against a non-intended public key. Also, this unlikely, theoretical binding means that in the unlikely discovery of a collision attack against SHA-3, an attacker would have to perform a public-key-specific collision search in order to find message pairs such that H(tr || m1) = H(tr || m2) since a direct hash collision H(m1) = H(m2) will not suffice. HashML-DSA removes both of these enhanced security properties.

9. References

9.1. Normative References

[FIPS204]
National Institute of Standards and Technology (NIST), "Module-Lattice-based Digital Signature Standard", FIPS PUB 204, , <https://csrc.nist.gov/projects/post-quantum-cryptography>.
[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/rfc/rfc2119>.
[RFC3647]
Chokhani, S., Ford, W., Sabett, R., Merrill, C., and S. Wu, "Internet X.509 Public Key Infrastructure Certificate Policy and Certification Practices Framework", RFC 3647, DOI 10.17487/RFC3647, , <https://www.rfc-editor.org/rfc/rfc3647>.
[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/rfc/rfc5280>.
[RFC5912]
Hoffman, P. and J. Schaad, "New ASN.1 Modules for the Public Key Infrastructure Using X.509 (PKIX)", RFC 5912, DOI 10.17487/RFC5912, , <https://www.rfc-editor.org/rfc/rfc5912>.
[RFC5958]
Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, , <https://www.rfc-editor.org/rfc/rfc5958>.
[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/rfc/rfc8174>.
[X680]
ITU-T, "Information Technology -- Abstract Syntax Notation One (ASN.1): Specification of basic notation", ITU-T Recommendation X.680, ISO/IEC 8824-1:2021, , <https://www.itu.int/rec/T-REC-X.680>.
[X690]
ITU-T, "Information Technology -- Abstract Syntax Notation One (ASN.1): ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)", ITU-T Recommendation X.690, ISO/IEC 8825-1:2021, , <https://www.itu.int/rec/T-REC-X.690>.

9.2. Informative References

[CDFFJ21]
Cremers, C., Düzlü, S., Fiedler, R., Fischlin, M., and C. Janson, "BUFFing signature schemes beyond unforgeability and the case of post-quantum signatures", In Proceedings of the 42nd IEEE Symposium on Security and Privacy , , <https://eprint.iacr.org/2020/1525.pdf>.
[Dilithium]
Bai, S., Ducas, L., Lepoint, T., Lyubashevsky, V., Schwabe, P., Seiler, G., and D. Stehlé, "CRYSTALS-Dilithium Algorithm Specifications and Supporting Documentation", , <https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf>.
[Fiat-Shamir]
Lyubashevsky, V., "Fiat-Shamir with aborts: Applications to lattice and factoring-based signatures", International Conference on the Theory and Application of Cryptology and Information Security , , <https://www.iacr.org/archive/asiacrypt2009/59120596/59120596.pdf>.
[NIST-PQC]
National Institute of Standards and Technology (NIST), "Post-Quantum Cryptography Project", , <https://csrc.nist.gov/Projects/post-quantum-cryptography>.
[RFC7468]
Josefsson, S. and S. Leonard, "Textual Encodings of PKIX, PKCS, and CMS Structures", RFC 7468, DOI 10.17487/RFC7468, , <https://www.rfc-editor.org/rfc/rfc7468>.

Appendix A. ASN.1 Module

This appendix includes the ASN.1 module [X680] for the ML-DSA. Note that as per [RFC5280], certificates use the Distinguished Encoding Rules; see [X690]. This module imports objects from [RFC5912].

<CODE BEGINS>
X509-ML-DSA-2024
{ iso(1) identified-organization(3) dod(6)
  internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
  id-mod-x509-ml-dsa-2024(TBD1) }

DEFINITIONS IMPLICIT TAGS ::=

BEGIN

-- EXPORTS ALL;

IMPORTS

PUBLIC-KEY, SIGNATURE-ALGORITHM
  FROM AlgorithmInformation-2009 -- From [RFC5912]
    { 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
--

sigAlgs OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16)
    us(840) organization(1) gov(101) csor(3) nistAlgorithms(4) 3 }

id-ml-dsa-44 OBJECT IDENTIFIER ::= { sigAlgs 17 }

id-ml-dsa-65 OBJECT IDENTIFIER ::= { sigAlgs 18 }

id-ml-dsa-87 OBJECT IDENTIFIER ::= { sigAlgs 19 }

--
-- Signature Algorithm Identifiers
--

sa-ml-dsa-44 SIGNATURE-ALGORITHM ::= {
  IDENTIFIER id-ml-dsa-44
  PARAMS ARE absent
  PUBLIC-KEYS { pk-ml-dsa-44 }
  SMIME-CAPS { IDENTIFIED BY id-ml-dsa-44 } }

sa-ml-dsa-65 SIGNATURE-ALGORITHM ::= {
  IDENTIFIER id-ml-dsa-65
  PARAMS ARE absent
  PUBLIC-KEYS { pk-ml-dsa-65 }
  SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 } }

sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= {
  IDENTIFIER id-ml-dsa-87
  PARAMS ARE absent
  PUBLIC-KEYS { pk-ml-dsa-87 }
  SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 } }

--
-- Public Keys
--

pk-ml-dsa-44 PUBLIC-KEY ::= {
  IDENTIFIER id-ml-dsa-44
  -- KEY no ASN.1 wrapping --
  CERT-KEY-USAGE
    { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
  -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-ml-dsa-65 PUBLIC-KEY ::= {
  IDENTIFIER id-ml-dsa-65
  -- KEY no ASN.1 wrapping --
  CERT-KEY-USAGE
    { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
  -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-ml-dsa-87 PUBLIC-KEY ::= {
  IDENTIFIER id-ml-dsa-87
  -- KEY no ASN.1 wrapping --
  CERT-KEY-USAGE
    { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
  -- PRIVATE-KEY no ASN.1 wrapping -- }

ML-DSA-PublicKey ::= OCTET STRING (SIZE (1312 | 1952 | 2592))

ML-DSA-PrivateKey ::= OCTET STRING (SIZE (32))

--
-- Expand SignatureAlgorithms from RFC 5912
--
SignatureAlgorithms SIGNATURE-ALGORITHM ::= {
  sa-ml-dsa-44 |
  sa-ml-dsa-65 |
  sa-ml-dsa-87,
  ... }

--
-- Expand SignatureAlgorithms from RFC 5912
--
PublicKeys PUBLIC-KEY ::= {
  pk-ml-dsa-44 |
  pk-ml-dsa-65 |
  pk-ml-dsa-87,
  ...
}

END

<CODE ENDS>

Appendix B. Security Strengths

Instead of defining the strength of a quantum algorithm in a traditional manner using the imprecise notion of bits of security, NIST has instead elected to define security levels by picking a reference scheme, which NIST expects to offer notable levels of resistance to both quantum and classical attack. To wit, an algorithm that achieves NIST PQC security level 1 must require computational resources to break the relevant security property, which are greater than those required for a brute-force key search on AES-128. Levels 3 and 5 use AES-192 and AES-256 as reference respectively. Levels 2 and 4 use collision search for SHA-256 and SHA-384 as reference.

The parameter sets defined for NIST security levels 2, 3 and 5 are listed in the Figure 1, along with the resulting signature size, public key, and private key sizes in bytes. Note that these are the sizes of the plain private and public keys; and not the sizes of the resultant OneAsymmetricKey and SubjectPublicKeyInfo objects in which they are wrapped.

|=======+=======+=====+========+========+========|
| Level | (k,l) | eta |  Sig.  | Public | Private|
|       |       |     |  (B)   | Key(B) | Key(B) |
|=======+=======+=====+========+========+========|
|   2   | (4,4) |  2  |  2420  |  1312  |  32    |
|   3   | (6,5) |  4  |  3309  |  1952  |  32    |
|   5   | (8,7) |  2  |  4627  |  2592  |  32    |
|=======+=======+=====+========+========+========|
Figure 1: ML-DSA Parameters

Appendix C. Examples

This appendix contains examples of ML-DSA public keys, private keys and certificates.

C.1. Example Private Key

The following is an example of a ML-DSA-44 private key with hex seed 000102…1e1f:

-----BEGIN PRIVATE KEY-----
MDICAQAwCwYJYIZIAWUDBAMRBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
HB0eHw==
-----END PRIVATE KEY-----

SEQUENCE {
  INTEGER { 0 }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
  }
  OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
1718191a1b1c1d1e1f` }
}

The following is an example of a ML-DSA-65 private key with hex seed 000102…1e1f:

-----BEGIN PRIVATE KEY-----
MDICAQAwCwYJYIZIAWUDBAMSBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
HB0eHw==
-----END PRIVATE KEY-----

SEQUENCE {
  INTEGER { 0 }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
  }
  OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
1718191a1b1c1d1e1f` }
}

The following is an example of a ML-DSA-87 private key with hex seed 000102…1e1f:

-----BEGIN PRIVATE KEY-----
MDICAQAwCwYJYIZIAWUDBAMTBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
HB0eHw==
-----END PRIVATE KEY-----

SEQUENCE {
  INTEGER { 0 }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
  }
  OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
1718191a1b1c1d1e1f` }
}

NOTE: The private key is the seed and all three examples keys use the same seed; therefore, the private above are the same except for the OID used to represent the ML-DSA algorithm's security strength.

C.2. Example Public Key

The following is the ML-DSA-44 public key corresponding to the private key in the previous section.

-----BEGIN PUBLIC KEY-----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-----END PUBLIC KEY-----

SEQUENCE {
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
  }
  BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d17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` }
}

The following is the ML-DSA-65 public key corresponding to the private key in the previous section.

-----BEGIN PUBLIC KEY-----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-----END PUBLIC KEY-----

SEQUENCE {
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
  }
  BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f62594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` }
}

The following is the ML-DSA-87 public key corresponding to the private key in the previous section.

-----BEGIN PUBLIC KEY-----
MIIKMjALBglghkgBZQMEAxMDggohAJeSvOwvJDBoaoL8zzwvX/Zl53HXq0G5AljP
p+kOyXEkpzsyO5uiGrZNdnxDP1pSHv/hj4bkahiJUsRGfgSLcp5/xNEV5+SNoYlt
X+EZsQ3N3vYssweVQHS0IzblKDbeYdqUH4036misgQb6vhkHBnmvYAhTcSD3B5O4
6pzA5ue3tMmlx0IcYPJEUboekz2xou4Wx5VZ8hs9G4MFhQqkKvuxPx9NW59INfnY
ffzrFi0O9Kf9xMuhdDzRyHu0ln2hbMh2S2Vp347lvcv/6aTgV0jm/fIlr55O63dz
ti6Phfm1a1SJRVUYRPvYmAakrDab7S0lYQD2iKatXgpwmCbcREnpHiPFUG5kI2Hv
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5VvgYiIvi6kKl0BzMmsxISrs4KNKYA==
-----END PUBLIC KEY-----

SEQUENCE {
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
  }
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3326b31212aece0a34a60` }
}

C.3. Example Certificates

The following is a self-signed certificate for the ML-DSA-44 public key in the previous section.

-----BEGIN CERTIFICATE-----
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AAAAABcmOEM=
-----END CERTIFICATE-----

SEQUENCE {
  SEQUENCE {
    [0] {
      INTEGER { 2 }
    }
    INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
    SEQUENCE {
      OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
    }
    SEQUENCE {
      SET {
        SEQUENCE {
          # organizationName
          OBJECT_IDENTIFIER { 2.5.4.10 }
          PrintableString { "IETF" }
        }
      }
      SET {
        SEQUENCE {
          # commonName
          OBJECT_IDENTIFIER { 2.5.4.3 }
          PrintableString { "LAMPS WG" }
        }
      }
    }
    SEQUENCE {
      UTCTime { "200203043210Z" }
      UTCTime { "400129043210Z" }
    }
    SEQUENCE {
      SET {
        SEQUENCE {
          # organizationName
          OBJECT_IDENTIFIER { 2.5.4.10 }
          PrintableString { "IETF" }
        }
      }
      SET {
        SEQUENCE {
          # commonName
          OBJECT_IDENTIFIER { 2.5.4.3 }
          PrintableString { "LAMPS WG" }
        }
      }
    }
    SEQUENCE {
      SEQUENCE {
        OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
      }
      BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f139
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8f315ba5925e8edefa679369a2202766151f16a965f9f81ece76cc070b55869e
4db9784cf05c830b3242c8312` }
    }
    [3] {
      SEQUENCE {
        SEQUENCE {
          # keyUsage
          OBJECT_IDENTIFIER { 2.5.29.15 }
          BOOLEAN { TRUE }
          OCTET_STRING {
            BIT_STRING { b`1000011` }
          }
        }
        SEQUENCE {
          # basicConstraints
          OBJECT_IDENTIFIER { 2.5.29.19 }
          BOOLEAN { TRUE }
          OCTET_STRING {
            SEQUENCE {
              BOOLEAN { TRUE }
            }
          }
        }
        SEQUENCE {
          # subjectKeyIdentifier
          OBJECT_IDENTIFIER { 2.5.29.14 }
          OCTET_STRING {
            OCTET_STRING { `329a07b1fabb48f52a309f11a1898f848e23
22ff` }
          }
        }
      }
    }
  }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
  }
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beeef101f232d6e97c2c4dff3f40000000000000000000000000017263843` }
}

The following is a self-signed certificate for the ML-DSA-65 public key in the previous section.

-----BEGIN CERTIFICATE-----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-----END CERTIFICATE-----

SEQUENCE {
  SEQUENCE {
    [0] {
      INTEGER { 2 }
    }
    INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
    SEQUENCE {
      OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
    }
    SEQUENCE {
      SET {
        SEQUENCE {
          # organizationName
          OBJECT_IDENTIFIER { 2.5.4.10 }
          PrintableString { "IETF" }
        }
      }
      SET {
        SEQUENCE {
          # commonName
          OBJECT_IDENTIFIER { 2.5.4.3 }
          PrintableString { "LAMPS WG" }
        }
      }
    }
    SEQUENCE {
      UTCTime { "200203043210Z" }
      UTCTime { "400129043210Z" }
    }
    SEQUENCE {
      SET {
        SEQUENCE {
          # organizationName
          OBJECT_IDENTIFIER { 2.5.4.10 }
          PrintableString { "IETF" }
        }
      }
      SET {
        SEQUENCE {
          # commonName
          OBJECT_IDENTIFIER { 2.5.4.3 }
          PrintableString { "LAMPS WG" }
        }
      }
    }
    SEQUENCE {
      SEQUENCE {
        OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
      }
      BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f6
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3e79c46ca5d5a6dca3d28ca50ad18bd13fca55059dd9b185f79f9c47196a4e81
b2104bc460a051e02f2e8444f` }
    }
    [3] {
      SEQUENCE {
        SEQUENCE {
          # keyUsage
          OBJECT_IDENTIFIER { 2.5.29.15 }
          BOOLEAN { TRUE }
          OCTET_STRING {
            BIT_STRING { b`1000011` }
          }
        }
        SEQUENCE {
          # basicConstraints
          OBJECT_IDENTIFIER { 2.5.29.19 }
          BOOLEAN { TRUE }
          OCTET_STRING {
            SEQUENCE {
              BOOLEAN { TRUE }
            }
          }
        }
        SEQUENCE {
          # subjectKeyIdentifier
          OBJECT_IDENTIFIER { 2.5.29.14 }
          OCTET_STRING {
            OCTET_STRING { `1b0563e3cd3346149c8c9ebcf23b0a4e5a90
0eea` }
          }
        }
      }
    }
  }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
  }
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00000000000000000000000000000000000060d0f131c20` }
}

The following is a self-signed certificate for the ML-DSA-87 public key in the previous section.

-----BEGIN CERTIFICATE-----
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-----END CERTIFICATE-----

SEQUENCE {
  SEQUENCE {
    [0] {
      INTEGER { 2 }
    }
    INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
    SEQUENCE {
      OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
    }
    SEQUENCE {
      SET {
        SEQUENCE {
          # organizationName
          OBJECT_IDENTIFIER { 2.5.4.10 }
          PrintableString { "IETF" }
        }
      }
      SET {
        SEQUENCE {
          # commonName
          OBJECT_IDENTIFIER { 2.5.4.3 }
          PrintableString { "LAMPS WG" }
        }
      }
    }
    SEQUENCE {
      UTCTime { "200203043210Z" }
      UTCTime { "400129043210Z" }
    }
    SEQUENCE {
      SET {
        SEQUENCE {
          # organizationName
          OBJECT_IDENTIFIER { 2.5.4.10 }
          PrintableString { "IETF" }
        }
      }
      SET {
        SEQUENCE {
          # commonName
          OBJECT_IDENTIFIER { 2.5.4.3 }
          PrintableString { "LAMPS WG" }
        }
      }
    }
    SEQUENCE {
      SEQUENCE {
        OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
      }
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74073326b31212aece0a34a60` }
    }
    [3] {
      SEQUENCE {
        SEQUENCE {
          # keyUsage
          OBJECT_IDENTIFIER { 2.5.29.15 }
          BOOLEAN { TRUE }
          OCTET_STRING {
            BIT_STRING { b`1000011` }
          }
        }
        SEQUENCE {
          # basicConstraints
          OBJECT_IDENTIFIER { 2.5.29.19 }
          BOOLEAN { TRUE }
          OCTET_STRING {
            SEQUENCE {
              BOOLEAN { TRUE }
            }
          }
        }
        SEQUENCE {
          # subjectKeyIdentifier
          OBJECT_IDENTIFIER { 2.5.29.14 }
          OCTET_STRING {
            OCTET_STRING { `89886750b57c24db3fc012e61ede59753337
374f` }
          }
        }
      }
    }
  }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
  }
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}

Appendix D. Pre-hashing (ExternalMu-ML-DSA)

Some applications require pre-hashing, where the signature generation process can be separated into a pre-hash step and a core signature step in order to ease operational requirements around large or inconsistently-sized payloads. Pre-hashing can be performed at the protocol layer, but not all protocols support it. Examples in [RFC5280] are certificates and CRLs; these do not include message digesting before signing. This can make signing large CRLs or a high volume of certificates with large public keys challenging.

As mentioned in the introduction, pure ML-DSA signing itself supports a pre-hashing flow by splitting the operation over two modules. In this section, we make this "ExternalMu-ML-DSA" more explicit.

There are two steps. First an ExternalMu-ML-DSA.Prehash() followed by ExternalMu-ML-DSA.Sign(). Together these are functionally equivalent to ML-DSA.Sign() from [FIPS204] in that used in sequence they create exactly the same signatures as regular pure ML-DSA, which can be verified by the unmodified ML-DSA.Verify().

An ML-DSA key and certificate can be used with either ML-DSA or ExternalMu-ML-DSA interchangeably. Note that ExternalMu-ML-DSA describes a different signature API from ML-DSA and therefore might require explicit support from hardware or software cryptographic modules.

Note that the signing mode defined here is different from HashML-DSA defined in Section 5.4 of [FIPS204]. This specification uses exclusively ExternalMu-ML-DSA for pre-hashed use cases. See Section 8.1 for additional discussion of why HashML-DSA is disallowed in PKIX.

All functions and notation used in Figure 2 and Figure 3 are defined in [FIPS204].

External operations:

ExternalMu-ML-DSA.Prehash(pk, M, ctx):

  if |ctx| > 255 then
    return error  # return an error indication if the context string is
                  # too long
  end if

  M' = BytesToBits(IntegerToBytes(0, 1) ∥ IntegerToBytes(|ctx|, 1)
                                                        || ctx) || M
  mu = H(BytesToBits(H(pk, 64)) || M', 64)
  return mu
Figure 2: External steps of ExternalMu-ML-DSA

Internal operations:

ExternalMu-ML-DSA.Sign(sk, mu):

  if |mu| != 512 then
    return error  # return an error indication if the input mu is not
                  # 64 bytes (512 bits).
  end if

  rnd = rand(32)  # for the optional deterministic variant,
                  # set rnd to all zeroes
  if rnd = NULL then
    return error  # return an error indication if random bit
                  # generation failed
  end if

  sigma = ExternalMu-ML-DSA.Sign_internal(sk, mu, rnd)
  return sigma

ExternalMu-ML-DSA.Sign_internal(sk, mu, rnd): # mu is passed as argument instead of M'
   ... identical to FIPS 204 Algorithm 7, but with Line 6 removed.
Figure 3: Internal steps of ExternalMu-ML-DSA

ExternalMu-ML-DSA requires the public key, or its prehash, as input to the pre-digesting function. This assumes the signer generating the pre-hash is in possession of the public key before signing and is different from conventional pre-hashing which only requires the message and the hash function as input.

Security-wise, during the signing operation of pure (or "one-step") ML-DSA, the cryptographic module extracts the public key hash tr from the secret key object, and thus there is no possibility of mismatch between tr and sk. In ExternalMu-ML-DSA, the public key or its hash needs to be provided to the Prehash() routine indpedendly of the secret key, and while the exact mechanism by which it is delivered will be implementation-specific, it does open a windown for mismatches between tr and sk. First, this will produce a signature which will fail to verify under the intended public key since a compliant Verify() routine will independently compute tr from the public key. Implementors should pay careful attention to how the public key or its hash is delivered to the ExternalMu-ML-DSA.Prehash() routine, and from where they are sourcing this data.

Acknowledgments

We would like to thank ... for their insightful comments.

Authors' Addresses

Jake Massimo
AWS
United States of America
Panos Kampanakis
AWS
United States of America
Sean Turner
sn3rd
Bas Westerbaan
Cloudflare