Internet-Draft jose-cose-dilithium December 2024
Prorock, et al. Expires 21 June 2025 [Page]
Workgroup:
CBOR Object Signing and Encryption
Internet-Draft:
draft-ietf-cose-dilithium-05
Published:
Intended Status:
Standards Track
Expires:
Authors:
M. Prorock
mesur.io
O. Steele
Transmute
R. Misoczki
Google
M. Osborne
IBM
C. Cloostermans
NXP

ML-DSA for JOSE and COSE

Abstract

This document describes JSON Object Signing and Encryption (JOSE) and CBOR Object Signing and Encryption (COSE) serializations for Module-Lattice-Based Digital Signature Standard (ML-DSA), a Post-Quantum Cryptography (PQC) digital signature scheme defined in FIPS 204.

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://cose-wg.github.io/draft-ietf-cose-dilithium/draft-ietf-cose-dilithium.html. Status information for this document may be found at https://datatracker.ietf.org/doc/draft-ietf-cose-dilithium/.

Discussion of this document takes place on the CBOR Object Signing and Encryption Working Group mailing list (mailto:cose@ietf.org), which is archived at https://mailarchive.ietf.org/arch/browse/cose/. Subscribe at https://www.ietf.org/mailman/listinfo/cose/.

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

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/.

Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."

This Internet-Draft will expire on 21 June 2025.

Table of Contents

1. Introduction

This document describes how to use ML-DSA keys and signatures as described in [FIPS-204] with JOSE and COSE.

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.

Some examples in this specification are truncated using "..." for readability.

3. Algorithm Key Pair Type

This section describes a generic cryptographic key structure for use with algorithms not limited to those registered in this document. The Algorithm Key Pair (AKP) Type is used to express Public and Private Keys for use with Algorithms. When this key type is used the "alg" JSON Web Key Parameter or COSE Key Common Parameter is REQUIRED.

The "pub" parameter contains a public key, this parameter contains public information. The "priv" parameter contains a private key, sometimes called a secret key, this parameter contains private information. The concept of public and private information classes originates from Section 8.1 of [RFC7517].

The "pub" and "priv" parameters contain byte strings in a format specified by the "alg" value. The values of "pub" and "priv" MAY have additional structure or length checks depending on the associated "alg" parameter and its requirements.

When AKP keys are expressed in JWK, "pub" and "priv" are base64url encoded.

This document requests the registration of the following key types in [IANA.jose]:

Table 1: Algorithm Key Pair Type for JOSE
Name kty Description
Algorithm Key Pair AKP JSON Web Key Type for the Algorithm Key Pair.

An example truncated private key for use with ML-DSA-44 in JWK format is provided below:

{
   "kid": "T4xl70S7MT6Zeq6r9V9fPJGVn76wfnXJ21-gyo0Gu6o",
   "kty": "AKP",
   "alg": "ML-DSA-44",
   "pub": "unH59k4Ru...DZgbTP07e7gEWzw4MFRrndjbDQ",
   "priv": "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"
}
Figure 1: The all zeros ML-DSA-44 JSON Web Key

This document requests the registration of the following key type in [IANA.cose]:

Table 2: Algorithm Key Pair Type for COSE
Name kty Description
AKP TBD (requested assignment 7) COSE Key Type for the Algorithm Key Pair.

An example truncated private key for use with ML-DSA-44 in COSE_Key format is provided below:

{
   / kid /   2: h'b8969ab4b37da9f068...6f0583bf5b8d3a8059a',
   / kty /   1: 7, / AKP /
   / alg /   3: -48, / ML-DSA-44 /
   / pub  / -1: h'ba71f9f64e11baeb58...c3830546b9dd8db0d',
   / priv / -2: h'00000000000000...0000000000000000'
}
Figure 2: The all zeros ML-DSA-44 COSE Key

The AKP key type and thumbprint computation for the AKP key type is generic, and suitable for use with algorithms other than ML-DSA.

4. ML-DSA Private Keys

Note that FIPS 204 defines 2 expressions for private keys: a seed, and a private key that is expanded from the seed. For the algorithms defined in this document, the "priv" parameter is always the seed, and never the expanded expression. This definition mirrors the one used in Section 6 of [I-D.draft-ietf-lamps-dilithium-certificates].

5. ML-DSA Algorithms

The ML-DSA Signature Scheme is parameterized to support different security levels.

In this document, the abbreviations ML-DSA-44, ML-DSA-65, and ML-DSA-87 are used to refer to ML-DSA with the parameter choices given in Table 1 of FIPS-204.

This document requests the registration of the following algorithms in [IANA.jose]:

Table 3: JOSE algorithms for ML-DSA
Name value Description
ML-DSA-44 ML-DSA-44 JSON Web Signature Algorithm for ML-DSA-44
ML-DSA-65 ML-DSA-65 JSON Web Signature Algorithm for ML-DSA-65
ML-DSA-87 ML-DSA-87 JSON Web Signature Algorithm for ML-DSA-87

This document requests the registration of the following algorithms in [IANA.cose]:

Table 4: COSE algorithms for ML-DSA
Name value Description
ML-DSA-44 TBD (requested assignment -48) CBOR Object Signing Algorithm for ML-DSA-44
ML-DSA-65 TBD (requested assignment -49) CBOR Object Signing Algorithm for ML-DSA-65
ML-DSA-87 TBD (requested assignment -50) CBOR Object Signing Algorithm for ML-DSA-87

In accordance with Algorithm Key Pair Type section of this document, when present in AKP Keys the "pub" and "priv" parameters have the following additional constraints:

The "pub" parameter is the ML-DSA public key, as described in Section 5.3 of FIPS-204.

The size of "pub", and the associated signature for each of these algorithms is defined in Table 2 of FIPS-204, and repeated here for convenience:

Table 5: Sizes (in bytes) of keys and signatures of ML-DSA
Algorithm Private Key Public Key Signature Size
ML-DSA-44 2560 1312 2420
ML-DSA-65 4032 1952 3309
ML-DSA-87 4896 2592 4627

Note that "priv" size is always 32 bytes, and that KeyGen_internal is called to produce the private key sizes in the table above. See the ML-DSA Private Keys section of this document for more details.

These algorithms are used to produce signatures as described in Algorithm 2 of FIPS-204. The ctx parameter MUST be the empty string for ML-DSA-44, ML-DSA-65 and ML-DSA-87.

Signatures are encoded as bytestrings using th algorithms defined in Section 7.2 of FIPS-204.

When producing JSON Web Signatures, the signature bytestrings are base64url encoded, and the encoded signature size is larger than described in the table above.

6. AKP Thumbprints

When computing the COSE Key Thumbprint as described in [I-D.draft-ietf-cose-key-thumbprint], the required parameters for algorithm key pairs are:

The COSE Key Thumbprint is produced according to the process described in Section 3 of [I-D.draft-ietf-cose-key-thumbprint].

When computing the JWK Thumbprint as described in [RFC7638], the required parameters for algorithm key pairs are:

Their lexicographic order, per Section 3.3 of [RFC7638], is:

The JWK Key Thumbprint is produced according to the process described in Section 3 of [RFC7638].

See the kid values in the JSON Web Key and COSE Key examples in the appendix for examples of AKP thumbprints.

7. Security Considerations

The security considerations of [RFC7515], [RFC7517] and [RFC9053] applies to this specification as well.

A detailed security analysis of ML-DSA is beyond the scope of this specification, see [FIPS-204] for additional details.

7.1. Size of keys and signatures

Table 2 of FIPS-204 describes the size of keys and signatures. ML-DSA might not be the best choice for use cases that require small keys or signatures. Use of thumbprints as described in [RFC7638] and [I-D.draft-ietf-cose-key-thumbprint] can reduce the need to repeat public key representations.

7.2. Regarding HashML-DSA

This document does not specify algorithms for use with HashML-DSA as described in Section 5.4 of FIPS-204.

7.3. Validation of keys

When an AKP algorithm requires or encourages that a key be validated before being used, the "pub" and "priv" parameters MUST be validated.

Section 7.2 of FIPS-204 describes the encoding of ML-DSA keys and signatures. The "pub" key parameter MUST be validated according to the pkEncode and pkDecode algorithms before being used. For the ML-DSA algorithms registered in this document, the "priv" key parameter is a seed, and as such only a length check MUST be performed. The length of the seed is 256 bits, which is 32 bytes. However, if the private key derived from the seed using KeyGen_internal is stored as part of some implementation, the skEncode and skDecode algorithms MUST be used. FIPS-204 notes, "skDecode should only be run on inputs that come from trusted sources" and that "as the seed can be used to compute the private key, it is sensitive data and shall be treated with the same safeguards as a private key".

7.4. Mismatched AKP parameters

When using an AKP key with an algorithm, it is possible that the "pub" and "priv" parameters have been tampered with or mismatched. Depending on the algorithm and implementation, the consequences of using mismatched parameters can range from operations failing to key compromise.

8. IANA Considerations

8.1. Additions to Existing Registries

8.1.1. New COSE Algorithms

IANA is requested to add the following entries to the COSE Algorithms Registry. The following completed registration templates are provided as described in RFC9053 and RFC9054.

8.1.1.1. ML-DSA-44
  • Name: ML-DSA-44

  • Value: TBD (requested assignment -48)

  • Description: CBOR Object Signing Algorithm for ML-DSA-44

  • Capabilities: [kty]

  • Reference: RFC XXXX

  • Recommended: Yes

8.1.1.2. ML-DSA-65
  • Name: ML-DSA-65

  • Value: TBD (requested assignment -49)

  • Description: CBOR Object Signing Algorithm for ML-DSA-65

  • Capabilities: [kty]

  • Reference: RFC XXXX

  • Recommended: Yes

8.1.1.3. ML-DSA-87
  • Name: ML-DSA-87

  • Value: TBD (requested assignment -50)

  • Description: CBOR Object Signing Algorithm for ML-DSA-87

  • Capabilities: [kty]

  • Reference: RFC XXXX

  • Recommended: Yes

8.1.2. New COSE Key Types

IANA is requested to add the following entries to the COSE Key Types Registry. The following completed registration templates are provided as described in RFC9053.

8.1.2.1. AKP
  • Name: AKP

  • Value: TBD (requested assignment 7)

  • Description: COSE Key Type for Algorithm Key Pairs

  • Capabilities: [kty(7)]

  • Reference: RFC XXXX

8.1.3. New COSE Key Type Parameters

IANA is requested to add the following entries to the COSE Key Type Parameters. The following completed registration templates are provided as described in RFC9053.

8.1.4. ML-DSA Public Key

  • Key Type: TBD (requested assignment 7)

  • Name: pub

  • Label: -1

  • CBOR Type: bstr

  • Description: Public key

  • Reference: RFC XXXX

8.1.5. ML-DSA Private Key

  • Key Type: TBD (requested assignment 7)

  • Name: priv

  • Label: -2

  • CBOR Type: bstr

  • Description: Private key or seed used to derive a private key.

  • Reference: RFC XXXX

8.1.6. New JOSE Algorithms

IANA is requested to add the following entries to the JSON Web Signature and Encryption Algorithms Registry. The following completed registration templates are provided as described in RFC7518.

8.1.6.1. ML-DSA-44
  • Algorithm Name: ML-DSA-44

  • Algorithm Description: ML-DSA-44 as described in FIPS 204.

  • Algorithm Usage Location(s): alg

  • JOSE Implementation Requirements: Optional

  • Change Controller: IETF

  • Value registry: [IANA.jose] Algorithms

  • Specification Document(s): RFC XXXX

  • Algorithm Analysis Documents(s): [FIPS-204]

8.1.6.2. ML-DSA-65
  • Algorithm Name: ML-DSA-65

  • Algorithm Description: ML-DSA-65 as described in FIPS 204.

  • Algorithm Usage Location(s): alg

  • JOSE Implementation Requirements: Optional

  • Change Controller: IETF

  • Value registry: [IANA.jose] Algorithms

  • Specification Document(s): RFC XXXX

  • Algorithm Analysis Documents(s): [FIPS-204]

8.1.6.3. ML-DSA-87
  • Algorithm Name: ML-DSA-87

  • Algorithm Description: ML-DSA-87 as described in FIPS 204.

  • Algorithm Usage Location(s): alg

  • JOSE Implementation Requirements: Optional

  • Change Controller: IETF

  • Value registry: [IANA.jose] Algorithms

  • Specification Document(s): RFC XXXX

  • Algorithm Analysis Documents(s): [FIPS-204]

8.1.7. New JOSE Key Types

IANA is requested to add the following entries to the JSON Web Key Types Registry. The following completed registration templates are provided as described in RFC7518 RFC7638.

8.1.7.1. AKP
  • "kty" Parameter Value: AKP

  • Key Type Description: Algorithm Key Pair

  • JOSE Implementation Requirements: Optional

  • Change Controller: IETF

  • Specification Document(s): RFC XXXX

8.1.8. New JSON Web Key Parameters

IANA is requested to add the following entries to the JSON Web Key Parameters Registry. The following completed registration templates are provided as described in RFC7517, and RFC7638.

8.1.8.1. AKP Public Key
  • Parameter Name: pub

  • Parameter Description: Public key

  • Used with "kty" Value(s): AKP

  • Parameter Information Class: Public

  • Change Controller: IETF

  • Specification Document(s): RFC XXXX

8.1.8.2. AKP Private Key
  • Parameter Name: priv

  • Parameter Description: Private key or seed used to derive a private key.

  • Used with "kty" Value(s): AKP

  • Parameter Information Class: Private

  • Change Controller: IETF

  • Specification Document(s): RFC XXXX

9. References

9.1. Normative References

[I-D.draft-ietf-cose-key-thumbprint]
Isobe, K., Tschofenig, H., and O. Steele, "CBOR Object Signing and Encryption (COSE) Key Thumbprint", Work in Progress, Internet-Draft, draft-ietf-cose-key-thumbprint-06, , <https://datatracker.ietf.org/doc/html/draft-ietf-cose-key-thumbprint-06>.
[IANA.cose]
IANA, "CBOR Object Signing and Encryption (COSE)", <https://www.iana.org/assignments/cose>.
[IANA.jose]
IANA, "JSON Object Signing and Encryption (JOSE)", <https://www.iana.org/assignments/jose>.
[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>.
[RFC7515]
Jones, M., Bradley, J., and N. Sakimura, "JSON Web Signature (JWS)", RFC 7515, DOI 10.17487/RFC7515, , <https://www.rfc-editor.org/rfc/rfc7515>.
[RFC7517]
Jones, M., "JSON Web Key (JWK)", RFC 7517, DOI 10.17487/RFC7517, , <https://www.rfc-editor.org/rfc/rfc7517>.
[RFC7638]
Jones, M. and N. Sakimura, "JSON Web Key (JWK) Thumbprint", RFC 7638, DOI 10.17487/RFC7638, , <https://www.rfc-editor.org/rfc/rfc7638>.
[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>.
[RFC9053]
Schaad, J., "CBOR Object Signing and Encryption (COSE): Initial Algorithms", RFC 9053, DOI 10.17487/RFC9053, , <https://www.rfc-editor.org/rfc/rfc9053>.

9.2. Informative References

[FIPS-204]
"Module-Lattice-Based Digital Signature Standard", n.d., <https://doi.org/10.6028/NIST.FIPS.204>.
[I-D.draft-ietf-lamps-dilithium-certificates]
Massimo, J., Kampanakis, P., Turner, S., and B. Westerbaan, "Internet X.509 Public Key Infrastructure: Algorithm Identifiers for ML-DSA", Work in Progress, Internet-Draft, draft-ietf-lamps-dilithium-certificates-05, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-dilithium-certificates-05>.
[NIST-PQC-2022]
"Selected Algorithms 2022", n.d., <https://csrc.nist.gov/Projects/post-quantum-cryptography/selected-algorithms-2022>.

Appendix A. Examples

A.1. JOSE

{
  "seed": "0000000000000000000000000000000000000000000000000000000000000000",
  "jwk": {
    "kid": "T4xl70S7MT6Zeq6r9V9fPJGVn76wfnXJ21-gyo0Gu6o",
    "kty": "AKP",
    "alg": "ML-DSA-44",
    "pub": "unH59k4RuutY-pxvu24U5h8YZD2rSVtHU5qRZsoBmBMcRPgmu9VuNOVdteXi1zNIXjnqJg_GAAxepLqA00Vc3lO0bzRIKu39VFD8Lhuk8l0V-cFEJC-zm7UihxiQMMUEmOFxe3x1ixkKZ0jqmqP3rKryx8tSbtcXyfea64QhT6XNje2SoMP6FViBDxLHBQo2dwjRls0k5a-XSQSu2OTOiHLoaWsLe8pQ5FLNfTDqmkrawDEdZyxr3oSWJAsHQxRjcIiVzZuvwxYy1zl2STiP2vy_fTBaPemkleynQzqPg7oPCyXEE8bjnJbrfWkbNNN8438e6tHPIX4l7zTuzz98YPhLjt_d6EBdT4MldsYe-Y4KLyjaGHcAlTkk9oa5RhRwW89T0z_t1DSO3dvfKLUGXh8gd1BD6Fz5MfgpF5NjoafnQEqDjsAAhrCXY4b-Y3yYJEdX4_dp3dRGdHG_rWcPmgX4JG7lCnser4f8QGnDriqiAzJYEXeS8LzUngg_0bx0lqv_KcyU5IaLISFO0xZSU5mmEPvdSoDnyAcV8pV44qhLtAvd29n0ehG259oRihtljTWeiu9V60a1N2tbZVl5mEqSK-6_xZvNYA1TCdzNctvweH24unV7U3wer9XA9Q6kvJWDVJ4oKaQsKMrCSMlteBJMRxWbGK7ddUq6F7GdQw-3j2M-qdJvVKm9UPjY9rc1lPgol25-oJxTu7nxGlbJUH-4m5pevAN6NyZ6lfhbjWTKlxkrEKZvQXs_Yf6cpXEwpI_ZJeriq1UC1XHIpRkDwdOY9MH3an4RdDl2r9vGl_IwlKPNdh_5aF3jLgn7PCit1FNJAwC8fIncAXgAlgcXIpRXdfJk4bBiO89GGccSyDh2EgXYdpG3XvNgGWy7npuSoNTE7WIyblAk13UQuO4sdCbMIuriCdyfE73mvwj15xgb07RZRQtFGlFTmnFcIdZ90zDrWXDbANntv7KCKwNvoTuv64bY3HiGbj-NQ-U9eMylWVpvr4hrXcES8c9K3PqHWADZC0iIOvlzFv4VBoc_wVflcOrL_SIoaNFCNBAZZq-2v5lAgpJTqVOtqJ_HVraoSfcKy5g45p-qULunXj6Jwq21fobQiKubBKKOZwcJFyJD7F4ACKXOrz-HIvSHMCWW_9dVrRuCpJw0s0aVFbRqopDNhu446nqb4_EDYQM1tTHMozPd_jKxRRD0sH75X8ZoToxFSpLBDbtdWcenxj-zBf6IGWfZnmaetjKEBYJWC7QDQx1A91pJVJCEgieCkoIfTqkeQuePpIyu48g2FG3P1zjRF-kumhUTfSjo5qS0YiZQy0E1BMs6M11EvuxXRsHClLHoy5nLYI2Sj4zjVjYyxSHyPRPGGo9hwB34yWxzYNtPPGiqXS_dNCpi_zRZwRY4lCGrQ-hYTEWIK1Dm5OlttvC4_eiQ1dv63NiGkLRJ5kJA3bICN0fzCDY-MBqnd1cWn8YVBijVkgtaoascjL9EywDgJdeHnXK0eeOvUxHHhXJVkNqcibn8O4RQdpVU60TSA-uiu675ytIjcBHC6kTv8A8pmkj_4oypPd-F92YIJC741swkYQoeIHj8rE-ThcMUkF7KqC5VORbZTRp8HsZSqgiJcIPaouuxd1-8Rxrid3fXkE6p8bkrysPYoxWEJgh7ZFsRCPDWX-yTeJwFN0PKFP1j0F6YtlLfK5wv-c4F8ZQHA_-yc_gODicy7KmWDZgbTP07e7gEWzw4MFRrndjbDQ",
    "priv": "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"
  },
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}
Figure 3: ML_DSA_44
{
  "seed": "0000000000000000000000000000000000000000000000000000000000000000",
  "jwk": {
    "kid": "Suiu29qbfuaBaR4Ats-c6XQBePB_OpAxAwcTR_0KXVM",
    "kty": "AKP",
    "alg": "ML-DSA-65",
    "pub": "QksvJn5Y1bO0TXGs_Gpla7JpUNV8YdsciAvPof6rRD8JQquL2619cIq7w1YHj22ZolInH-YsdAkeuUr7m5JkxQqIjg3-2AzV-yy9NmfmDVOevkSTAhnNT67RXbs0VaJkgCufSbzkLudVD-_91GQqVa3mk4aKRgy-wD9PyZpOMLzP-opHXlOVOWZ067galJN1h4gPbb0nvxxPWp7kPN2LDlOzt_tJxzrfvC1PjFQwNSDCm_l-Ju5X2zQtlXyJOTZSLQlCtB2C7jdyoAVwrftUXBFDkisElvgmoKlwBks23fU0tfjhwc0LVWXqhGtFQx8GGBQ-zol3e7P2EXmtIClf4KbgYq5u7Lwu848qwaItyTt7EmM2IjxVth64wHlVQruy3GXnIurcaGb_qWg764qZmteoPl5uAWwuTDX292Sa071S7GfsHFxue5lydxIYvpVUu6dyfwuExEubCovYMfz_LJd5zNTKMMatdbBJg-Qd6JPuXznqc1UYC3CccEXCLTOgg_auB6EUdG0b_cy-5bkEOHm7Wi4SDipGNig_ShzUkkot5qSqPZnd2I9IqqToi_0ep2nYLBB3ny3teW21Qpccoom3aGPt5Zl7fpzhg7Q8zsJ4sQ2SuHRCzgQ1uxYlFx21VUtHAjnFDSoMOkGyo4gH2wcLR7-z59EPPNl51pljyNefgCnMSkjrBPyz1wiET-uqi23f8Bq2TVk1jmUFxOwdfLsU7SIS30WOzvwD_gMDexUFpMlEQyL1-Y36kaTLjEWGCi2tx1FTULttQx5JpryPW6lW5oKw5RMyGpfRliYCiRyQePYqipZGoxOHpvCWhCZIN4meDY7H0RxWWQEpiyCzRQgWkOtMViwao6Jb7wZWbLNMebwLJeQJXWunk-gTEeQaMykVJobwDUiX-E_E7fSybVRTZXherY1jrvZKh8C5Gi5VADg5Vs319uN8-dVILRyOOlvjjxclmsRcn6HEvTvxd9MS7lKm2gI8BXIqhzgnTdqNGwTpmDHPV8hygqJWxWXCltBSSgY6OkGkioMAmXjZjYq_Ya9o6AE7WU_hUdm-wZmQLExwtJWEIBdDxrUxA9L9JL3weNyQtaGItPjXcheZiNBBbJTUxXwIYLnXtT1M0mHzMqGFFWXVKsN_AIdHyv4yDzY9m-tuQRfbQ_2K7r5eDOL1Tj8DZ-s8yXG74MMBqOUvlglJNgNcbuPKLRPbSDoN0E3BYkfeDgiUrXy34a5-vU-PkAWCsgAh539wJUUBxqw90V1Du7eTHFKDJEMSFYwusbPhEX4ZTwoeTHg--8Ysn4HCFWLQ00pfBCteqvMvMflcWwVfTnogcPsJb1bEFVSc3nTzhk6Ln8J-MplyS0Y5mGBEtVko_WlyeFsoDCWj4hqrgU7L-ww8vsCRSQfskH8lodiLzj0xmugiKjWUXbYq98x1zSnB9dmPy5P3UNwwMQdpebtR38N9I-jup4Bzok0-JsaOe7EORZ8ld7kAgDWa4K7BAxjc2eD540Apwxs-VLGFVkXbQgYYeDNG2tW1Xt20-XezJqZVUl6-IZXsqc7DijwNInO3fT5o8ZAcLKUUlzSlEXe8sIlHaxjLoJ-oubRtlKKUbzWOHeyxmYZSxYqQhSQj4sheedGXJEYWJ-Y5DRqB-xpy-cftxL10fdXIUhe1hWFBAoQU3b5xRY8KCytYnfLhsFF4O49xhnax3vuumLpJbCqTXpLureoKg5PvWfnpFPB0P-ZWQN35mBzqbb3ZV6U0rU55DvyXTuiZOK2Z1TxbaAd1OZMmg0cpuzewgueV-Nh_UubIqNto5RXCd7vqgqdXDUKAiWyYegYIkD4wbGMqIjxV8Oo2ggOcSj9UQPS1rD5u0rLckAzsxyty9Q5JsmKa0w8Eh7Jwe4Yob4xPVWWbJfm916avRgzDxXo5gmY7txdGFYHhlolJKdhBU9h6f0gtKEtbiUzhp4IWsqAR8riHQs7lLVEz6P537a4kL1r5FjfDf_yjJDBQmy_kdWMDqaNln-MlKK8eENjUO-qZGy0Ql4bMZtNbHXjfJUuSzapA-RqYfkqSLKgQUOW8NTDKhUk73yqCU3TQqDEKaGAoTsPscyMm7u_8QrvUK8kbc-XnxrWZ0BZJBjdinzh2w-QvjbWQ5mqFp4OMgY94__tIU8vvCUNJiYA1RdyodlfPfH5-avpxOCvBD6C7ZIDyQ-6huGEQEAb6DP8ydWIZQ8xY603DoEKKXkJWcP6CJo3nHFEdj_vcEbDQ-WESDpcQFa1fRIiGuALj-sEWcjGdSHyE8QATOcuWl4TLVzRPKAf4tCXx1zyvhJbXQu0jf0yfzVpOhPun4n-xqK4SxPBCeuJOkQ2VG9jDXWH4pnjbAcrqjveJqVti7huMXTLGuqU2uoihBw6mGqu_WSlOP2-XTEyRyvxbv2t-z9V6GPt1V9ceBukA0oGwtJqgD-q7NXFK8zhw7desI5PZMXf3nuVgbJ3xdvAlzkmm5f9RoqQS6_hqwPQEcclq1MEZ3yML5hc99TDtZWy9gGkhR0Hs3QJxxgP7bEqGFP-HjTPnJsrGaT6TjKP7qCxJlcFKLUr5AU_kxMULeUysWWtSGJ9mpxBvsyW1Juo",
    "priv": "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"
  },
  "jws": "eyJhbGciOiJNTC1EU0EtNjUiLCJraWQiOiJTdWl1MjlxYmZ1YUJhUjRBdHMtYzZYUUJlUEJfT3BBeEF3Y1RSXzBLWFZNIn0.SXTigJlzIGEgZGFuZ2Vyb3VzIGJ1c2luZXNzLCBGcm9kbywgZ29pbmcgb3V0IHlvdXIgZG9vci4.zmO9_0bLgJAegoVNymfRo4nGPK5lVtSFGnDbzfzYAD5mUEXpaBUg4itvZ8rAUZi4HLb59QqDQSBSpMXC0axajXOMV_YttfmwGgC6FMyaMRZkx-A92bGiNLutqX9jcwRLJqXjMkUGhz2YpHe_mV9QpxokRCH9K6jkyFZp4hZIwFXhRt1z0OGIa5rOoHKsxOCAUZhTXKiASb3vk9lUASW0-Y58WKT4rVmst7_dvk7FVbe9A9I21IH-Tqlg1zSMoI8ozh1aBSG92uPursBd5KRcOlJwhNUYJDgHScIHXM6Hzk6u98W5orKPHu1rDIK7rHJI4Zrui4wBjmQLsPE01LcZHRx4zexDCTMCGSojbL1FiT9CU3oUep4oWOytTEAf2eCi3qDD0iSrp5IslCueoNjtGOFSnUKlsnCeiZF-tNqTy1KpJ3ErTaNPcCzCvsEalhJwFa7NOWyQOEJUzcLaPY_VEFwcCX1Gk4bEI-1rLDiyZqkXgny-U2oRnll0d3u-e2S_Rg-_eL1H_XEbPs_km-822G7JY9li4muZ5KVvfQf_5hza1V4GweqvmeWuZL1gBU2HPS7x1tWL798ALOk1rMnxsvBOPiSLxAEdPoIuw0_qMlKjTavJcDFaihgCgGMUk5SjU65IWQS9t4rgxv9Idu0OCsozo9iCBqrVcnaOwUpkMhV6KeiXA7kQNcegVaMio40cjSyMiEkhGIOEOf8L6eohOh_bPPRYs-8NrZ-VOBJCa0ubJcDU1cTuGNCa7nWWxAqfVjcMyNDx9XHBYBnSOcFNfMP7S9nvqw3KC50U_t2PH5SfwS9w4DLvcgrlEP_gwSgOXuf-i0tRGLQly3IMB7O8QOnkofyFaCUDZeurFkGTpoBfT6lzbJznQAMIDPNcWUsRlNTXsH7atC1nxl4xDJLmmPLCxiErfxbCW5gMWox0kLDwfsFj57hsXG75cZ4jiBbq9b0VjD7Vkf8xlc06ExdzBhGXz8oJiaT5WHDsuzGtrFmh6diN1cO4Cxjr6KdNE8IlyxsfXxQ4AI-0ke3gMyi0DOGeHgHuNc-JHD7oZ6njUMSTBkR1aUMNT7n_2nfFTDCdqW1HaMsMwIHfLOk6dayKXE1oMqY5Op8S5k_SAaknR0vNxmhlTA5h3bZJ28NZxM6R7D00_eBEYrH20rmRP7G7kXKzLvmWeaKAh4oQHiqjVhgauiePDRiMmjx0OhdQnMCtO8PWbx06SiviRn_5hswdVV08B48MVHqbM2AxCLLJYinC2Ep0302Uo0DI-rTNZ1Znn58kM7VCskcxDLsH9AYvPz-HQr3H7Xg0ElwjYn-jJXgZ_cdnLFt4_TuKQdpw_qhvyrNjOx0Mdc-1PrwoWqpA9sSv_pS5lwI2qNVHI2Vj2mZHByod1QUeOQExf3SBjP_FHEAUzUu1OK8M-1SQZGzJT2su3a6ZnMnp0U5qdXyMONFoI2jJ2hDjt7QEQsLx-rvaLxZMJtc2z0MHdwJGAC_kug7XjH3SWQZzBu7zzreIaSwr2A2oobeZiAydwb8LX2QsY9Jr_NphGAMAqzrpkuaMyBd_pFTKMp9s0GYxwyG1ZD9uRuPI9imA4CS7bt-O8YvbWg6eQ-qa9OqDlxNt3Xc32TniQFVxVxN6PDY33XXU-Rpvd1w47NZ48nkyJzjD8Xlbvk9p2ynxWHr-Sto5HXZdru4j8ETUW7ri3mEG1m_dxAbAe2kVbsBp2I1vQppugbmRexuMRLdYFIKqNm0qpQoWTr_k2t5KHnWolrSbFH7Usm8Pwyi4sNhh4_yRHADO2q2o19zCCx2plDSMeYI74CQPRGLlK_GLM4E5Bzfny3E2eaE5_gQBTSGNHpQtJB0ipPwDjqsjDCXqXupCkRta1vxng4coi2-vWYvKu6mq9HhdovHAaWrZRyvuPPI4ZDN_NkmfQR8HogR6NLVhLlRp1cwMArSSDA3f8QlnjdbaeutxRXvFnCCjBk79ws8VGdWAuRmIWgoEFeVAVxkJjJ07zOW8I3kNfB6pnxsZmJwWAGqWc1UlPmkNBstmSXinAzbdl-W-kn1XRDuhzTafHnkCbKS5XgJKsWD2FrhcnCaxxRxuxIGxijofjD4ihmJoYDFh1FYs9IcC-szEfMSekanWOIZCHd1fVzTSbLr5bNaOXR2sO1muFX7w22m8pBVD3fyOHK2JnK4FBCnEBrruMIDaqqu8Z4xesAHKfxY67w-25eUuvVCGL3xpXSyp90684ICkG4STztP1shLVsxKDA-37sKKplqemERlMPY4vDM1Np8JlVawbSGIuom20g6p2KV_zpIPwx9vd1nAiaeZbryf3N5gtL-dOq-c6uZhTCx9OLBtLGE3BcAmn5JFjMGQFxyTL07BluNu24Kf-lttGj9jzbwPZYrok-SnMilXGFEqB3D3cKCOlWjsgg_3cUW1uMp4KlWQvkimV9Pd7cY70w607jcYBJ3MlFZ8EeWeYPZ9qu6xwidA8XlLHxXxfLIJOgfpU8MTppfxdnMhqNSvH_Hx57oDphbUks5K1Z8-O4dSnNqQ-ZWbhaAydYQFDKuUF6HYTAvaWhJmACxhTkTp2t6-P3bev-FcdFIdszJC9LxWtJ96LY_GV4Qvp0hiIdyP1BukWNHtsXK2Rxres3_4Cndg2BOGxVcKZ9YpQDCUy76GRbTCenqjD-SG5sVUEVha5yxbKArPr2-Xpgk8cuZBRSAdmPNRdxCgUtldfCLeL7xhJvryMouxfQ75PMBaImHcsMd95075ePt_VkClUaUj55Y9E81FbOEchPfud2w3TtSvRPvB8-RgY8sLJUAclxcUGE4PnKSZJ7TIBUtHD6uyZ0-nC5KGxbXZsBEzUeHns4ix0Wmo6-6vAM4PGK3qRA1VAhtKXyvNcAfVccVi8KJMK9Mz2eIOXPATvyRy34Ltrcg8tcgK0ftYqEWYpAZ2fVpZBXcYfTIinuLN0-qLra388EZuu59jvmRD7mUv1msMWVMGVeBoNP3lJaJGGWK8iYyu4q7Grq-6WXr5qCz_7kwAtVJdb-zW8U3jLJ3tRSYlyjlpzeVAGjDQ6Yni5y9x4BF-5QUqcoGMLLglyx2WOCELT8IW7nsV21QnqqAbtCzZ76UtEdmUuEOTyqiKQZ0lrjMRm3YrCvJKxtR5thhTRka708NzBvwSRs-JxGG__EWjHhT-aB4VL3IL_oz3mt3iQoszfA-SzHcKU1laZMBuUCyxks6KiJgQGZRPXyaxxDtqZdaRP8Ic5CmuPeyu3kafi0L6LFijsUxnSGxTpgu7hfvcmowQijfE9_ylvg8k_EbI2miG11giODVCYb7k9Yjyriwc9dSUUZ7XoiS24hWYUX6BGGQNN3wVHPkDkOVSDBYTjto99ulquryx4K_UMCu9sQVNxBfMh8tLN7O9-MXlnJbHfKfqFHiPGdIYOBpwuqJdAJiyiuSG3gJxMG_wuwNkBWoO--iOm6PIarCyvL8_P-tuUfT4zIgjJJ3o6YJhbo-q2K82ZFmHuILyzfDSGtHDZpZIR7XnRQWet90cJEHL5k653kvyEHJg0iUiE0iwNA5d_4gBq3vmw1J74hwAHx0Z_iYEcPS6hDGow8M8D7UJTZDkUV_86zj2YqGm_QC_aAeD__NP6sa61bI9-gTOzvYc0JiExKTDjOK9fIvHaV-HN4xr2vWner8o6jPyETvGM8D7aEezlUVOEFwALmhJPSMAq_Fk9JlcIUuC-ITJZNtNz9Awfiru3wkPja1bXN76WAuRHjia0x5ptgMCy2py_vSHZybfIS85ZjsOQ-i_e_niBzhyzXwzBaLEyEitbF4ZQx5c88lXKDMpe9tirAI6XAcqLf4UZkD8Wm2YV7hhVfxLQ1AWLekWE9DZljCtE-SbS1EWNGR8faXKCvaZznRyoqdWz8IN3w7KvaA_ZrEKkIXkkreztG6pI06DlDHCl_sU6rCOoyQf6y1AY77Ob4SdkSRoBHGgR6Uv-LrxHpyJ6trzccu0kqxubHrkW2yHcqe6enVf43zYwWKUeJJZ10bt3a92ziSne-3aj6v3guiKoJoLnV_9h8rUF6zorTWE-Tq58tYfb5SmGf4iCJ5cy9LTY0COIfwJtPkUmyBCZwUhWJnV24P5pOZPe_CckQ28xv5J7Zf4Bvqrq_rhubFEhTJ5JvdMfz8Whc56WSHX7GRKEMqXVp3pHohBvOyT9BmotzIlibVklJy4gzkzUcjJJOld-BOaM_cnMiHpoyKXSJAXTNwXngzEpbvDP2Y0fnrgqDpO3RR3gINaZLRmeG0WI4wWBMMfw8PHjpyV17C_1hmfRI-darbZcX7PD3N4Rw4lBACyk_wnOHBcAS-5cLZEzNmFmhc4iO4msz_seQ1N0drbB0NoUVWBmcY3pGC9TiY6f6Pn-FBUnQkuBhIyPtgAAAAAAAAAABgwVHCUv",
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}
Figure 4: ML_DSA_65
{
  "seed": "0000000000000000000000000000000000000000000000000000000000000000",
  "jwk": {
    "kid": "tRn1JNIkgMsABVQBlXeDHxAIcclh-2IX0UdDEzPt5XU",
    "kty": "AKP",
    "alg": "ML-DSA-87",
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    "priv": "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"
  },
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}
Figure 5: ML_DSA_87

A.2. COSE

{
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Figure 6: ML_DSA_44
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}
Figure 7: ML_DSA_65
{
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}
Figure 8: ML_DSA_87

Acknowledgments

We would like to thank Simo Sorce, Ilari Liusvaara, Neil Madden, Anders Rundgren, David Waite, Russ Housley, and Lucas Prabel for their comments and reviews of this document.

Authors' Addresses

Michael Prorock
mesur.io
Orie Steele
Transmute
Rafael Misoczki
Google
Michael Osborne
IBM
Christine Cloostermans
NXP