LAMPS WG J. Massimo
Internet-Draft P. Kampanakis
Intended status: Standards Track AWS
Expires: 6 August 2025 S. Turner
sn3rd
B. E. Westerbaan
Cloudflare
2 February 2025
Internet X.509 Public Key Infrastructure: Algorithm Identifiers for ML-
DSA
draft-ietf-lamps-dilithium-certificates-07
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
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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.
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document authors. All rights reserved.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 3
2. Identifiers . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. ML-DSA Signatures in PKIX . . . . . . . . . . . . . . . . . . 4
4. ML-DSA Public Keys in PKIX . . . . . . . . . . . . . . . . . 5
5. Key Usage Bits . . . . . . . . . . . . . . . . . . . . . . . 7
6. Private Key Format . . . . . . . . . . . . . . . . . . . . . 7
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 8
8. Security Considerations . . . . . . . . . . . . . . . . . . . 9
8.1. Rationale for disallowing HashML-DSA . . . . . . . . . . 10
9. References . . . . . . . . . . . . . . . . . . . . . . . . . 11
9.1. Normative References . . . . . . . . . . . . . . . . . . 11
9.2. Informative References . . . . . . . . . . . . . . . . . 12
Appendix A. ASN.1 Module . . . . . . . . . . . . . . . . . . . . 13
Appendix B. Security Strengths . . . . . . . . . . . . . . . . . 15
Appendix C. Examples . . . . . . . . . . . . . . . . . . . . . . 16
C.1. Example Private Key . . . . . . . . . . . . . . . . . . . 16
C.2. Example Public Key . . . . . . . . . . . . . . . . . . . 17
C.3. Example Certificates . . . . . . . . . . . . . . . . . . 25
Appendix D. Pre-hashing (ExternalMu-ML-DSA) . . . . . . . . . . 49
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Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 51
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 51
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
}
| NOTE: The above syntax is from [RFC5912] and is compatible with
| the 2021 ASN.1 syntax [X680]. See [RFC5280] for the 1988 ASN.1
| syntax.
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The fields in AlgorithmIdentifier have the following meanings:
* algorithm identifies the cryptographic algorithm with an object
identifier.
* parameters, which are optional, are the associated parameters for
the algorithm identifier in the algorithm field.
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.
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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:
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SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE {
algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}},
subjectPublicKey BIT STRING
}
| NOTE: The above syntax is from [RFC5912] and is compatible with
| the 2021 ASN.1 syntax [X680]. See [RFC5280] for the 1988 ASN.1
| syntax.
The fields in SubjectPublicKeyInfo have the following meaning:
* algorithm is the algorithm identifier and parameters for the
public key (see above).
* subjectPublicKey contains the byte stream of the public key.
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.
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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.
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[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,
...
}
| NOTE: The above syntax is from [RFC5958] and is compatible with
| the 2021 ASN.1 syntax [X680].
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).
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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).
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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.
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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, August 2023, <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, March 1997,
<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, November 2003,
<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, May 2008,
<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, June 2010,
<https://www.rfc-editor.org/rfc/rfc5912>.
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[RFC5958] Turner, S., "Asymmetric Key Packages", RFC 5958,
DOI 10.17487/RFC5958, August 2010,
<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,
May 2017, <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, February 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, February 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 , 2021,
<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", 2021, <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 , 2009,
<https://www.iacr.org/archive/
asiacrypt2009/59120596/59120596.pdf>.
[NIST-PQC] National Institute of Standards and Technology (NIST),
"Post-Quantum Cryptography Project", 20 December 2016,
<https://csrc.nist.gov/Projects/post-quantum-
cryptography>.
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[RFC7468] Josefsson, S. and S. Leonard, "Textual Encodings of PKIX,
PKCS, and CMS Structures", RFC 7468, DOI 10.17487/RFC7468,
April 2015, <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 ::= {
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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
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--
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.
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|=======+=======+=====+========+========+========|
| 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-----
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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.
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-----BEGIN PUBLIC KEY-----
MIIFMjALBglghkgBZQMEAxEDggUhANeytHJUquDbReeTDUqY0sl9jxOX0Xidr6Fw
JLMW6b7JT8mUbULxm3mnQTu6oz5xSctC7VEVaTrAQfrLmIretf4OHYYxGEmVtZLD
l9IpTi4U+QqkFLo4JomaxD9MzKy8JumoMrlRGNXLQzy++WYLABOOCBf2HnYsonTD
atVU6yKqwRYuSrAay6HjjE79j4C2WzM9D3LlXf5xzpweu5iJ58VhBsD9c4A6Kuz+
r97XqjyyztpU0SvYzTanjPl1lDtHq9JeiArEUuV0LtHo0agq+oblkMdYwVrk0oQN
kryhpQkPQElll/yn2LlRPxob2m6VCqqY3kZ1B9Sk9aTwWZIWWCw1cvYu2okFqzWB
ZwxKAnd6M+DKcpX9j0/20aCjp2g9ZfX19/xg2gI+gmxfkhRMAvfRuhB1mHVT6pNn
/NdtmQt/qZzUWv24g21D5Fn1GH3wWEeXCaAepoNZNfpwRgmQzT3BukAbqUurHd5B
rGerMxncrKBgSNTE7vJ+4TqcF9BTj0MPLWQtwkFWYN54h32NirxyUjl4wELkKF9D
GYRsRBJiQpdoRMEOVWuiFbWnGeWdDGsqltOYWQcf3MLN51JKe+2uVOhbMY6FTo/i
svPt+slxkSgnCq/R5QRMOk/a/Z/zH5B4S46ORZYUSg2vWGUR09mWK56pWvGXtOX8
YPKx7RXeOlvvX4m9x52RBR2bKBbnT6VFMe/cHL501EiFf0drzVjyHAtlOzt2pOB2
plWaMCcYVVzGP3SFmqurkl8COGHKjND3utsocfZ9VTJtdFETWtRfShumkRj7ssij
DuyTku8/l3Bmya3VxxDMZHsVFNIX2VjHAXw+kP0gwE5nS5BIbpNwoxoAHTL0c5ee
SQZ0nn5Hf6C3RQj4pfI3gxK4PCW9OIygsP/3R4uvQrcWZ+2qyXxGsSlkPlhuWwVa
DCEZRtTzbmdb7Vhg+gQqMV2YJhZNapI3w1pfv0lUkKW9TfJIuVxKrneEtgVnMWas
QkW1tLCCoJ6TI+YvIHjFt2eDRG3v1zatOjcC1JsImESQCmGDM5e8RBmzDXqXoLOH
wZEUdMTUG1PjKpd6y28Op122W7OeWecB52lX3vby1EVZwxp3EitSBOO1whnxaIsU
7QvAuAGz5ugtzUPpwOn0F0TNmBW9G8iCDYuxI/BPrNGxtoXdWisbjbvz7ZM2cPCV
oYC08ZLQixC4+rvfzCskUY4y7qCl4MkEyoRHgAg/OwzS0Li2r2e8NVuUlAJdx7Cn
j6gOOi2/61EyiFHWB4GY6Uk2Ua54fsAlH5Irow6fUd9iptcnhM890gU5MXbfoySl
Er2Ulwo23TSlFKhnkfDrNvAUWwmrZGUbSgMTsplhGiocSIkWJ1mHaKMRQGC6RENI
bfUVIqHOiLMJhcIW+ObtF43VZ7MEoNTK+6iCooNC8XqaomrljbYwCD0sNY/fVmw/
XWKkKFZ7yeqM6VyqDzVHSwv6jzOaJQq0388gg76O77wQVeGP4VNw7ssmBWbYP/Br
IRquxDyim1TM0A+IFaJGXvC0ZRXMfkHzEk8J7/9zkwmrWLKaFFmgC85QOOk4yWeP
cusOTuX9quZtn4Vz/Jf8QrSVn0v4th14Qz6GsDNdbpGRxNi/SHs5BcEIz9asJLDO
t9y3z1H4TQ7Wh7lerrHFM8BvDZcCPZKnCCWDe1m6bLfU5WsKh8IDhiro8xW6WSXo
7e+meTaaIgJ2YVHxapZfn4Hs52zAcLVYaeTbl4TPBcgwsyQsgxI=
-----END PUBLIC KEY-----
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SEQUENCE {
SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
}
BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d17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` }
}
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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-----
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SEQUENCE {
SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
}
BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f62594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, et al. Expires 6 August 2025 [Page 21]
Internet-Draft ML-DSA in Certificates February 2025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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-----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, et al. Expires 6 August 2025 [Page 22]
Internet-Draft ML-DSA in Certificates February 2025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-----END PUBLIC KEY-----
SEQUENCE {
SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
}
BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab4
1b90258cfa7e90ec97124a73b323b9ba21ab64d767c433f5a521effe18f86e46
a188952c4467e048b729e7fc4d115e7e48da1896d5fe119b10dcddef62cb3079
54074b42336e52836de61da941f8d37ea68ac8106fabe19070679af600853712
0f70793b8ea9cc0e6e7b7b4c9a5c7421c60f24451ba1e933db1a2ee16c79559f
21b3d1b8305850aa42afbb13f1f4d5b9f4835f9d87dfceb162d0ef4a7fdc4cba
1743cd1c87bb4967da16cc8764b6569df8ee5bdcbffe9a4e05748e6fdf225af9
e4eeb7773b62e8f85f9b56b548945551844fbd89806a4ac369bed2d256100f68
8a6ad5e0a709826dc4449e91e23c5506e642361ef5a313712f79bc4b3186861c
a85a4bab17e7f943d1b8a333aa3ae7ce16b440d6018f9e04daf5725c7f1a93fa
d1a5a27b67895bd249aa91685de20af32c8b7e268c7f96877d0c85001135a4f0
Massimo, et al. Expires 6 August 2025 [Page 23]
Internet-Draft ML-DSA in Certificates February 2025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, et al. Expires 6 August 2025 [Page 24]
Internet-Draft ML-DSA in Certificates February 2025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` }
}
C.3. Example Certificates
| The example certificates in this section have key usage bits
| set to digitalSignature, keyCertSign, and cRLSign to lessen the
| number of examples, i.e., brevity. Certificate Policies (CPs)
| [RFC3647] for production CAs should consider whether this
| combination is appropriate.
The following is a self-signed certificate for the ML-DSA-44 public
key in the previous section.
-----BEGIN CERTIFICATE-----
MIIPlDCCBgqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMR
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Massimo, et al. Expires 6 August 2025 [Page 25]
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Massimo, et al. Expires 6 August 2025 [Page 26]
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-----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 }
Massimo, et al. Expires 6 August 2025 [Page 27]
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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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Massimo, et al. Expires 6 August 2025 [Page 28]
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}
[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
Massimo, et al. Expires 6 August 2025 [Page 29]
Internet-Draft ML-DSA in Certificates February 2025
22ff` }
}
}
}
}
}
SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
}
BIT_STRING { `00` `67a8951fc308e12f6867611fdc254bf4bcb514f7f5f
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Massimo, et al. Expires 6 August 2025 [Page 30]
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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-----
MIIVjTCCCIqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMS
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
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X2JZSf2PWKVh5pa9TCfQWzjbsu3wHmZO/YG+HqiTaIzmiqLVHFlY+LvG606J7mfS
Massimo, et al. Expires 6 August 2025 [Page 31]
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wDIJVNVyEsrHIp/x1urwOSi9UVEfjYjYR3NsfeJzDVl45UEHExYJeIZ3Eb9VOaC/
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KqRRVdbIrhU2fk6wA7j994UQcZSXOfn/8JAj6vRRBNKoSkWQbu1GcaRNwo0nmHu1
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dKqqE/riSaAGscNPW6C4gvJjeCIvs28ig8JD8P/rXxu0FKCnDVXj1ApWtsvIiuHw
O3sogtmN7qKOFFyd7f2OrxzvLtlKiwUPiWT0bR6g0MKkPg3aYYKtv09u0XW2dCJX
hZvyLzpBfs8fnYkxe15TnVh68WueExPgRRT/pkuos/8rgyH4gRyz+wIsj2ROcKS4
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jL84SvgarJXisylOBHiayDcnpdwEVZ+Wr0HYoFNRb+7uvFJ0brarKBngkQhxDYNf
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Massimo, et al. Expires 6 August 2025 [Page 32]
Internet-Draft ML-DSA in Certificates February 2025
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Massimo, et al. Expires 6 August 2025 [Page 33]
Internet-Draft ML-DSA in Certificates February 2025
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IA==
-----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 {
Massimo, et al. Expires 6 August 2025 [Page 34]
Internet-Draft ML-DSA in Certificates February 2025
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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a45906eed4671a44dc28d27987bb55df69e9e8561f61a80a72699503865fed9b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, et al. Expires 6 August 2025 [Page 35]
Internet-Draft ML-DSA in Certificates February 2025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` }
}
[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 {
Massimo, et al. Expires 6 August 2025 [Page 36]
Internet-Draft ML-DSA in Certificates February 2025
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 }
}
BIT_STRING { `00` `11816868a90c66934bdbb1d19c53a6a5dc30535ff6d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6b9d41d8b9f70ba499218ae7d55afb97b47b26caf666f4dea790e0830a427052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, et al. Expires 6 August 2025 [Page 37]
Internet-Draft ML-DSA in Certificates February 2025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, et al. Expires 6 August 2025 [Page 38]
Internet-Draft ML-DSA in Certificates February 2025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` }
}
The following is a self-signed certificate for the ML-DSA-87 public
key in the previous section.
-----BEGIN CERTIFICATE-----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, et al. Expires 6 August 2025 [Page 39]
Internet-Draft ML-DSA in Certificates February 2025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Massimo, et al. Expires 6 August 2025 [Page 40]
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Massimo, et al. Expires 6 August 2025 [Page 41]
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-----END CERTIFICATE-----
Massimo, et al. Expires 6 August 2025 [Page 42]
Internet-Draft ML-DSA in Certificates February 2025
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 }
Massimo, et al. Expires 6 August 2025 [Page 43]
Internet-Draft ML-DSA in Certificates February 2025
}
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56b51adbec8d8bdb6983979a7e3a21b44b5d1518ca97d0b5195f51ed6a24350c
89747e1edea51b448e3e9147054ce927873c90db394d86888e07dff177593d6f
79e152302204aeb03be2386af3e24078bd028b1689f5e147c9f452c8ceb02ec5
9cc9db63a03576ceeafe98239023897da0236630a53c0de7f435a19869792fab
36e7b9e635760f09069e6432e700035ac2a02879fff0a1e1bec522047193d94e
b5df1efd53eea1144ca78940852f5ec9727904b366ede4f5e2d331fad5fc282e
a2c47e923142771c3dd75a87357487def99e5f18e9d9ed623c175d02888c51f8
2c07a80d54716b3c3c2bdbe2e9f0a9bbaaebeb4d52936876406f5c00e8e4bbd0
a5ec05797e6207c5ab6c88f1a688421bd05a114f4d7de2ac241fa0e8bedff47f
762ddcbeaa91004f8d31e85095c81054994ad3826e344ba96040810fc0b2ad1d
e48cfade002c62e5a49a0731ab38344bc1636df16bf607d56855e56d684003c7
Massimo, et al. Expires 6 August 2025 [Page 44]
Internet-Draft ML-DSA in Certificates February 2025
18e4bad9e5a099979fcddeeb1c4a7776cd37a3417cb0e184e29ef9bc0e87475b
a663be09e00ab562eb7c0f7165f969a9b42414198ccf1bff2a2c8d689a414ece
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8be28e78fe0b5ce45fbb7a1af1a3b28a8d94b7890e3c882e39bc98e9f0ad7602
5bf0dd2f00298e7141a226b3d7cee414f604d1e0ba54d11d5fe58bccea6ad77a
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4c132aaacb7e0146f14efd11cfcaf4caa4f775a716ce325e0a435a4d349d720b
cf137450afc45046fc1a1f83a9d329777a7084e4aadae7122ce97005930528eb
3c7f7f1129b372887a371155a3ba201a25cbf1dcb64e7cdee092c3141fb5550f
e3d0dd82e870e578b2b46500818113b8f6569773c677385b69a42b77dcba7acf
fd95fd4452e23aaa1d37e1da2151ea658d40a3596b27ac9f8129dc6cf0643772
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3b1d0dda4a6533965bef1b7b8292e254c014d090fed857c44c1839c694c0a64e
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a28ffaa00b5d349f8a547ad875b96a8c2b2910c9301309a3f9138a5693111f55
b3c009ca947c39dfc82d98eb1caa4a9cbe885f786fa86e55be062222f8ba90a9
74073326b31212aece0a34a60` }
}
[3] {
SEQUENCE {
SEQUENCE {
# keyUsage
OBJECT_IDENTIFIER { 2.5.29.15 }
BOOLEAN { TRUE }
OCTET_STRING {
BIT_STRING { b`1000011` }
}
}
SEQUENCE {
# basicConstraints
Massimo, et al. Expires 6 August 2025 [Page 45]
Internet-Draft ML-DSA in Certificates February 2025
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 }
}
BIT_STRING { `00` `08783d565efc7b97440f8bd9818b466be538dbccedb
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85911997ab02a656c1f9f3b7c9fb043f811883fef3c05fb5a1703ce56776ee6f
Massimo, et al. Expires 6 August 2025 [Page 46]
Internet-Draft ML-DSA in Certificates February 2025
29b63d47e79f3ccc2837d545292c42b42024fd8e1e88ced0c0d21030c09bc1fa
3bf780ccc18586c5ab7d26a97c27348c1581f9aeeb0d76daaceb77e49b99bc49
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4e01f2c6719724fd87dba13cb6820c54645b2b8ad8ce2d14ecf38385380fd77e
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122aec6dea01b6c6ece4a45e5d63fa0e5beb9612d3289ed1d5515eff83f51216
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645b8f9c7907c40ece541c8a0ff34cefcb813bf187b270af0fe4346694be4b1a
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140124ee215da5ce9a11d865bf83017cdfab6b4014e31f9da293078ddf7c5125
Massimo, et al. Expires 6 August 2025 [Page 47]
Internet-Draft ML-DSA in Certificates February 2025
4e2da95f19a508d01dc8f846b1652d4de57a7251e6393240ed14303e395fb188
079345e0fb853f876cc1edb4290e2684cc35311e8602c71a57bd3a6c9a804591
727be34f6fab723f48a196febc6f0f9b34f344fd9706790a3e63d1a989cbcfdf
30f8eb71fcb024635adec568fe9d39a194c8cd2fbbf6a131390dc311e9c5381b
5542466b3c60a8eeb621e6e653b8b52fd5dd3f8d0f3fe3f0ea948b0c7862de25
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380cd0ea8be776e7cf7ca0d1bd59c5584fece0db84d1a767a162029d682e4063
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73e6347149a1cf4b5332289d635d5d23c2730b30368a5ce3cceba6155347f0df
21f611044505bce3806bd8edba86324637c6a9210830b636602a83527b41eee6
0f2d2df4c7c6a571ee8514848a47beb0a7203f8e4b91e4fa67ea3022fe9d9f94
14884016e66fe48536167e12f0dc550e801004c11a86c5b798e26ca9b1f25841
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6f36e2afc6eb084cdb2159be5437e5c437a738ef80ada9eb1d08b173d22a3a6e
Massimo, et al. Expires 6 August 2025 [Page 48]
Internet-Draft ML-DSA in Certificates February 2025
4eae6b29b329a93c2dc6b47993606e7ecff40431831e83aa7c64a09e7eb291b1
a9f671c14ff8517251b0419b517095b97fd7010ac59063be3652d27414262ecd
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1ff24618465b6651297cd34d38f61c62f31fb8e970c30653225eed4ad93a9340
2d67beed1e6c368aee7bdf4ca85e54eb2b17bbda501d0d096f5cb4e47575f0fa
8c60f8ed3bf2766de6374342014c5d8c72a9a9d981ce6c7069f75f843fb97819
d104a584f12b1a3b480b9fd774052b698259368ea5bb7af675809421fa3ac6e9
feebe427a13ece5e96fe85cd382b2e10607ab911877ad07e74a200621d3cc2d9
02dca836e92b8ae754b483a8a91b80a0b0c113c48b0f1253c599bb9cf01bdca0
5112c6378a1b2de49053c507c82b5e11b6e91abb2d5e90000000000000000000
0000000000000000000000000000000000000000000040c12151d1e252c` }
}
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().
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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:
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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
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Jake Massimo
AWS
United States of America
Email: jakemas@amazon.com
Panos Kampanakis
AWS
United States of America
Email: kpanos@amazon.com
Sean Turner
sn3rd
Email: sean@sn3rd.com
Bas Westerbaan
Cloudflare
Email: bas@cloudflare.com
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