Internet-Draft SLH-DSA Signature Algorithm in CMS November 2024
Housley, et al. Expires 22 May 2025 [Page]
Workgroup:
Network Working Group
Internet-Draft:
draft-ietf-lamps-cms-sphincs-plus-16
Published:
Intended Status:
Standards Track
Expires:
Authors:
R. Housley
Vigil Security
S. Fluhrer
Cisco Systems
P. Kampanakis
Amazon Web Services
B. Westerbaan
Cloudflare

Use of the SLH-DSA Signature Algorithm in the Cryptographic Message Syntax (CMS)

Abstract

SLH-DSA is a stateless hash-based signature scheme. This document specifies the conventions for using the SLH-DSA signature algorithm with the Cryptographic Message Syntax (CMS). In addition, the algorithm identifier and public key syntax are provided.

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 22 May 2025.

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Table of Contents

1. Introduction

This document specifies the conventions for using the SLH-DSA hash-based signature algorithm [FIPS205] with the Cryptographic Message Syntax (CMS) [RFC5652] signed-data content type.

SLH-DSA offers two signature modes: pure mode and pre-hash mode. SLH-DSA signature operations include a context string as input. The context string has a maximum length of 255 bytes. By default, the context string is the empty string. This document only specifies the use of pure mode with an empty context string for the CMS signed-data content type.

SLH-DSA offers three security levels. The parameters for each of the security levels were chosen to provide 128 bits of security, 192 bits of security, and 256 bits of security. Separate algorithm identifiers have been assigned for SLH-DSA at each of these security levels.

SLH-DSA is a stateless hash-based signature algorithm. Other hash-based signature algorithms are stateful, including HSS/LMS [RFC8554] and XMSS [RFC8391]. Without the need for state kept by the signer, SLH-DSA is much less fragile.

1.1. ASN.1

CMS values are generated using ASN.1 [X680], using the Basic Encoding Rules (BER) and the Distinguished Encoding Rules (DER) [X690].

1.2. Motivation

There have been recent advances in cryptanalysis and advances in the development of quantum computers. Each of these advances pose a threat to widely deployed digital signature algorithms.

If cryptographically relevant quantum computers (CRQC) are ever built, they will be able to break many of the public-key cryptosystems currently in use, including RSA, DSA, ECDSA, and EdDSA. A post-quantum cryptosystem (PQC) is secure against quantum computers that have more than a trivial number of quantum bits (qu-bits). It is open to conjecture when it will be feasible to build such quantum computers; however, it is prudent to use cryptographic algorithms that remain secure if a CRQC is invented. SLH-DSA is a PQC signature algorithm.

One use of a PQC signature algoritm is the protection of software updates, perhaps using the format described in [RFC4108], to enable deployment of software that implements other new PQC algorithms for key management and confidentiality.

1.3. 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.

2. SLH-DSA Hash-based Signature Algorithm Overview

SLH-DSA is a hash-based signature scheme which consists of a few time signature construction, namely Forest of Random Subsets (FORS) and a hypertree. FORS signs a message with a private key. The corresponding FORS public keys are the leaves in k binary trees. The roots of these trees are hashed together to form a FORS root. SLH-DSA uses a one-time signature scheme called WOTS+. The FORS tree roots are signed by a WOTS+ one-time signature private key. The corresponding WOTS+ public keys form the leaves in d-layers of Merkle subtrees in the SLH-DSA hypertree. The bottom layer of that hypertree signs the FORS roots with WOTS+. The root of the bottom Merkle subtrees are then signed with WOTS+ and the corresponding WOTS+ public keys form the leaves of the next level up subtree. Subtree roots are consequently signed by their corresponding subtree layers until we reach the top subtree. The top layer subtree forms the hypertree root which is trusted at the verifier.

A SLH-DSA signature consists of the randomization string, the FORS signature, the WOTS+ signature in each layer, and the path to the root of each subtree until the root of the hypertree is reached.

A SLH-DSA signature is verified by verifying the FORS signature, the WOTS+ signatures and the path to the root of each subtree. When reaching the root of the hypertree, the signature verifies only if it hashes to the pre-trusted root of the SLH-DSA hypertree.

SLH-DSA is a stateless hash-based signature algorithm. Stateful hash-based signature schemes require that the WOTS+ private key (generated by using a state index) is never reused or the scheme loses it security. Although its security decreases, FORS which is used at the bottom of the SLH-DSA hypertree does not collapse if the same private key used to sign two or more different messages like in stateful hash-based signature schemes. Without the need for state kept by the signer to ensure it is not reused, SLH-DSA is much less fragile.

SLH-DSA was designed to sign up to 2^64 messages and offers three security levels. The parameters of the SLH-DSA hypertree include the security parameter, the hash function, the tree height, the number of layers of subtrees, the Winternitz parameter of WOTS+, the number of FORS trees and leaves in each. The parameters for each of the security levels were chosen to at least as secure as a generic block cipher of 128, 192, or 256 bits.

3. SLH-DSA Public Key Identifier

The AlgorithmIdentifier for a SLH-DSA public key MUST use one of the twelve id-slh-dsa object identifiers listed below, based on the security level used to generate the SLH-DSA hypertree, the small or fast version of the algorithm, and the use of SHA-256 [FIPS180] or SHAKE256 [FIPS202]. For example, id-slh-dsa-shake-256s represents the 256-bit security level, the small version of the algorithm, and the use of SHAKE256. The parameters field of the AlgorithmIdentifier for the SLH-DSA public key MUST be absent.

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

   sigAlgs OBJECT IDENTIFIER ::= { nistAlgorithms 3 }

   id-slh-dsa-sha2-128s OBJECT IDENTIFIER ::= { sigAlgs 20 }

   id-slh-dsa-sha2-128f OBJECT IDENTIFIER ::= { sigAlgs 21 }

   id-slh-dsa-sha2-192s OBJECT IDENTIFIER ::= { sigAlgs 22 }

   id-slh-dsa-sha2-192f OBJECT IDENTIFIER ::= { sigAlgs 23 }

   id-slh-dsa-sha2-256s OBJECT IDENTIFIER ::= { sigAlgs 24 }

   id-slh-dsa-sha2-256f OBJECT IDENTIFIER ::= { sigAlgs 25 }

   id-slh-dsa-shake-128s OBJECT IDENTIFIER ::= { sigAlgs 26 }

   id-slh-dsa-shake-128f OBJECT IDENTIFIER ::= { sigAlgs 27 }

   id-slh-dsa-shake-192s OBJECT IDENTIFIER ::= { sigAlgs 28 }

   id-slh-dsa-shake-192f OBJECT IDENTIFIER ::= { sigAlgs 29 }

   id-slh-dsa-shake-256s OBJECT IDENTIFIER ::= { sigAlgs 30 }

   id-slh-dsa-shake-256f OBJECT IDENTIFIER ::= { sigAlgs 31 }

When this AlgorithmIdentifier appears in the SubjectPublicKeyInfo field of an X.509 certificate [RFC5280], the certificate key usage extension MAY contain digitalSignature, nonRepudiation, keyCertSign, and cRLSign; the certificate key usage extension MUST NOT contain other values.

   pk-slh-dsa-sha2-128s PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-sha2-128s
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-sha2-128f PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-sha2-128f
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-sha2-192s PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-sha2-192s
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-sha2-192f PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-sha2-192f
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-sha2-256s PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-sha2-256s
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-sha2-256f PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-sha2-256f
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-shake-128s PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-shake-128s
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-shake-128f PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-shake-128f
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-shake-192s PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-shake-192s
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-shake-192f PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-shake-192f
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-shake-256s PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-shake-256s
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-slh-dsa-shake-256f PUBLIC-KEY ::= {
       IDENTIFIER id-slh-dsa-shake-256f
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

   SLH-DSA-PublicKey ::= OCTET STRING

   SLH-DSA-PrivateKey ::= OCTET STRING

No additional encoding of the SLH-DSA public key is applied in the SubjectPublicKeyInfo field of an X.509 certificate [RFC5280].

No additional encoding of the SLH-DSA private key is applied in the PrivateKeyInfo field of the privateKey field of the OneAsymmetricKey type of an Asymmetric Key Package [RFC5958].

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

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

4. Signed-data Conventions

As specified in CMS [RFC5652], the digital signature is produced from the message digest and the signer's private key. The signature is computed over different values depending on whether signed attributes are absent or present.

When signed attributes are absent, the SLH-DSA (pure mode) signature is computed over the content. When signed attributes are present, a hash is computed over the content using the same hash function that is used in the SLH-DSA tree. The signed attributes MUST include a content-type attribute and a message-digest attribute. The message-digest attribute contains the hash value of the content. The SLH-DSA signature is computed over the DER encoding of the set of signed attributes. The SLH-DSA signature generation operation is called slh_sign; see Section 10.2.1 of [FIPS205]. In summary:

   IF (signed attributes are absent)
   THEN slh_sign(content)
   ELSE message-digest attribute = Hash(content);
        slh_sign(DER(SignedAttributes))

In some implementations, performance may be significantly improved by signing and verifying DER(SignedAttributes) when the content is large. That is, passing an entire large message content to the signing function or the signature validation function can have an impact on performance. When the signed attributes are present, Section 5.3 of [RFC5652] requires the inclusion of the content-type attribute and the message-digest attribute. Other attributes can also be included.

When using SLH-DSA and signed attributes are present in the SignerInfo, the digestAlgorithms field in the SignedData MUST include the identifier for the one-way hash function used to compute the message digest.

When using SLH-DSA, the fields in the SignerInfo are used as follows:

digestAlgorithm:

The digestAlgorithm MUST identify a one-way hash function. To ensure collision resistance, the identified hash function SHOULD produce a hash value that is at least twice the size of the hash function used in the SLH-DSA tree. The hash functions defined in [FIPS180] and [FIPS202] MUST be supported for use with the variants of SLH-DSA as shown below; however, other hash functions MAY also be supported:

      id-slh-dsa-sha2-128s:  SHA-256
      id-slh-dsa-sha2-128f:  SHA-256
      id-slh-dsa-sha2-192s:  SHA-512
      id-slh-dsa-sha2-192f:  SHA-512
      id-slh-dsa-sha2-256s:  SHA-512
      id-slh-dsa-sha2-256f:  SHA-512
      id-slh-dsa-shake-128s: SHAKE128 with 256 bit output
      id-slh-dsa-shake-128f: SHAKE128 with 256 bit output
      id-slh-dsa-shake-192s: SHAKE256 with 512 bit output
      id-slh-dsa-shake-192f: SHAKE256 with 512 bit output
      id-slh-dsa-shake-256s: SHAKE256 with 512 bit output
      id-slh-dsa-shake-256f: SHAKE256 with 512 bit output

      The object identifiers for SHA-256 and SHA-512 are included
      in [RFC5754].  The object identifiers for SHAKE128 and
      SHAKE256 are included in [RFC8702].  In all four cases, the
      AlgorithmIdentifier SHOULD NOT include parameters.
signatureAlgorithm:

The signatureAlgorithm MUST contain one of the the SLH-DSA algorithm identifiers, and the algorithm parameters field MUST be absent. The algorithm identifier MUST be one of the following:

      id-slh-dsa-sha2-128s,  id-slh-dsa-sha2-128f,
      id-slh-dsa-sha2-192s,  id-slh-dsa-sha2-192f,
      id-slh-dsa-sha2-256s,  id-slh-dsa-sha2-256f,
      id-slh-dsa-shake-128s, id-slh-dsa-shake-128f,
      id-slh-dsa-shake-192s, id-slh-dsa-shake-192f,
      id-slh-dsa-shake-256s, id-slh-dsa-shake-256f.
signature:

The signature contains the signature value resulting from the SLH-DSA signing operation with the parameters associated with the selected signatureAlgorithm. The SLH-DSA signature generation operation is specified in Section 10.2.1 of [FIPS205], and the SLH-DSA signature verification operation is specified in Section 10.3 of [FIPS205]. Signature verification MUST include checking that the signatureAlgorithm field identifies SLH-DSA parameters that are consistent with public key used to validate the signature.

5. Security Considerations

Implementations MUST protect the private keys. Compromise of the private keys may result in the ability to forge signatures.

When generating an SLH-DSA key pair, an implementation MUST generate each key pair independently of all other key pairs in the SLH-DSA hypertree.

A SLH-DSA tree MUST NOT be used for more than 2^64 signing operations.

The generation of private keys relies on random numbers. The use of inadequate pseudo-random number generators (PRNGs) to generate these values can result in little or no security. An attacker may find it much easier to reproduce the PRNG environment that produced the keys, searching the resulting small set of possibilities, rather than brute force searching the whole key space. The generation of quality random numbers is difficult, and [RFC4086] offers important guidance in this area.

When computing signatures, the same hash function SHOULD be used to compute the message digest of the content and the signed attributes, if they are present.

To avoid algorithm substitution attacks, the CMSAlgorithmProtection attribute defined in [RFC6211] SHOULD be included in signed attributes.

Implementers SHOULD consider their particular use cases and may choose to implement OPTIONAL fault attack countermeasures [CMP2018] [Ge2023]. Verifying a signature before releasing the signature value is a typical fault attack countermeasure; however, this countermeasure is not effective for SLH-DSA [Ge2023]. Redundancy by replicating the signature generation process MAY be used as an effective fault attack countermeasure for SLH-DSA [Ge2023]; however, the SLH-DSA signature generation is already considered slow.

Likewise, Implementers SHOULD consider their particular use cases and may choose to implement protections against passive power and emissions side-channel attacks [SLotH].

6. Operational Considerations

If slh_sign is implemented in a hardware device such as hardware security module (HSM) or portable cryptographic token, implementations might want to avoid sending the full content to the device. By including signed attributes, which necessarily include the message-digest attribute and the content-type attribute as described in Section 5.3 of [RFC5652], the much smaller set of signed attributes are sent to the device for signing.

Following the approach in the previous paragraph is essentially the same as using SLH-DSA in pre-hash mode, which means that a hash of the content is passed to the SLH-DSA signature operation instead of the full message content. For this reason, this document only specifies the use of SLH-DSA pure mode.

When using SLH-DSA in pure mode, it is not possible to single-pass process the content to verify a SignedData message that does not contain signed attributes. To assist recipients that might make use of stream-based APIs, implementers SHOULD include signed attributes within any SignerInfo that uses SLH-DSA as signature algorithm. Doing so allows the recipient implementation to avoid keeping the signed content in memory. Recall that when signed attributes are present, they MUST contain a content-type attribute and a message-digest attribute, and they SHOULD contain a CMSAlgorithmProtection attribute.

7. IANA Considerations

For the ASN.1 Module in the Appendix of this document, IANA is requested to assign an object identifier (OID) for the module identifier (TBD1) with a Description of "id-mod-slh-dsa-2024". The OID for the module should be allocated in the "SMI Security for S/MIME Module Identifier" (1.2.840.113549.1.9.16.0).

8. Acknowledgements

Thanks to Mike Ounsworth, Tomas Gustavsson, Daniel Van Geest, Carl Wallace, Phillip Hallam-Baker, and Dieter Bratko for their careful review and constructive comments.

9. References

9.1. Normative References

[FIPS180]
National Institute of Standards and Technology (NIST), "Secure Hash Standard (SHS)", FIPS PUB 180-4, .
[FIPS202]
National Institute of Standards and Technology (NIST), "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions", FIPS PUB 202, .
[FIPS205]
National Institute of Standards and Technology (NIST), "Stateless Hash-Based Digital Signature Standard", FIPS PUB 205, , <https://doi.org/10.6028/NIST.FIPS.205>.
[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>.
[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>.
[RFC5652]
Housley, R., "Cryptographic Message Syntax (CMS)", STD 70, RFC 5652, DOI 10.17487/RFC5652, , <https://www.rfc-editor.org/rfc/rfc5652>.
[RFC5754]
Turner, S., "Using SHA2 Algorithms with Cryptographic Message Syntax", RFC 5754, DOI 10.17487/RFC5754, , <https://www.rfc-editor.org/rfc/rfc5754>.
[RFC5958]
Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, , <https://www.rfc-editor.org/rfc/rfc5958>.
[RFC6211]
Schaad, J., "Cryptographic Message Syntax (CMS) Algorithm Identifier Protection Attribute", RFC 6211, DOI 10.17487/RFC6211, , <https://www.rfc-editor.org/rfc/rfc6211>.
[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>.
[RFC8702]
Kampanakis, P. and Q. Dang, "Use of the SHAKE One-Way Hash Functions in the Cryptographic Message Syntax (CMS)", RFC 8702, DOI 10.17487/RFC8702, , <https://www.rfc-editor.org/rfc/rfc8702>.
[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 -- 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

[CMP2018]
Castelnovi, L., Martinelli, A., and T. Prest, "Grafting Trees: A Fault Attack Against the SPHINCS Framework", Post-Quantum Cryptography pp. 165-184, PQCrypto 2018, Lecture Notes in Computer Science vol 10786, , <https://link.springer.com/chapter/10.1007/978-3-319-79063-3_8>.
[Ge2023]
Genêt, A., "On Protecting SPHINCS+ Against Fault Attacks", TCHES 2023/02, DOI 10.46586/tches.v2023.i2.80-114, , <https://tches.iacr.org/index.php/TCHES/article/view/10278/9726>.
[RFC4086]
Eastlake 3rd, D., Schiller, J., and S. Crocker, "Randomness Requirements for Security", BCP 106, RFC 4086, DOI 10.17487/RFC4086, , <https://www.rfc-editor.org/rfc/rfc4086>.
[RFC4108]
Housley, R., "Using Cryptographic Message Syntax (CMS) to Protect Firmware Packages", RFC 4108, DOI 10.17487/RFC4108, , <https://www.rfc-editor.org/rfc/rfc4108>.
[RFC5911]
Hoffman, P. and J. Schaad, "New ASN.1 Modules for Cryptographic Message Syntax (CMS) and S/MIME", RFC 5911, DOI 10.17487/RFC5911, , <https://www.rfc-editor.org/rfc/rfc5911>.
[RFC8391]
Huelsing, A., Butin, D., Gazdag, S., Rijneveld, J., and A. Mohaisen, "XMSS: eXtended Merkle Signature Scheme", RFC 8391, DOI 10.17487/RFC8391, , <https://www.rfc-editor.org/rfc/rfc8391>.
[RFC8554]
McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554, , <https://www.rfc-editor.org/rfc/rfc8554>.
[SLotH]
Saarinen, M.-J., "Accelerating SLH-DSA by Two Orders of Magnitude with a Single Hash Unit", , <https://eprint.iacr.org/2024/367.pdf>.

Appendix A. Appendix: ASN.1 Module

This ASN.1 Module builds upon the conventions established in [RFC5911].

<CODE BEGINS>
SLH-DSA-Module-2024
  { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)
    id-smime(16) id-mod(0) id-mod-slh-dsa-2024(TBD1) }

DEFINITIONS IMPLICIT TAGS ::= BEGIN

EXPORTS ALL;

IMPORTS
  PUBLIC-KEY, SIGNATURE-ALGORITHM, SMIME-CAPS
    FROM AlgorithmInformation-2009  -- in [RFC5911]
    { 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
--

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

sigAlgs OBJECT IDENTIFIER ::= { nistAlgorithms 3 }

id-slh-dsa-sha2-128s OBJECT IDENTIFIER ::= { sigAlgs 20 }

id-slh-dsa-sha2-128f OBJECT IDENTIFIER ::= { sigAlgs 21 }

id-slh-dsa-sha2-192s OBJECT IDENTIFIER ::= { sigAlgs 22 }

id-slh-dsa-sha2-192f OBJECT IDENTIFIER ::= { sigAlgs 23 }

id-slh-dsa-sha2-256s OBJECT IDENTIFIER ::= { sigAlgs 24 }

id-slh-dsa-sha2-256f OBJECT IDENTIFIER ::= { sigAlgs 25 }

id-slh-dsa-shake-128s OBJECT IDENTIFIER ::= { sigAlgs 26 }

id-slh-dsa-shake-128f OBJECT IDENTIFIER ::= { sigAlgs 27 }

id-slh-dsa-shake-192s OBJECT IDENTIFIER ::= { sigAlgs 28 }

id-slh-dsa-shake-192f OBJECT IDENTIFIER ::= { sigAlgs 29 }

id-slh-dsa-shake-256s OBJECT IDENTIFIER ::= { sigAlgs 30 }

id-slh-dsa-shake-256f OBJECT IDENTIFIER ::= { sigAlgs 31 }

--
-- Signature Algorithm, Public Key, and Private Key
--

sa-slh-dsa-sha2-128s SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-sha2-128s
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-sha2-128s }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-sha2-128s } }

sa-slh-dsa-sha2-128f SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-sha2-128f
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-sha2-128f }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-sha2-128f } }

sa-slh-dsa-sha2-192s SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-sha2-192s
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-sha2-192s }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-sha2-192s } }

sa-slh-dsa-sha2-192f SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-sha2-192f
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-sha2-192f }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-sha2-192f } }

sa-slh-dsa-sha2-256s SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-sha2-256s
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-sha2-256s }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-sha2-256s } }

sa-slh-dsa-sha2-256f SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-sha2-256f
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-sha2-256f }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-sha2-256f } }

sa-slh-dsa-shake-128s SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-shake-128s
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-shake-128s }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-shake-128s } }

sa-slh-dsa-shake-128f SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-shake-128f
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-shake-128f }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-shake-128f } }

sa-slh-dsa-shake-192s SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-shake-192s
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-shake-192s }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-shake-192s } }

sa-slh-dsa-shake-192f SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-shake-192f
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-shake-192f }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-shake-192f } }

sa-slh-dsa-shake-256s SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-shake-256s
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-shake-256s }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-shake-256s } }

sa-slh-dsa-shake-256f SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-slh-dsa-shake-256f
    PARAMS ARE absent
    PUBLIC-KEYS { pk-slh-dsa-shake-256f }
    SMIME-CAPS { IDENTIFIED BY id-slh-dsa-shake-256f } }

pk-slh-dsa-sha2-128s PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-sha2-128s
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-sha2-128f PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-sha2-128f
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-sha2-192s PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-sha2-192s
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-sha2-192f PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-sha2-192f
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-sha2-256s PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-sha2-256s
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-sha2-256f PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-sha2-256f
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-shake-128s PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-shake-128s
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-shake-128f PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-shake-128f
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-shake-192s PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-shake-192s
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-shake-192f PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-shake-192f
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-shake-256s PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-shake-256s
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

pk-slh-dsa-shake-256f PUBLIC-KEY ::= {
    IDENTIFIER id-slh-dsa-shake-256f
    -- KEY no ASN.1 wrapping --
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    -- PRIVATE-KEY no ASN.1 wrapping -- }

SLH-DSA-PublicKey ::= OCTET STRING

SLH-DSA-PrivateKey ::= OCTET STRING

--
-- Expand the signature algorithm set used by CMS [RFC5911]
--

SignatureAlgorithmSet SIGNATURE-ALGORITHM ::=
    { sa-slh-dsa-sha2-128s |
      sa-slh-dsa-sha2-128f |
      sa-slh-dsa-sha2-192s |
      sa-slh-dsa-sha2-192f |
      sa-slh-dsa-sha2-256s |
      sa-slh-dsa-sha2-256f |
      sa-slh-dsa-shake-128s |
      sa-slh-dsa-shake-128f |
      sa-slh-dsa-shake-192s |
      sa-slh-dsa-shake-192f |
      sa-slh-dsa-shake-256s |
      sa-slh-dsa-shake-256f,
      ... }

--
-- Expand the S/MIME capabilities set used by CMS [RFC5911]
--

SMimeCaps SMIME-CAPS ::=
    { sa-slh-dsa-sha2-128s.&smimeCaps |
      sa-slh-dsa-sha2-128f.&smimeCaps |
      sa-slh-dsa-sha2-192s.&smimeCaps |
      sa-slh-dsa-sha2-192f.&smimeCaps |
      sa-slh-dsa-sha2-256s.&smimeCaps |
      sa-slh-dsa-sha2-256f.&smimeCaps |
      sa-slh-dsa-shake-128s.&smimeCaps |
      sa-slh-dsa-shake-128f.&smimeCaps |
      sa-slh-dsa-shake-192s.&smimeCaps |
      sa-slh-dsa-shake-192f.&smimeCaps |
      sa-slh-dsa-shake-256s.&smimeCaps |
      sa-slh-dsa-shake-256f.&smimeCaps,
      ... }

END

<CODE ENDS>

Authors' Addresses

Russ Housley
Vigil Security, LLC
Scott Fluhrer
Cisco Systems
Panos Kampanakis
Amazon Web Services
Bas Westerbaan
Cloudflare