Internet-Draft SLH-DSA for X.509 October 2024
Bashiri, et al. Expires 17 April 2025 [Page]
Workgroup:
LAMPS - Limited Additional Mechanisms for PKIX and SMIME
Internet-Draft:
draft-ietf-lamps-x509-slhdsa-02
Published:
Intended Status:
Standards Track
Expires:
Authors:
K. Bashiri
BSI
S. Fluhrer
Cisco Systems
S. Gazdag
genua GmbH
D. Van Geest
CryptoNext Security
S. Kousidis
BSI

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

Abstract

Digital signatures are used within X.509 Public Key Infrastructure such as X.509 certificates, Certificate Revocation Lists (CRLs), and to sign messages. This document describes the conventions for using the Stateless Hash-Based Digital Signature Standard (SLH-DSA) in X.509 Public Key Infrastructure. The conventions for the associated signatures, subject public keys, and private keys are also described.

About This Document

This note is to be removed before publishing as an RFC.

Status information for this document may be found at https://datatracker.ietf.org/doc/draft-ietf-lamps-x509-slhdsa/.

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

Source for this draft and an issue tracker can be found at https://github.com/x509-hbs/draft-x509-slhdsa.

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 17 April 2025.

▲

Table of Contents

1. Introduction

Stateless Hash-Based Digital Signatures (SLH-DSA) is a quantum-resistant digital signature scheme standardized in [FIPS205] by the US National Institute of Standards and Technology (NIST) PQC project [NIST-PQC]. Prior to standardization, the algorithm was known as SPHINCS+. SLH-DSA and SPHINCS+ are not compatible. This document defines the ASN.1 Object Identifiers (OIDs) and conventions for the encoding of SLH-DSA digital signatures, public keys and private keys in the X.509 Public Key Infrastructure.

SLH-DSA offers three security levels. The parameters for each of the security levels were chosen to be at least as secure as a generic block cipher of 128, 192, or 256 bits. There are small (s) and fast (f) versions of the algorithm, and the option to use SHA-256 [FIPS180] or SHAKE256 [FIPS202] as internal hash functions. The fast versions are optimized for key generation and signing speed, they are actually slower at verification than the small parameter sets. For example, id-slh-dsa-shake-256s represents the 256-bit security level, the small version of the algorithm, and the use of SHAKE256.

Separate algorithm identifiers have been assigned for SLH-DSA at each of these security levels, fast vs small, and SHA-256 vs SHAKE256.

SLH-DSA offers two signature modes: pure mode and predigest 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 use in the X.509 Public Key Infrastructure.

2. Conventions and Definitions

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

3. Algorithm Identifiers

The AlgorithmIdentifier type, which is included herein for convenience, is defined as follows:

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

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 AlgorithmIdentifier have the following meanings:

The SLH-DSA OIDs are:

   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 }

The contents of the parameters component for each algorithm are absent.

4. SLH-DSA Signatures

SLH-DSA is a digital signature scheme built upon hash functions. The security of SLH-DSA relies on the presumed difficulty of finding preimages for hash functions as well as several related properties of the same hash functions.

Signatures can be placed in a number of different ASN.1 structures. The top level structure for a certificate is given below as being illustrative of how signatures are frequently encoded with an algorithm identifier and a location for the signature.

   Certificate  ::=  SEQUENCE  {
      tbsCertificate       TBSCertificate,
      signatureAlgorithm   AlgorithmIdentifier,
      signatureValue       BIT STRING }

The same algorithm identifiers are used for signatures as are used for public keys. When used to identify signature algorithms, the parameters MUST be absent.

The data to be signed is prepared for SLH-DSA. Then, a private key operation is performed to generate the raw signature value.

Section 9.2 of [FIPS205] defines an SLH-DSA signature as three elements, R, SIG_FORS and SIG_HT. The raw octet string encoding of an SLH-DSA public key is the concatenation of these three elements, i.e. R || SIG_FORS || SIG_HT. The raw octet string representing the signature is encoded directly in the BIT STRING without adding any additional ASN.1 wrapping. For example, in the Certificate structure, the raw signature value is encoded in the "signatureValue" BIT STRING field.

5. Subject Public Key Fields

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

   SubjectPublicKeyInfo  ::=  SEQUENCE  {
      algorithm         AlgorithmIdentifier,
      subjectPublicKey  BIT STRING }

The fields in SubjectPublicKeyInfo have the following meanings:

[I-D.draft-ietf-lamps-cms-sphincs-plus] defines the following public key identifiers for SLH-DSA:

   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

Section 9.1 of [FIPS205] defines an SLH-DSA public key as two n-byte elements, PK.seed and PK.root. The raw octet string encoding of an SLH-DSA public key is the concatenation of these two elements, i.e. PK.seed || PK.root. The octet string length is 2*n bytes, where n is 16, 24, or 32, depending on the parameter set. When used in a SubjectPublicKeyInfo type, the subjectPublicKey BIT STRING contains the raw octet string encoding of the public key.

[I-D.draft-ietf-lamps-cms-sphincs-plus] defines the SLH-DSA-PublicKey ASN.1 OCTET STRING type to provide an option for encoding a public key in an environment that uses ASN.1 encoding but doesn't define its own mapping of an SLH-DSA raw octet string to ASN.1. To map an SLH-DSA-PublicKey OCTET STRING to a SubjectPublicKeyInfo, the OCTET STRING is mapped to the subjectPublicKey field (a value of type BIT STRING) as follows: the most significant bit of the OCTET STRING value becomes the most significant bit of the BIT STRING value, and so on; the least significant bit of the OCTET STRING becomes the least significant bit of the BIT STRING.

The id-slh-dsa-* identifiers in Section 3 MUST be used as the algorithm field in the SubjectPublicKeyInfo sequence [RFC5280] to identify a SLH-DSA public key.

Appendix C.1 contains an example of an id-slh-dsa-sha2-128s public key encoded using the textual encoding defined in [RFC7468].

6. 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 an id-slh-dsa-* identifier 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 an id-slh-dsa-* identifier 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.

7. Private Key Format

"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 optionally 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 PrivateKeyAlgorithmIdentifier,
      privateKey PrivateKey,
      attributes [0] IMPLICIT Attributes OPTIONAL,
      ...,
      [[2: publicKey [1] IMPLICIT PublicKey OPTIONAL ]],
      ...
   }

   PrivateKey ::= OCTET STRING

   PublicKey ::= BIT STRING

Section 9.1 of [FIPS205] defines an SLH-DSA private key as four n-byte elements, SK.seed, SK.prf, PK.seed and PK.root. The raw octet string encoding of an SLH-DSA private key is the concatenation of these four elements, i.e. SK.seed || SK.prf || PK.seed || PK.root. The octet string length is 4*n bytes, where n is 16, 24, or 32, depending on the parameter set. When used in a OneAsymmetricKey type, the privateKey OCTET STRING contains the raw octet string encoding of the private key.

When an SLH-DSA public key is included in a OneAsymmetricKey type, it is encoded in the same manner as in a SubjectPublicKeyInfo type. That is, the publicKey BIT STRING contains the raw octet string encoding of the public key.

Appendix C.2 contains an example of an id-slh-dsa-sha2-128s private key encoded using the textual encoding defined in [RFC7468].

NOTE: There exist some private key import functions that have not picked up the new ASN.1 structure OneAsymmetricKey that is defined in [RFC5958]. This means that they will not accept a private key structure that contains the public key field. This means a balancing act needs to be done between being able to do a consistency check on the key pair and widest ability to import the key.

8. Security Considerations

The security considerations of [RFC5280] apply accordingly.

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, implementations SHOULD include protections against fault injection attacks [CMP2018],[SLotH]. Protections against these attacks include signature verification prior to releasing the signature value to confirm that no error injected and generating the signature a few times to confirm that the same signature value is produced each time.

9. 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-x509-slh-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).

10. References

10.1. Normative References

[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>.
[I-D.draft-ietf-lamps-cms-sphincs-plus]
Housley, R., Fluhrer, S., Kampanakis, P., and B. Westerbaan, "Use of the SLH-DSA Signature Algorithm in the Cryptographic Message Syntax (CMS)", Work in Progress, Internet-Draft, draft-ietf-lamps-cms-sphincs-plus-09, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-cms-sphincs-plus-09>.
[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>.
[RFC5958]
Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, , <https://www.rfc-editor.org/rfc/rfc5958>.
[RFC8174]
Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, , <https://www.rfc-editor.org/rfc/rfc8174>.

10.2. Informative References

[CMP2018]
Castelnovi, L., A, Martinelli, and T. Prest, "Grafting Trees: A Fault Attack Against the SPHINCS Framework", Lecture Notes in Computer Science vol 10786, PQCrypto 2018, Post-Quantum Cryptography pp. 165-184, , <https://link.springer.com/chapter/10.1007/978-3-319-79063-3_8>.
[FIPS180]
Dang, Q. H. and NIST, "Secure Hash Standard", NIST Federal Information Processing Standards Publications 180-4, DOI 10.6028/NIST.FIPS.180-4, , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf>.
[FIPS202]
Dworkin, M., Dworkin, M. J., and NIST, "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions", FIPS PUB 202, NIST Federal Information Processing Standards Publications 202, DOI 10.6028/nist.fips.202, DOI 10.6028/NIST.FIPS.202, , <http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf>.
[I-D.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-04, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-dilithium-certificates-04>.
[NIST-PQC]
National Institute of Standards and Technology, "Post-Quantum Cryptography Project", , <https://csrc.nist.gov/projects/post-quantum-cryptography>.
[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>.
[RFC5912]
Hoffman, P. and J. Schaad, "New ASN.1 Modules for the Public Key Infrastructure Using X.509 (PKIX)", RFC 5912, DOI 10.17487/RFC5912, , <https://www.rfc-editor.org/rfc/rfc5912>.
[RFC7468]
Josefsson, S. and S. Leonard, "Textual Encodings of PKIX, PKCS, and CMS Structures", RFC 7468, DOI 10.17487/RFC7468, , <https://www.rfc-editor.org/rfc/rfc7468>.
[RFC8410]
Josefsson, S. and J. Schaad, "Algorithm Identifiers for Ed25519, Ed448, X25519, and X448 for Use in the Internet X.509 Public Key Infrastructure", RFC 8410, DOI 10.17487/RFC8410, , <https://www.rfc-editor.org/rfc/rfc8410>.
[RFC8411]
Schaad, J. and R. Andrews, "IANA Registration for the Cryptographic Algorithm Object Identifier Range", RFC 8411, DOI 10.17487/RFC8411, , <https://www.rfc-editor.org/rfc/rfc8411>.
[SLotH]
Saarinen, M-J., "Accelerating SLH-DSA by Two Orders of Magnitude with a Single Hash Unit", , <https://eprint.iacr.org/2024/367.pdf>.
[X680]
ITU-T, "Information Technology - Abstract Syntax Notation One (ASN.1): Specification of basic notation. ITU-T Recommendation X.680 (2021) | ISO/IEC 8824-1:2021.", , <https://www.itu.int/rec/T-REC-X.680>.

Appendix A. ASN.1 Module

RFC EDITOR: Please replace TBD2 with the value assigned by IANA during the publication of [I-D.draft-ietf-lamps-cms-sphincs-plus].

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

DEFINITIONS IMPLICIT TAGS ::= BEGIN

EXPORTS ALL;

IMPORTS
  PUBLIC-KEY, SIGNATURE-ALGORITHM
    FROM AlgorithmInformation-2009  -- in [RFC5912]
    { iso(1) identified-organization(3) dod(6) internet(1)
      security(5) mechanisms(5) pkix(7) id-mod(0)
      id-mod-algorithmInformation-02(58) }

  pk-slh-dsa-sha2-128s, pk-slh-dsa-sha2-128f,
  pk-slh-dsa-sha2-192s, pk-slh-dsa-sha2-192f,
  pk-slh-dsa-sha2-256s, pk-slh-dsa-sha2-256f,
  pk-slh-dsa-shake-128s, pk-slh-dsa-shake-128f,
  pk-slh-dsa-shake-192s, pk-slh-dsa-shake-192f,
  pk-slh-dsa-shake-256s, pk-slh-dsa-shake-256f,
  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
    FROM SLH-DSA-Module-2024  -- in [I-D.draft-ietf-lamps-cms-sphincs-plus]
    { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)
      id-smime(16) id-mod(0) id-mod-slh-dsa-2024(TBD2) } ;

--
-- Expand SignatureAlgorithms from RFC 5912
--
SignatureAlgorithms 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 PublicKeyAlgorithms from RFC 5912
--
PublicKeyAlgorithms PUBLIC-KEY ::= {
   pk-slh-dsa-sha2-128s |
   pk-slh-dsa-sha2-128f |
   pk-slh-dsa-sha2-192s |
   pk-slh-dsa-sha2-192f |
   pk-slh-dsa-sha2-256s |
   pk-slh-dsa-sha2-256f |
   pk-slh-dsa-shake-128s |
   pk-slh-dsa-shake-128f |
   pk-slh-dsa-shake-192s |
   pk-slh-dsa-shake-192f |
   pk-slh-dsa-shake-256s |
   pk-slh-dsa-shake-256f,
   ... }

END
<CODE ENDS>

Appendix B. Security Strengths

Instead of defining the strength of a quantum algorithm in a traditional manner using precise estimates of the number of bits of security, NIST has instead elected to define a collection of broad security strength categories. Each category is defined by a comparatively easy-to-analyze reference primitive that cover a range of security strengths offered by existing NIST standards in symmetric cryptography, which NIST expects to offer significant resistance to quantum cryptanalysis. These categories describe any attack that breaks the relevant security definition that must require computational resources comparable to or greater than those required for: Level 1 - key search on a block cipher with a 128-bit key (e.g., AES128), Level 2 - collision search on a 256-bit hash function (e.g., SHA256/ SHA3-256), Level 3 - key search on a block cipher with a 192-bit key (e.g., AES192), Level 4 - collision search on a 384-bit hash function (e.g. SHA384/SHA3-384), Level 5 - key search on a block cipher with a 256-bit key (e.g., AES 256).

The parameter sets defined for NIST security levels 1, 3 and 5 are listed in Table 1, along with the resulting signature size, public key, and private key sizes in bytes.

Table 1: SLH-DSA security strengths
OID NIST Level Sig. Pub. Key Priv. Key
id-slh-dsa-sha2-128s 1 7856 32 64
id-slh-dsa-sha2-128f 1 17088 32 64
id-slh-dsa-sha2-192s 3 16224 48 96
id-slh-dsa-sha2-192f 3 35664 48 96
id-slh-dsa-sha2-256s 5 29792 64 128
id-slh-dsa-sha2-256f 5 49856 64 128
id-slh-dsa-shake-128s 1 7856 32 64
id-slh-dsa-shake-128f 1 17088 32 64
id-slh-dsa-shake-192s 3 16224 48 96
id-slh-dsa-shake-192f 3 35664 48 96
id-slh-dsa-shake-256s 5 29792 64 128
id-slh-dsa-shake-256f 5 49856 64 128

Appendix C. Examples

This section contains examples of SLH-DSA public keys, private keys and certificates.

C.1. Example Public Key

An example of a SLH-DSA public key using id-slh-dsa-sha2-128s:

-----BEGIN PUBLIC KEY-----
MDAwCwYJYIZIAWUDBAMUAyEAK4EJ7Hd8qk4fAkzPz5SX2ZGAUJKA9CVq8rB6+AKJ
tJQ=
-----END PUBLIC KEY-----

  0  48: SEQUENCE {
  2  11:   SEQUENCE {
  4   9:     OBJECT IDENTIFIER '2 16 840 1 101 3 4 3 20'
       :     }
 15  33:   BIT STRING
       :     2B 81 09 EC 77 7C AA 4E 1F 02 4C CF CF 94 97 D9
       :     91 80 50 92 80 F4 25 6A F2 B0 7A F8 02 89 B4 94
       :   }

C.2. Example Private Key

An example of a SLH-DSA private key without the public key using id-slh-dsa-sha2-128s:

-----BEGIN PRIVATE KEY-----
MFICAQAwCwYJYIZIAWUDBAMUBECiJjvKRYYINlIxYASVI9YhZ3+tkNUetgZ6Mn4N
HmSlASuBCex3fKpOHwJMz8+Ul9mRgFCSgPQlavKwevgCibSU
-----END PRIVATE KEY-----

  0  82: SEQUENCE {
  2   1:   INTEGER 0
  5  11:   SEQUENCE {
  7   9:     OBJECT IDENTIFIER '2 16 840 1 101 3 4 3 20'
       :     }
 18  64:   OCTET STRING
       :     A2 26 3B CA 45 86 08 36 52 31 60 04 95 23 D6 21
       :     67 7F AD 90 D5 1E B6 06 7A 32 7E 0D 1E 64 A5 01
       :     2B 81 09 EC 77 7C AA 4E 1F 02 4C CF CF 94 97 D9
       :     91 80 50 92 80 F4 25 6A F2 B0 7A F8 02 89 B4 94
       :   }

C.3. Example Certificate

An example or a self-signed SLH-DSA certificate using id-slh-dsa-sha2-128s:

Certificate:
    Data:
        Version: 3 (0x2)
        Serial Number:
            70:fb:96:41:c3:74:53:9b:27:cb:07:bc:d2:bb:4a:bc:
            8a:5d:7a:25
        Signature Algorithm: slhdsa_sha2_128s
        Issuer: C=FR, L=Paris, O=Bogus SLH-DSA-SHA2-128s CA
        Validity
            Not Before: Oct  7 12:51:29 2024 GMT
            Not After : Oct  5 12:51:29 2034 GMT
        Subject: C=FR, L=Paris, O=Bogus SLH-DSA-SHA2-128s CA
        Subject Public Key Info:
            Public Key Algorithm: slhdsa_sha2_128s
                slhdsa_sha2_128s public key:
                PQ key material:
                    2b:81:09:ec:77:7c:aa:4e:1f:02:4c:cf:cf:94:97:
                    d9:91:80:50:92:80:f4:25:6a:f2:b0:7a:f8:02:89:
                    b4:94
        X509v3 extensions:
            X509v3 Subject Key Identifier:
                CD:59:36:AA:FE:C4:11:C7:A4:72:69:3F:0B:E8:B3:8B:
                21:7B:19:ED
            X509v3 Authority Key Identifier:
                CD:59:36:AA:FE:C4:11:C7:A4:72:69:3F:0B:E8:B3:8B:
                21:7B:19:ED
            X509v3 Basic Constraints: critical
                CA:TRUE
            X509v3 Key Usage:
                Certificate Sign, CRL Sign
    Signature Algorithm: slhdsa_sha2_128s
    Signature Value:
        11:b2:e9:ee:da:b9:9b:da:da:db:eb:28:2f:9a:2d:31:e2:78:
        40:14:20:f6:67:ec:ca:3e:fa:db:c3:b9:ab:9e:fd:d1:b8:77:
        29:47:1b:40:c0:73:68:7e:89:de:ac:d8:9f:43:71:58:3f:3d:
        da:28:58:57:6d:e0:99:28:ae:30:e9:17:a7:20:c8:11:e1:fa:
        f6:d0:21:ef:01:60:79:93:ac:b4:94:63:97:af:71:14:4c:c5:
        cf:77:40:df:60:f5:8f:20:95:a4:c1:35:02:43:14:b8:1c:4a:
        01:1e:bd:17:01:b7:36:12:80:ab:29:58:98:bf:da:1d:52:8a:
        be:de:67:af:26:6f:61:46:cd:95:a4:de:4e:66:92:27:1a:e0:
        23:9f:66:18:d6:27:30:9f:d7:fe:b3:bb:28:3e:94:4a:88:20:
        93:18:07:cb:ce:1d:6b:10:f9:bc:b5:e8:c1:32:2a:1d:52:e0:
        39:ba:d5:e4:d6:01:a1:de:6f:11:90:5d:40:bb:73:fe:d9:7c:
        2c:ea:c7:05:85:d1:34:47:83:af:d8:43:37:94:ce:8d:89:ac:
        fc:0f:8c:2f:47:1d:ff:be:bd:7a:c5:e9:76:fc:9d:fc:95:19:
        45:a3:7d:80:1f:1d:c8:52:e6:05:4b:ed:f6:57:5e:82:92:78:
        dd:5d:bd:86:48:12:5f:ad:09:85:9e:16:aa:cc:23:9f:3f:60:
        b9:a6:e1:f1:76:41:2c:89:08:e4:b6:96:eb:20:93:bd:83:21:
        96:a4:55:fb:74:a9:11:2f:97:ec:76:02:4e:97:5c:d8:27:26:
        ee:78:03:1e:df:4b:ed:a6:d4:f9:70:6c:cb:04:29:50:3f:6c:
        a9:32:3e:08:55:89:71:e3:4e:dd:e3:cd:30:a0:5d:29:ff:40:
        d3:92:09:22:56:e2:31:fc:22:39:5b:46:c2:11:ed:93:04:1c:
        65:08:2d:4b:2f:ad:30:ef:ac:f9:b8:c1:a3:9f:5d:8c:c0:20:
        38:16:8c:43:75:ee:52:3b:20:a3:ec:8d:ea:90:5f:cd:77:86:
        42:fb:69:fe:a1:01:c4:4e:3b:55:b8:79:b4:36:1b:f4:be:a7:
        51:0f:ce:53:83:be:3a:68:0e:61:58:1b:18:cc:8b:e5:85:b5:
        3c:89:42:82:31:d4:00:d3:bd:b0:3e:9b:47:23:6a:b0:50:e9:
        37:66:17:d2:82:08:6d:26:07:e7:8a:a0:6e:07:62:4e:61:f9:
        a8:37:ce:91:9a:c9:a1:44:ee:73:a4:a1:b7:ae:6c:19:1d:d7:
        45:a2:15:4a:6f:83:25:c6:9c:0a:d8:78:24:ce:26:80:8d:b5:
        a5:71:09:ba:40:17:7b:43:be:53:84:2f:0f:1e:49:7a:a9:82:
        73:73:55:52:22:83:72:2b:87:5d:31:f3:ef:39:58:18:12:6a:
        8b:30:65:d9:24:85:7d:db:3e:95:9e:99:4a:88:75:bd:21:19:
        e3:bc:2f:a9:cb:75:3c:19:f9:69:c7:88:f8:34:c0:f4:4d:1e:
        1b:40:70:98:7a:d9:04:d8:b1:06:d1:18:21:5e:bb:d0:fc:18:
        e0:c8:85:5b:89:09:19:ad:9d:ee:d8:32:d5:94:ab:93:30:7f:
        52:b3:fc:9e:20:69:48:33:a5:55:7f:f5:d7:77:b0:e6:9f:44:
        09:9c:d4:d8:9a:39:e6:84:fd:77:8e:21:b8:f6:cb:da:a2:af:
        5d:45:0b:97:50:bb:0c:41:09:a3:3b:c6:dd:b5:db:a1:56:df:
        f6:e4:1e:a4:05:ff:30:cb:8b:c8:45:9a:c1:70:9d:25:b2:7c:
        25:36:4e:72:04:2c:0e:07:0c:19:5f:f5:e4:7b:32:3b:6f:87:
        8c:c2:7a:f4:b3:74:f4:63:10:13:1e:ca:a5:bd:4a:99:ca:ca:
        3a:68:c6:d2:7d:1c:86:8c:13:af:23:12:cd:94:91:91:f3:6f:
        5e:85:a3:00:4d:a0:6b:c8:b3:49:51:ef:27:b5:9b:3e:4e:9b:
        9f:98:8a:e1:d6:b0:f1:13:15:90:c7:29:af:9a:9c:ad:d9:0e:
        cb:a0:de:8d:3d:bd:49:27:40:a0:86:3e:be:33:d4:fa:6d:c4:
        22:6b:2d:93:aa:89:70:1a:c0:f7:cd:ed:f5:80:9d:6d:f2:11:
        9b:ce:14:c9:07:40:d5:ec:d2:d9:54:57:d7:31:ef:89:e4:21:
        ca:f6:b9:66:99:8d:d9:96:3b:80:39:c8:4a:e7:10:dd:d4:b6:
        73:85:55:18:6d:98:16:62:b8:3a:57:24:7b:d9:fb:9b:e4:3d:
        39:4e:6c:cf:30:a1:c4:4a:67:d1:e2:c7:84:bf:68:85:c8:08:
        86:ce:b1:e7:f5:2e:58:6d:81:00:09:43:dd:0d:c2:99:6e:e5:
        ec:1e:c5:be:1b:43:3c:15:b4:69:7c:b7:36:75:ec:d2:b0:f2:
        67:8c:0f:a2:c1:f1:04:61:09:3a:d7:04:38:90:99:5b:d2:fc:
        1a:66:89:16:6d:01:93:76:81:38:a0:88:a5:2c:e7:eb:f6:e6:
        6a:ee:bf:6a:a1:c2:d1:cf:58:9a:00:54:ed:88:a3:fb:94:70:
        8b:f4:93:29:d8:d6:82:96:52:cd:aa:49:19:28:04:4b:85:a9:
        11:96:01:83:4d:5b:b0:16:25:7f:ba:c6:f4:e0:33:58:78:36:
        d8:9f:10:26:98:6f:d8:1f:03:5e:16:01:8b:32:6f:22:88:6c:
        16:88:c4:62:aa:23:1f:88:68:65:2c:89:21:28:72:17:6b:49:
        22:39:51:81:99:76:f8:1f:e3:09:66:90:a0:7b:57:57:bf:e2:
        c1:e2:92:b0:ea:e1:35:55:a8:d4:0f:69:d7:9d:4a:7d:25:fd:
        0e:92:bb:27:b1:fd:2f:55:21:6e:1d:ca:6b:37:51:d1:3f:56:
        3b:d8:7d:3e:4c:5b:4b:59:9a:db:1b:75:29:ca:8f:22:fa:b7:
        b7:72:dc:47:4c:9f:d4:bb:fb:dc:a5:ef:d4:08:54:95:85:7a:
        8a:9a:03:b0:cf:6b:7a:a5:50:78:f8:87:59:38:b4:24:c9:e1:
        2c:16:b6:82:b4:5b:73:6f:78:e3:0a:ec:5e:9b:b1:74:87:74:
        80:8f:ea:c8:eb:f8:ec:ad:20:96:a4:ff:44:3a:7a:e1:ba:b6:
        ba:d7:b5:0c:34:89:e1:84:83:2c:1c:b8:4f:2b:62:ec:da:68:
        4b:3a:23:97:0e:6f:50:3d:4c:e1:1a:54:67:5a:6c:97:65:bd:
        3c:19:db:e8:15:fd:19:13:33:c4:e1:59:3c:62:e4:19:09:b5:
        0a:d4:72:2b:60:2b:e3:be:5f:51:d9:b7:c1:56:b2:05:de:0e:
        26:ec:fc:a6:bc:8e:34:82:5f:8b:9f:5c:4e:e0:0f:10:40:64:
        f0:8d:9c:69:20:3b:da:38:07:df:01:41:4f:50:c1:27:6b:cb:
        7a:3b:4c:25:18:b6:d4:fd:ca:ee:47:d1:14:25:d4:d7:e1:3f:
        1a:62:78:74:1e:82:83:84:d2:6c:dd:fb:4c:11:6f:17:1f:35:
        d8:33:df:89:31:63:b4:c9:33:37:0a:ba:d6:f4:9b:2d:95:ed:
        ed:f1:b8:c4:bc:e4:e3:7b:73:6d:02:05:f4:27:69:42:f9:f1:
        11:24:a0:21:fa:14:01:15:94:ea:3a:cb:f8:d8:bc:84:2e:54:
        13:84:59:ac:6b:4b:c4:02:02:a3:c2:cb:a5:f0:4b:c8:05:2a:
        fd:84:5a:dd:b7:d6:30:9a:3f:c2:a3:71:87:d8:f1:68:c0:d9:
        08:05:91:a0:cb:f2:81:af:b8:b5:be:88:07:a6:80:3a:6b:a5:
        9b:27:55:31:1f:33:cd:93:d8:c3:49:2d:f9:92:57:64:f0:a5:
        79:06:5b:48:a6:97:e0:b5:d4:6f:0c:27:84:b1:34:e6:a9:9c:
        2f:8e:9b:95:8b:ed:94:14:61:84:54:fc:09:b0:8e:62:9c:49:
        00:20:e2:55:bb:9e:53:0a:27:ff:47:59:ea:36:52:d5:fd:80:
        fd:a6:9d:1c:67:ac:53:18:4c:37:fa:4e:88:18:b5:24:f7:36:
        78:7b:c0:0c:b5:3d:65:f1:86:34:70:38:bf:19:b4:23:ab:72:
        bd:20:77:8a:58:4b:46:a6:3f:62:08:47:e5:58:57:d1:c2:0b:
        00:eb:5e:89:17:48:5e:a6:ec:c4:00:42:9d:42:6e:72:d7:2d:
        51:c9:0c:5f:a9:f6:80:a7:80:f1:1d:63:2e:8d:cf:29:12:bd:
        9b:c6:3f:f5:bf:34:f2:45:2a:cc:23:20:30:f9:a2:bc:d7:d0:
        b4:f5:1f:8e:ca:9c:9b:0c:58:00:f2:b7:a7:90:5c:72:e3:d5:
        20:fa:38:cc:e9:90:7e:09:57:51:48:0f:ab:ca:9c:b8:ca:d4:
        6b:0d:2f:0d:00:29:6b:5e:4a:e2:4f:c9:f4:98:fa:97:9e:6e:
        da:09:0d:00:ba:3b:97:79:b0:d6:6f:f7:66:87:75:c3:ca:df:
        ad:78:41:e6:51:fb:90:05:2e:aa:72:ed:e6:8d:69:c7:19:81:
        84:8a:65:f3:20:dc:97:f3:bd:a5:5f:d8:51:89:01:81:78:42:
        e5:38:ed:92:8e:d0:f3:5b:ff:cb:29:70:02:ec:d0:e1:cb:7e:
        9f:b5:7b:aa:6f:2d:1c:2a:cf:8e:69:7a:b2:b3:b4:0f:cb:1b:
        3b:3a:5f:c9:44:7b:06:cd:40:40:c0:b3:a5:b2:1d:97:43:90:
        14:c6:96:6c:c6:25:b7:fb:78:2b:fe:b7:db:1b:cb:9f:59:77:
        8e:0f:4f:d3:6d:37:56:11:01:b6:73:ec:a3:d1:27:12:13:0f:
        29:1e:74:c0:88:92:9a:62:65:e1:c2:bd:ea:79:04:d6:ef:71:
        41:43:99:c3:32:2a:f1:69:9f:53:10:5a:bf:93:8b:b9:91:75:
        b6:f9:cb:70:9a:02:87:c0:a8:2c:18:54:d4:b4:96:82:00:d0:
        b2:5b:89:1b:42:02:8a:56:35:7c:0a:40:02:7e:71:e8:3e:c9:
        75:55:c0:3e:18:e4:2d:40:ec:6b:93:c5:56:77:00:d5:c6:4b:
        f9:d7:95:9b:f0:96:67:5b:8d:25:23:64:0c:41:e3:68:3d:9a:
        11:5a:fa:7c:bc:62:30:ce:c3:52:c3:7c:6b:94:51:b6:b9:46:
        e8:1c:df:25:a5:e2:f7:3f:5d:5a:f5:a7:1d:25:24:5a:89:3c:
        83:38:57:7e:aa:62:2f:fb:69:0f:7b:a5:05:57:59:37:63:26:
        60:ed:b6:c4:35:fb:65:9b:1a:31:ff:f7:a3:69:2a:eb:bf:71:
        ef:b7:be:92:39:58:0f:9a:7f:b2:45:81:87:fd:e0:d4:80:e0:
        fb:67:ea:ad:9f:72:1a:d6:72:29:0b:67:f4:cf:be:f6:d2:a3:
        9d:c4:8a:df:c1:49:d2:7c:c7:e5:bc:a8:dc:35:6a:8b:bf:e1:
        8f:8a:03:88:8d:b2:8f:68:82:02:05:5a:71:32:c7:45:4c:d5:
        01:42:c6:1a:25:6d:66:22:33:a9:1a:cb:d9:c0:67:ac:7b:10:
        3c:7c:2b:db:25:26:c2:03:4f:cb:0b:10:47:96:66:8d:cd:5c:
        64:30:ba:65:51:5e:39:d3:7a:c8:60:8c:08:b2:26:1c:65:44:
        51:2a:cd:0a:49:59:c3:0e:de:8f:a0:49:d2:23:aa:2e:5f:9b:
        00:fa:ac:10:d5:bd:1b:ae:2f:d6:cd:e6:7b:27:f9:d4:47:32:
        c4:b9:dc:fd:85:e1:af:87:36:68:37:ad:f3:13:f1:b5:3d:a7:
        b5:5c:32:34:31:b4:84:83:76:1f:89:9c:10:99:8d:ec:c8:77:
        ec:ab:ab:fd:fd:3f:46:10:a7:8c:e8:2d:02:a4:e2:2a:ed:47:
        4f:ff:86:be:17:76:5e:d7:e6:f0:98:30:37:8e:87:f6:e4:40:
        d8:6e:3b:b6:20:13:b4:87:15:bf:63:25:f7:94:f9:bd:85:f9:
        8b:43:47:d8:70:da:86:d8:2e:ff:9b:1f:ec:c9:f2:79:55:33:
        71:47:1e:0d:00:39:09:aa:e3:d7:3d:53:cb:05:b4:86:11:1c:
        e4:f3:e9:f5:6d:3f:bb:7e:78:50:6e:e9:fc:79:39:94:45:24:
        f0:5f:4c:5c:e9:12:2e:8e:b9:32:05:b4:2f:6e:73:cb:86:71:
        c9:60:39:9f:4f:0b:8f:d0:95:8b:6a:46:d4:15:28:ac:8b:51:
        73:f3:6d:7e:23:ae:89:1e:9f:1b:9e:1d:cf:0a:14:1a:64:39:
        16:b3:66:84:fd:10:65:33:9d:1e:4d:c9:e6:7c:f9:fe:5f:29:
        57:58:73:e4:30:53:af:39:fa:63:71:1a:33:e0:d4:ce:fb:3a:
        14:56:1d:9a:87:49:a0:02:41:c4:80:5f:06:0e:68:45:4d:1c:
        ca:35:4e:22:dd:e0:16:3d:a5:ef:e6:52:0c:32:7a:6a:f4:36:
        60:5e:78:39:61:f8:1e:34:e3:9f:ef:a1:44:6e:8d:80:fb:56:
        05:e5:17:13:54:a7:25:be:78:5b:35:55:42:d7:be:5d:d9:22:
        d9:ec:fc:01:9d:4e:47:e7:34:fc:51:ce:41:b8:be:d2:af:c6:
        17:c6:49:40:9c:f5:b5:6d:39:d0:a0:f9:7d:1d:39:eb:ea:26:
        79:3f:aa:96:8e:45:cf:68:e5:b4:30:0e:82:d7:2c:46:5b:6c:
        1f:a4:37:dc:04:d6:f6:10:9a:5e:27:a6:d3:b6:9a:7a:d3:e0:
        44:f1:59:96:36:f1:35:6f:60:62:78:5c:27:93:80:7e:14:16:
        32:d2:99:0b:fa:b3:eb:79:bc:0e:06:7e:06:26:46:8d:03:6a:
        f7:e0:86:d2:a9:3d:af:3c:90:ad:1e:b1:e8:90:4f:e0:32:47:
        59:a6:15:8e:f5:c6:98:45:fe:a0:87:e4:0d:d8:dc:ae:51:18:
        a7:6d:7a:f7:b0:51:b9:e0:9f:4a:91:d4:98:b3:88:a4:68:d9:
        6b:8c:09:f4:90:2d:f0:bc:c0:4a:79:13:73:b1:6e:ef:bb:0e:
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-----END CERTIFICATE-----

Acknowledgments

Much of the structure and text of this document is based on [RFC8410] and [I-D.ietf-lamps-dilithium-certificates]. The remainder comes from [I-D.draft-ietf-lamps-cms-sphincs-plus]. Thanks to those authors, and the ones they based their work on, for making our work earier. "Copying always makes things easier and less error prone" - [RFC8411].

Authors' Addresses

Kaveh Bashiri
BSI
Scott Fluhrer
Cisco Systems
Stefan-Lukas Gazdag
genua GmbH
Daniel Van Geest
CryptoNext Security
Stavros Kousidis
BSI