



LAMPS - Limited Additional Mechanisms for PKIX and SMIME      K. Bashiri
Internet-Draft                                                       BSI
Intended status: Standards Track                              S. Fluhrer
Expires: 1 January 2026                                    Cisco Systems
                                                               S. Gazdag
                                                              genua GmbH
                                                            D. Van Geest
                                                     CryptoNext Security
                                                             S. Kousidis
                                                                     BSI
                                                            30 June 2025


Internet X.509 Public Key Infrastructure: Algorithm Identifiers for SLH-
                                  DSA
                    draft-ietf-lamps-x509-slhdsa-09

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 specifies the conventions for using
   the Stateless Hash-Based Digital Signature Algorithm (SLH-DSA) in
   X.509 Public Key Infrastructure.  The conventions for the associated
   signatures, subject public keys, and private keys are also specified.

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.






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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .   4
   2.  Conventions and Definitions . . . . . . . . . . . . . . . . .   4
   3.  Algorithm Identifiers . . . . . . . . . . . . . . . . . . . .   4
   4.  SLH-DSA Signatures  . . . . . . . . . . . . . . . . . . . . .   7
   5.  Subject Public Key Fields . . . . . . . . . . . . . . . . . .   8
   6.  Key Usage Bits  . . . . . . . . . . . . . . . . . . . . . . .  13
   7.  Private Key Format  . . . . . . . . . . . . . . . . . . . . .  14
   8.  Operational Considerations  . . . . . . . . . . . . . . . . .  15
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  16
   10. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  17
   11. References  . . . . . . . . . . . . . . . . . . . . . . . . .  17
     11.1.  Normative References . . . . . . . . . . . . . . . . . .  17
     11.2.  Informative References . . . . . . . . . . . . . . . . .  18
   Appendix A.  ASN.1 Module . . . . . . . . . . . . . . . . . . . .  19
   Appendix B.  Security Strengths . . . . . . . . . . . . . . . . .  27
   Appendix C.  Examples . . . . . . . . . . . . . . . . . . . . . .  28
     C.1.  Example Public Key  . . . . . . . . . . . . . . . . . . .  28
     C.2.  Example Private Key . . . . . . . . . . . . . . . . . . .  29
     C.3.  Example Certificate . . . . . . . . . . . . . . . . . . .  29



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   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  43
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  43

1.  Introduction

   The Stateless Hash-Based Digital Signature Algorithm (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 the SHA2
   algorithm family [FIPS180] or SHAKE256 [FIPS202] as internal
   functions.  While the fast versions are optimized for key generation
   and signing speed, they are actually slower at verification than the
   SLH-DSA small parameter sets.  The small versions are optimized for
   signature size, see Table 1.  As an example, id-slh-dsa-shake-256s
   represents the 256-bit security level, the small version of the
   algorithm, and the use of SHAKE256.

   NIST [CSOR] has assigned separate algorithm identifiers for SLH-DSA
   for each combination of these security levels, fast vs small, SHA2 vs
   SHAKE256, and pure mode vs pre-hash mode.

   SLH-DSA signature operations include as input an optional context
   string (ctx), defined in Section 10.2 of [FIPS205].  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
   the empty context string for use in the X.509 Public Key
   Infrastructure.

   SLH-DSA offers two signature modes: pure mode, where the entire
   content is signed directly, and pre-hash mode, where a digest of the
   content is signed.  This document uses the term SLH-DSA to refer to
   the algorithm in general.  When a pure or pre-hash mode needs to be
   differentiated, the terms Pure SLH-DSA and HashSLH-DSA are used.
   This document specifies the use of both Pure SLH-DSA and HashSLH-DSA
   in Public Key Infrastructure X.509 (PKIX) certificates and
   Certificate Revocation Lists (CRLs).






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1.1.  Notation

   The following notation is used in this document:

   *  a || b: concatenation of a and b

   *  id-slh-dsa-*: A shorthand to refer to all 12 OIDs used to specify
      the different parameter combinations for Pure SLH-DSA.

   *  id-hash-slh-dsa-*: A shorthand to refer to all 12 OIDs used to
      specify the different parameter combinations for HashSLH-DSA.

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 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.

   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 object identifiers for SLH-DSA are defined in the NIST Computer
   Security Objects Register [CSOR], and are reproduced here for
   convenience.  The same algorithm identifiers are used for identifying
   a public key, a private key, and a signature.




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   The Pure SLH-DSA OIDs are defined in
   [I-D.ietf-lamps-cms-sphincs-plus]'s ASN.1 module and reproduced here
   for convenience:

      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 HashSLH-DSA OIDs are:

















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      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-hash-slh-dsa-sha2-128s-with-sha256 OBJECT IDENTIFIER ::= {
         sigAlgs 35 }

      id-hash-slh-dsa-sha2-128f-with-sha256 OBJECT IDENTIFIER ::= {
         sigAlgs 36 }

      id-hash-slh-dsa-sha2-192s-with-sha512 OBJECT IDENTIFIER ::= {
         sigAlgs 37 }

      id-hash-slh-dsa-sha2-192f-with-sha512 OBJECT IDENTIFIER ::= {
         sigAlgs 38 }

      id-hash-slh-dsa-sha2-256s-with-sha512 OBJECT IDENTIFIER ::= {
         sigAlgs 39 }

      id-hash-slh-dsa-sha2-256f-with-sha512 OBJECT IDENTIFIER ::= {
         sigAlgs 40 }

      id-hash-slh-dsa-shake-128s-with-shake128 OBJECT IDENTIFIER ::= {
         sigAlgs 41 }

      id-hash-slh-dsa-shake-128f-with-shake128 OBJECT IDENTIFIER ::= {
         sigAlgs 42 }

      id-hash-slh-dsa-shake-192s-with-shake256 OBJECT IDENTIFIER ::= {
         sigAlgs 43 }

      id-hash-slh-dsa-shake-192f-with-shake256 OBJECT IDENTIFIER ::= {
         sigAlgs 44 }

      id-hash-slh-dsa-shake-256s-with-shake256 OBJECT IDENTIFIER ::= {
         sigAlgs 45 }

      id-hash-slh-dsa-shake-256f-with-shake256 OBJECT IDENTIFIER ::= {
         sigAlgs 46 }

   The contents of the parameters component for each algorithm MUST be
   absent.








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4.  SLH-DSA Signatures

   SLH-DSA is a digital signature scheme built upon hash functions.  The
   security of SLH-DSA relies on the security properties of the
   underlying hash functions, such as the presumed difficulty of finding
   preimages.

   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  ::=  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}))
     }

      |  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 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.

   When signing data using the Pure SLH-DSA signature algorithm,
   Algorithm 22 (slh_sign) from Section 10.2.1 of [FIPS205] is used.
   When verifying Pure SLH-DSA signed data, Algorithm 24 (slh_verify)
   from Section 10.3 of [FIPS205] is used.  When signing data using the
   HashSLH-DSA signature algorithm, Algorithm 23 (hash_slh_sign) from
   Section 10.2.2 of [FIPS205] is used.  When verifying HashSLH-DSA
   signed data, Algorithm 25 (hash_slh_verify) from Section 10.3 of
   [FIPS205] is used.  All four of these algorithms create a message,



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   M', from the message to be signed along with other data, and M' is
   operated on by internal SLH-DSA algorithms.  M' may be constructed
   outside the module that performs the internal SLH-DSA algorithms.

   In the case of HashSLH-DSA, there is a pre-hash component (PH_M) of
   M'.  PH_M may be computed in the signing/verifying module, in which
   case the entire message to be signed is sent to the module.
   Alternatively, PH_M may be computed in a different module.  In this
   case, either PH_M is sent to the signing/verifying module, which
   creates M', or M' is created outside the signing/verifying module and
   is sent to the module.  HashSLH-DSA allows this implementation
   flexibility in order to reduce, and make consistent, the amount of
   data transferred to signing/verifying modules.  The hash algorithm or
   XOF used to generate the pre-hash when signing and verifying with
   HashSLH-DSA is specified after the "-with-" component of the
   signature algorithm name.  For example, when signing with id-hash-
   slh-dsa-sha2-128s-with-sha256, SHA-256 is used as the pre-hash
   algorithm.  When pre-hashing is performed using SHAKE128, the output
   length is 256 bits.  When pre-hashing is performed using SHAKE256,
   the output length is 512 bits.

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

      |  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 meanings:

   *  algorithm is the algorithm identifier and parameters for the
      public key (see above).




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   *  subjectPublicKey contains the byte stream of the public key.

   [I-D.ietf-lamps-cms-sphincs-plus] defines the following public key
   identifiers for Pure 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 ::= {



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         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

   The public key identifiers for HashSLH-DSA are defined here:





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      pk-hash-slh-dsa-sha2-128s-with-sha256 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-sha2-128s-with-sha256
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-sha2-128f-with-sha256 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-sha2-128f-with-sha256
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-sha2-192s-with-sha512 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-sha2-192s-with-sha512
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-sha2-192f-with-sha512 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-sha2-192f-with-sha512
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-sha2-256s-with-sha512 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-sha2-256s-with-sha512
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-sha2-256f-with-sha512 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-sha2-256f-with-sha512
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-shake-128s-with-shake128 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-shake-128s-with-shake128
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }



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      pk-hash-slh-dsa-shake-128f-with-shake128 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-shake-128f-with-shake128
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-shake-192s-with-shake256 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-shake-192s-with-shake256
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-shake-192f-with-shake256 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-shake-192f-with-shake256
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-shake-256s-with-shake256 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-shake-256s-with-shake256
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

      pk-hash-slh-dsa-shake-256f-with-shake256 PUBLIC-KEY ::= {
         IDENTIFIER id-hash-slh-dsa-shake-256f-with-shake256
         -- KEY no ASN.1 wrapping --
         CERT-KEY-USAGE
            { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
         -- PRIVATE-KEY no ASN.1 wrapping -- }

   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 SLH-DSA parameter set.  When used in
   a SubjectPublicKeyInfo type, the subjectPublicKey BIT STRING contains
   the raw octet string encoding of the public key.

   [I-D.ietf-lamps-cms-sphincs-plus] defines the SLH-DSA-PublicKey and
   SLH-DSA-PrivateKey ASN.1 OCTET STRING types to provide an option for
   encoding a Pure SLH-DSA public or private 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.  HashSLH-DSA public and private keys can



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   use SLH-DSA-PublicKey and SLH-DSA-PrivateKey in the same way.  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 AlgorithmIdentifier for an SLH-DSA public key MUST use one of the
   id-slh-dsa-* or id-hash-slh-dsa-* object identifiers from Section 3.
   The parameters field of the AlgorithmIdentifier for the SLH-DSA
   public key MUST be absent.

   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-* (Pure SLH-DSA) or id-hash-slh-dsa-* (HashSLH-DSA)
   identifier in the SubjectPublicKeyInfo, then at least one of the
   following MUST be present:

       digitalSignature
       nonRepudiation
       keyCertSign
       cRLSign

   If the keyUsage extension is present in a certificate that indicates
   an id-slh-dsa-* (Pure SLH-DSA) or id-hash-slh-dsa-* (HashSLH-DSA)
   identifier in the SubjectPublicKeyInfo, then the following MUST NOT
   be present:

       keyEncipherment,
       dataEncipherment,
       keyAgreement,
       encipherOnly, and
       decipherOnly.

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








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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

      |  The above syntax is from [RFC5958] and is compatible with the
      |  2021 ASN.1 syntax [X680].

   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 SLH-DSA 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.



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8.  Operational Considerations

   SLH-DSA uses the same OID to identify a public key and a signature
   algorithm.  The implication of this is that, despite being
   mathematically possible, an SLH-DSA key identified by a Pure SLH-DSA
   OID is not permitted to be used to generate or verify a signature
   identified by an HashSLH-DSA OID, and vice-versa.

   CA operators will need to decide in advance whether their CA
   certificates will use Pure SLH-DSA or HashSLH-DSA and assign the
   appropriate OID to the public and private keys when generating their
   certificate.  Some of the following considerations may affect this
   decision.

   *  When using an external signing module, such as an HSM, the size of
      data that can be transferred to and processed by the signature
      module may be limited.  SLH-DSA performs two passes on the
      internal M' message, so it must be held in memory.  Using HashSLH-
      DSA reduces the size of M'.

   *  Large CRLs might also exceed the size limits of HSM signing
      operations when using Pure SLH-DSA.  One way to limit the size of
      CRLs is to make use of CRL Distribution Points and Issuing
      Distribution Points to create partitioned CRLs in accordance with
      Section 5.2.5 of [RFC5280].

   *  EE certificates with many SANs might also exceed the size limits
      of HSM signing operations.

   *  Potential verifiers' environments might need to be considered.
      The entire certificate or CRL needs to be held in memory during
      SLH-DSA signature verification, it cannot be streamed.  In
      particular, there is a randomizer (R) which is extracted from the
      SLH-DSA signature and fed to a digest function before M' is.
      Thus, to stream a message for SLH-DSA verification the signature
      must come before the message.  This is not the case for
      certificates and CRLs.  Using HashSLH-DSA reduces the size of the
      M' being held in memory.

   An SLH-DSA private key has a very large (2^64) number of signatures
   it can safely generate (see Section 9).  If an operator might
   conceivably generate a number of signatures approaching this limit,
   they should mitigate potential harm by tracking the number of
   signatures generated and destroying the private key once an
   appropriate limit is reached, or by setting the "Not After"
   (expiration) date of the certificate such that the the limit couldn't
   possibly be surpassed given the rate of signing.




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9.  Security Considerations

   The security considerations of [RFC5280] apply accordingly.
   Moreover, the security aspects mentioned throughout [FIPS205] should
   be taken into account; see for instance Sections 3.1 and 3.2 or the
   beginning of Section 11.

   The security of SLH-DSA relies on the security properties of the
   internal hash and XOF functions.  In particular, it relies on these
   functions being preimage resistant, but it does not rely on them
   being collision resistant.  Since HashSLH-DSA performs a pre-hash
   before signing, it relies on both preimage resistance and collision
   resistance of the pre-hash function.  In order to achieve an
   appropriate level of collision resistance, the output length of the
   pre-hash functions used for HashSLH-DSA is twice the length of the
   internal hash and XOF functions.

   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.

   An 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; see Section 3.1 of [FIPS205] for some
   additional information.

   Fault attacks can lead to forgeries of message signatures [CMP2018]
   and [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 can be used as an
   effective fault attack countermeasure for SLH-DSA [Ge2023]; however,
   the SLH-DSA signature generation is already considered slow.

   Likewise, passive power and emissions side-channel attacks can leak
   the SLH-DSA private signing key, and countermeasures can be taken
   against these attacks [SLotH].




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10.  IANA Considerations

   For the ASN.1 Module in Appendix A 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).

11.  References

11.1.  Normative References

   [CSOR]     NIST, "Computer Security Objects Register", 20 August
              2024, <https://csrc.nist.gov/projects/computer-security-
              objects-register/algorithm-registration>.

   [FIPS205]  National Institute of Standards and Technology (NIST),
              "Stateless Hash-Based Digital Signature Standard", FIPS
              PUB 205, 13 August 2024,
              <https://doi.org/10.6028/NIST.FIPS.205>.

   [I-D.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-19, 13
              January 2025, <https://datatracker.ietf.org/doc/html/
              draft-ietf-lamps-cms-sphincs-plus-19>.

   [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>.

   [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>.

   [RFC5958]  Turner, S., "Asymmetric Key Packages", RFC 5958,
              DOI 10.17487/RFC5958, August 2010,
              <https://www.rfc-editor.org/rfc/rfc5958>.



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   [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>.

11.2.  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,
              2018, <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, July 2015,
              <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, August 2015,
              <http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf>.

   [Ge2023]   Genêt, A., "On Protecting SPHINCS+ Against Fault Attacks",
              TCHES 2023/02, n.d.,
              <https://doi.org/10.46586/tches.v2023.i2.80-114>.










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   [I-D.ietf-lamps-dilithium-certificates]
              Massimo, J., Kampanakis, P., Turner, S., and B.
              Westerbaan, "Internet X.509 Public Key Infrastructure -
              Algorithm Identifiers for the Module-Lattice-Based Digital
              Signature Algorithm (ML-DSA)", Work in Progress, Internet-
              Draft, draft-ietf-lamps-dilithium-certificates-12, 26 June
              2025, <https://datatracker.ietf.org/doc/html/draft-ietf-
              lamps-dilithium-certificates-12>.

   [NIST-PQC] National Institute of Standards and Technology, "Post-
              Quantum Cryptography Project", 20 December 2016,
              <https://csrc.nist.gov/projects/post-quantum-
              cryptography>.

   [RFC7468]  Josefsson, S. and S. Leonard, "Textual Encodings of PKIX,
              PKCS, and CMS Structures", RFC 7468, DOI 10.17487/RFC7468,
              April 2015, <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, August 2018,
              <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, August 2018,
              <https://www.rfc-editor.org/rfc/rfc8411>.

   [SLotH]    Saarinen, M-J., "Accelerating SLH-DSA by Two Orders of
              Magnitude with a Single Hash Unit", 2024,
              <https://eprint.iacr.org/2024/367.pdf>.

Appendix A.  ASN.1 Module

   This appendix includes the ASN.1 module [X680] for SLH-DSA.  Note
   that as per [RFC5280], certificates use the Distinguished Encoding
   Rules; see [X690].  This module imports objects from [RFC5912] and
   [I-D.ietf-lamps-cms-sphincs-plus].

      |  RFC EDITOR: Please replace [I-D.ietf-lamps-cms-sphincs-plus]
      |  throughout this document with a reference to the published RFC.









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   <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, SMIME-CAPS
       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.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(81) } ;

   --
   -- HashSLH-DSA object identifiers from [CSOR]
   --

   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-hash-slh-dsa-sha2-128s-with-sha256 OBJECT IDENTIFIER ::= {
     sigAlgs 35 }

   id-hash-slh-dsa-sha2-128f-with-sha256 OBJECT IDENTIFIER ::= {
     sigAlgs 36 }

   id-hash-slh-dsa-sha2-192s-with-sha512 OBJECT IDENTIFIER ::= {



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     sigAlgs 37 }

   id-hash-slh-dsa-sha2-192f-with-sha512 OBJECT IDENTIFIER ::= {
     sigAlgs 38 }

   id-hash-slh-dsa-sha2-256s-with-sha512 OBJECT IDENTIFIER ::= {
     sigAlgs 39 }

   id-hash-slh-dsa-sha2-256f-with-sha512 OBJECT IDENTIFIER ::= {
     sigAlgs 40 }

   id-hash-slh-dsa-shake-128s-with-shake128 OBJECT IDENTIFIER ::= {
     sigAlgs 41 }

   id-hash-slh-dsa-shake-128f-with-shake128 OBJECT IDENTIFIER ::= {
     sigAlgs 42 }

   id-hash-slh-dsa-shake-192s-with-shake256 OBJECT IDENTIFIER ::= {
     sigAlgs 43 }

   id-hash-slh-dsa-shake-192f-with-shake256 OBJECT IDENTIFIER ::= {
     sigAlgs 44 }

   id-hash-slh-dsa-shake-256s-with-shake256 OBJECT IDENTIFIER ::= {
     sigAlgs 45 }

   id-hash-slh-dsa-shake-256f-with-shake256 OBJECT IDENTIFIER ::= {
     sigAlgs 46 }

   --
   -- HashSLH-DSA public key identifiers
   --

   pk-hash-slh-dsa-sha2-128s-with-sha256 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-128s-with-sha256
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-sha2-128f-with-sha256 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-128f-with-sha256
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-sha2-192s-with-sha512 PUBLIC-KEY ::= {



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     IDENTIFIER id-hash-slh-dsa-sha2-192s-with-sha512
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-sha2-192f-with-sha512 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-192f-with-sha512
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-sha2-256s-with-sha512 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-256s-with-sha512
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-sha2-256f-with-sha512 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-256f-with-sha512
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-shake-128s-with-shake128 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-shake-128s-with-shake128
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-shake-128f-with-shake128 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-shake-128f-with-shake128
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-shake-192s-with-shake256 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-shake-192s-with-shake256
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }




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   pk-hash-slh-dsa-shake-192f-with-shake256 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-shake-192f-with-shake256
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-shake-256s-with-shake256 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-shake-256s-with-shake256
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-hash-slh-dsa-shake-256f-with-shake256 PUBLIC-KEY ::= {
     IDENTIFIER id-hash-slh-dsa-shake-256f-with-shake256
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   --
   -- HashSLH-DSA signature algorithm identifiers
   --

   sa-hash-slh-dsa-sha2-128s-with-sha256 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-128s-with-sha256
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-sha2-128s-with-sha256 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-sha2-128s-with-sha256 } }

   sa-hash-slh-dsa-sha2-128f-with-sha256 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-128f-with-sha256
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-sha2-128f-with-sha256 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-sha2-128f-with-sha256 } }

   sa-hash-slh-dsa-sha2-192s-with-sha512 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-192s-with-sha512
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-sha2-192s-with-sha512 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-sha2-192s-with-sha512 } }

   sa-hash-slh-dsa-sha2-192f-with-sha512 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-192f-with-sha512



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     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-sha2-192f-with-sha512 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-sha2-192f-with-sha512 } }

   sa-hash-slh-dsa-sha2-256s-with-sha512 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-256s-with-sha512
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-sha2-256s-with-sha512 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-sha2-256s-with-sha512 } }

   sa-hash-slh-dsa-sha2-256f-with-sha512 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-sha2-256f-with-sha512
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-sha2-256f-with-sha512 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-sha2-256f-with-sha512 } }

   sa-hash-slh-dsa-shake-128s-with-shake128 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-shake-128s-with-shake128
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-shake-128s-with-shake128 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-shake-128s-with-shake128 } }

   sa-hash-slh-dsa-shake-128f-with-shake128 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-shake-128f-with-shake128
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-shake-128f-with-shake128 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-shake-128f-with-shake128 } }

   sa-hash-slh-dsa-shake-192s-with-shake256 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-shake-192s-with-shake256
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-shake-192s-with-shake256 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-shake-192s-with-shake256 } }

   sa-hash-slh-dsa-shake-192f-with-shake256 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-shake-192f-with-shake256
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-shake-192f-with-shake256 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-shake-192f-with-shake256 } }

   sa-hash-slh-dsa-shake-256s-with-shake256 SIGNATURE-ALGORITHM ::= {



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     IDENTIFIER id-hash-slh-dsa-shake-256s-with-shake256
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-shake-256s-with-shake256 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-shake-256s-with-shake256 } }

   sa-hash-slh-dsa-shake-256f-with-shake256 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-hash-slh-dsa-shake-256f-with-shake256
     PARAMS ARE absent
     PUBLIC-KEYS { pk-hash-slh-dsa-shake-256f-with-shake256 }
     SMIME-CAPS {
       IDENTIFIED BY id-hash-slh-dsa-shake-256f-with-shake256 } }

   --
   -- 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 |
     sa-hash-slh-dsa-sha2-128s-with-sha256 |
     sa-hash-slh-dsa-sha2-128f-with-sha256 |
     sa-hash-slh-dsa-sha2-192s-with-sha512 |
     sa-hash-slh-dsa-sha2-192f-with-sha512 |
     sa-hash-slh-dsa-sha2-256s-with-sha512 |
     sa-hash-slh-dsa-sha2-256f-with-sha512 |
     sa-hash-slh-dsa-shake-128s-with-shake128 |
     sa-hash-slh-dsa-shake-128f-with-shake128 |
     sa-hash-slh-dsa-shake-192s-with-shake256 |
     sa-hash-slh-dsa-shake-192f-with-shake256 |
     sa-hash-slh-dsa-shake-256s-with-shake256 |
     sa-hash-slh-dsa-shake-256f-with-shake256,
     ... }

   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 |



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     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 |
     sa-hash-slh-dsa-sha2-128s-with-sha256.&smimeCaps |
     sa-hash-slh-dsa-sha2-128f-with-sha256.&smimeCaps |
     sa-hash-slh-dsa-sha2-192s-with-sha512.&smimeCaps |
     sa-hash-slh-dsa-sha2-192f-with-sha512.&smimeCaps |
     sa-hash-slh-dsa-sha2-256s-with-sha512.&smimeCaps |
     sa-hash-slh-dsa-sha2-256f-with-sha512.&smimeCaps |
     sa-hash-slh-dsa-shake-128s-with-shake128.&smimeCaps |
     sa-hash-slh-dsa-shake-128f-with-shake128.&smimeCaps |
     sa-hash-slh-dsa-shake-192s-with-shake256.&smimeCaps |
     sa-hash-slh-dsa-shake-192f-with-shake256.&smimeCaps |
     sa-hash-slh-dsa-shake-256s-with-shake256.&smimeCaps |
     sa-hash-slh-dsa-shake-256f-with-shake256.&smimeCaps,
     ... }

   --
   -- 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 |
     pk-hash-slh-dsa-sha2-128s-with-sha256 |
     pk-hash-slh-dsa-sha2-128f-with-sha256 |
     pk-hash-slh-dsa-sha2-192s-with-sha512 |
     pk-hash-slh-dsa-sha2-192f-with-sha512 |
     pk-hash-slh-dsa-sha2-256s-with-sha512 |
     pk-hash-slh-dsa-sha2-256f-with-sha512 |
     pk-hash-slh-dsa-shake-128s-with-shake128 |
     pk-hash-slh-dsa-shake-128f-with-shake128 |
     pk-hash-slh-dsa-shake-192s-with-shake256 |
     pk-hash-slh-dsa-shake-192f-with-shake256 |



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     pk-hash-slh-dsa-shake-256s-with-shake256 |
     pk-hash-slh-dsa-shake-256f-with-shake256,
      ... }

   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 defined 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 SLH-DSA 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.  The HashSLH-DSA
   parameter sets have the same values as the Pure SLH-DSA equivalents.





















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   +==============================+============+=======+======+=======+
   | OID                          | NIST Level | Sig.  | Pub. | Priv. |
   |                              |            |       | Key  | Key   |
   +==============================+============+=======+======+=======+
   | id-(hash-)slh-dsa-sha2-128s  | 1          | 7856  | 32   | 64    |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-sha2-128f  | 1          | 17088 | 32   | 64    |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-sha2-192s  | 3          | 16224 | 48   | 96    |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-sha2-192f  | 3          | 35664 | 48   | 96    |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-sha2-256s  | 5          | 29792 | 64   | 128   |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-sha2-256f  | 5          | 49856 | 64   | 128   |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-shake-128s | 1          | 7856  | 32   | 64    |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-shake-128f | 1          | 17088 | 32   | 64    |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-shake-192s | 3          | 16224 | 48   | 96    |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-shake-192f | 3          | 35664 | 48   | 96    |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-shake-256s | 5          | 29792 | 64   | 128   |
   +------------------------------+------------+-------+------+-------+
   | id-(hash-)slh-dsa-shake-256f | 5          | 49856 | 64   | 128   |
   +------------------------------+------------+-------+------+-------+

                   Table 1: SLH-DSA security strengths

Appendix C.  Examples

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

C.1.  Example Public Key

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

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







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     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 an 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 of a self-signed SLH-DSA certificate using id-slh-dsa-
   sha2-128s:

   Certificate:
       Data:
           Version: 3 (0x2)
           Serial Number:
               43:85:63:a2:69:01:99:2c:39:cf:bc:40:57:1b:5f:a3:
               cc:c7:88:45
           Signature Algorithm: slhdsa_sha2_128s
           Issuer: C=FR, L=Paris, O=Bogus SLH-DSA-SHA2-128s CA
           Validity
               Not Before: Oct 16 13:42:12 2024 GMT
               Not After : Oct 14 13:42:12 2034 GMT
           Subject: C=FR, L=Paris, O=Bogus SLH-DSA-SHA2-128s CA



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           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: critical
                   Certificate Sign, CRL Sign
       Signature Algorithm: slhdsa_sha2_128s
       Signature Value:
           aa:a0:51:de:b0:c3:14:d0:cd:fb:12:46:a2:31:20:c9:ed:ab:
           3f:dc:57:a5:fb:45:f6:f0:3b:7f:e3:5a:8c:b5:87:1e:1f:0b:
           15:9f:aa:56:68:43:7e:ea:23:05:21:d1:33:cb:84:61:55:7e:
           39:74:18:3c:ea:8e:01:a4:8d:9a:fb:35:74:69:c9:62:35:7f:
           0e:34:01:1c:90:41:97:13:ff:c5:a4:65:ae:0f:bf:9b:32:d2:
           2a:2c:97:86:2d:49:eb:ba:ae:9a:70:e7:35:67:3f:0a:7e:3a:
           dd:0b:66:4e:f8:45:b2:e6:d8:70:ab:fb:72:60:eb:85:ae:62:
           3c:a4:bf:3c:7a:e5:dd:4a:24:e2:4e:d0:b5:3b:c3:ac:e9:26:
           f8:6c:ca:3b:e1:46:15:7f:18:c5:41:40:90:73:b9:19:63:86:
           23:3a:b2:7f:12:3a:5f:bb:c3:10:6c:4e:b2:62:ee:3b:4b:c5:
           e2:69:24:74:3e:6e:81:e2:68:48:c8:27:25:bc:b2:ac:da:a8:
           ae:75:5a:5c:09:22:1c:be:95:0a:0b:5e:0c:08:49:42:3a:0d:
           2d:fb:89:3b:b3:15:de:ee:e7:b2:5e:1f:a6:f0:4a:f6:65:c1:
           5d:5e:05:7a:6d:2a:e7:c2:c3:20:37:ce:ab:0f:6c:ea:c9:39:
           f3:28:d1:75:81:31:7f:01:e2:09:c8:56:81:50:cf:4e:fa:82:
           1a:60:3e:87:bf:61:ca:a0:40:27:95:bf:f8:4f:04:b1:fd:1f:
           7f:ce:29:fa:15:5c:ef:94:9a:f6:f0:0c:7f:09:7f:ec:b6:36:
           26:83:69:aa:2d:69:9e:17:7a:15:aa:9b:51:43:c1:90:7c:c9:
           69:3a:5a:b1:ee:77:c9:28:e7:21:d8:93:0a:80:19:9c:5e:b7:
           61:5f:14:6c:9a:00:22:aa:4d:b8:86:03:b5:83:4a:e9:f3:5a:
           76:cc:a3:3b:e4:13:94:f7:56:96:56:33:dd:19:d9:3d:8d:55:
           ab:99:e5:00:24:f7:ff:f4:ee:08:47:8d:43:b3:f4:e3:3a:d5:
           12:ef:04:00:99:62:a1:5e:cd:5f:9f:90:f3:c2:8e:35:9b:8a:
           46:ec:54:4e:13:20:59:5f:63:d9:61:b1:e2:c4:36:d2:e5:27:
           56:1f:53:59:9c:24:ec:6a:79:2b:1d:6a:f2:93:38:d8:eb:7a:
           cd:d7:8a:c8:98:d4:87:61:bf:79:3c:2a:64:42:0f:5b:15:b4:
           bd:c0:c7:c4:de:20:4c:bb:d8:0f:61:2e:aa:67:e1:a7:ff:0d:
           b7:dd:05:cf:5c:cb:0c:46:26:e0:d9:48:cb:45:76:27:88:51:



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           49:df:4c:16:65:8c:1a:84:82:09:f3:d4:ee:c4:2a:17:a9:7b:
           c0:77:24:fd:4f:00:98:12:ed:10:e7:67:c3:7d:54:78:0f:c8:
           67:7f:f4:f2:80:2b:1b:34:0c:fa:5f:c4:12:85:1c:5f:e6:84:
           8d:ce:12:e7:ae:f5:ef:eb:96:5f:62:6f:87:3a:35:67:ca:d8:
           ad:b5:55:0b:0d:06:91:d3:9d:1a:96:2e:67:d8:b1:0e:8f:07:
           3f:7b:d6:fe:b5:76:62:19:83:f6:d2:08:35:3b:9f:1d:0a:f7:
           14:d2:45:50:70:5c:91:cc:b5:0f:4b:ef:79:ef:d3:c7:bd:02:
           7a:fa:8b:83:cd:31:07:b0:f7:8a:79:c4:68:19:de:01:f8:73:
           1a:6d:8a:c7:54:c8:4b:9a:40:53:e3:4b:e4:bd:3a:52:50:c6:
           de:de:19:d7:9e:a8:88:70:f1:70:a6:11:55:b0:46:5e:40:37:
           b2:90:5c:91:76:bd:20:1d:24:db:71:33:81:b8:47:ef:ec:7e:
           78:d2:25:2b:4b:e2:6e:01:81:d4:12:ff:40:ff:e0:d7:90:29:
           85:80:e6:4a:f5:5b:32:6c:b7:05:1c:20:27:e0:98:57:80:e7:
           a2:97:cb:91:ce:d9:c1:a3:5f:dc:24:7f:b8:f5:5c:da:91:83:
           e5:ae:8c:65:73:84:6a:5b:c9:3f:97:51:7d:cc:3f:d6:39:e1:
           71:f1:54:8d:1f:4f:33:70:cc:07:f8:03:70:be:8c:81:e1:5d:
           73:c1:9c:be:7c:3d:69:c0:cc:72:90:cf:65:38:35:71:16:ae:
           1d:e2:a6:08:c8:7b:dd:c0:30:f4:b4:2a:45:fc:05:e6:1c:ef:
           af:f3:53:03:2f:76:b5:7b:f1:a9:7d:16:33:b1:b5:c2:4f:9b:
           55:7b:0d:22:f6:08:4b:38:b2:67:4e:d9:f8:f1:65:03:d6:5a:
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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.ietf-lamps-cms-sphincs-plus].  Thanks to those authors, and
   the ones they based their work on, for making our work easier.
   "Copying always makes things easier and less error prone" -
   [RFC8411].  Thanks to Sean Turner for helpful text and to Markku-
   Juhani O.  Saarinen for side-channel clarifications.

Authors' Addresses

   Kaveh Bashiri
   BSI
   Email: kaveh.bashiri.ietf@gmail.com


   Scott Fluhrer
   Cisco Systems
   Email: sfluhrer@cisco.com


   Stefan-Lukas Gazdag
   genua GmbH
   Email: ietf@gazdag.de


   Daniel Van Geest
   CryptoNext Security
   Email: daniel.vangeest@cryptonext-security.com


   Stavros Kousidis
   BSI
   Email: kousidis.ietf@gmail.com







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