Internet X.509 Public Key Infrastructure: Algorithm Identifiers for Hash-based Signatures
draft-gazdag-x509-hash-sigs-01

LAMPS - Limited Additional Mechanisms for PKIX and SMIME      S. Fluhrer
Internet-Draft                                             Cisco Systems
Intended status: Informational                                 S. Gazdag
Expires: 28 October 2023                                      genua GmbH
                                                            D. Van Geest
                                                       ISARA Corporation
                                                             S. Kousidis
                                                                     BSI
                                                           26 April 2023

  Internet X.509 Public Key Infrastructure: Algorithm Identifiers for
                         Hash-based Signatures
                     draft-gazdag-x509-hash-sigs-01

Abstract

   This document specifies algorithm identifiers and ASN.1 encoding
   formats for the Hash-Based Signature (HBS) schemes Hierarchical
   Signature System (HSS), eXtended Merkle Signature Scheme (XMSS), and
   XMSS^MT, a multi-tree variant of XMSS, as well as SPHINCS+, the
   latter being the only stateless scheme.  This specification applies
   to the Internet X.509 Public Key infrastructure (PKI) when those
   digital signatures are used in Internet X.509 certificates and
   certificate revocation lists.

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-gazdag-x509-hash-sigs/.

   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-gazdag-x509-hash-sigs.

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
   2.  Conventions and Definitions . . . . . . . . . . . . . . . . .   3
   3.  Subject Public Key Algorithms . . . . . . . . . . . . . . . .   4
     3.1.  HSS Public Keys . . . . . . . . . . . . . . . . . . . . .   4
     3.2.  XMSS Public Keys  . . . . . . . . . . . . . . . . . . . .   5
     3.3.  XMSS^MT Public Keys . . . . . . . . . . . . . . . . . . .   5
     3.4.  SPHINCS+ Public Keys  . . . . . . . . . . . . . . . . . .   6
   4.  Key Usage Bits  . . . . . . . . . . . . . . . . . . . . . . .   7
   5.  Signature Algorithms  . . . . . . . . . . . . . . . . . . . .   8
     5.1.  HSS Signature Algorithm . . . . . . . . . . . . . . . . .   8
     5.2.  XMSS Signature Algorithm  . . . . . . . . . . . . . . . .   9
     5.3.  XMSS^MT Signature Algorithm . . . . . . . . . . . . . . .   9
     5.4.  SPHINCS+ Signature Algorithm  . . . . . . . . . . . . . .   9
   6.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . . . .  10
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  13
     7.1.  Algorithm Security Considerations . . . . . . . . . . . .  13
     7.2.  Implementation Security Considerations  . . . . . . . . .  14
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  15
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  15
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  15

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     9.2.  Informative References  . . . . . . . . . . . . . . . . .  16
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  16
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  17

1.  Introduction

   Hash-Based Signature (HBS) Schemes combine Merkle trees with One/Few
   Time Signatures (OTS/FTS) in order to provide digital signature
   schemes that remain secure even when quantum computers become
   available.  There security is well understood and depends only on the
   security of the underlying hash function.  As such they can serve as
   an important building block for quantum computer resistant
   information and communication technology.

   The private key of HSS, XMSS and XMSS^MT is a finite collection of
   OTS keys, hence only a limited number of messages can be signed and
   the private key's state must be updated and persisted after signing
   to prevent reuse of OTS keys.  Due to thise statefulness of the
   private key and the limited number of signatures that can be created,
   these signature algorithms might not be appropriate for use in
   interactive protocols.  While the right selection of algorithm
   parameters would allow a private key to sign a virtually unbounded
   number of messages (e.g. 2^60), this is at the cost of a larger
   signature size and longer signing time.  Since these algorithms are
   already known to be secure against quantum attacks, and because roots
   of trust are generally long-lived and can take longer to be deployed
   than end-entity certificates, these signature algorithms are more
   appropriate to be used in root and subordinate CA certificates.  They
   are also appropriate in non-interactive contexts such as code
   signing.  In particular, there are multi-party IoT ecosystems where
   publicly trusted code signing certificates are useful.

   The private key of SPHINCS+ is a finite but very large collection of
   FTS keys and hence stateless.  This typically comes at the cost of
   larger signatures compared to the stateful HBS variants.  Thus
   SPHINCS+ is suitable for more use-cases if the signature sizes fit
   the requirements.

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.

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   The parameter 'n' is the security parameter, given in bytes.  In
   practice this is typically aligned to the standard output length of
   the hash function in use, i.e. either 24, 32 or 64 bytes.  The height
   of a single tree is typically given by the parameter 'h'.  The number
   of levels of trees is either called 'L' (HSS) or 'd' (XMSS, XMSS^MT,
   SPHINCS+).

3.  Subject Public Key Algorithms

   Certificates conforming to [RFC5280] can convey a public key for any
   public key algorithm.  The certificate indicates the algorithm
   through an algorithm identifier.  An algorithm identifier consists of
   an OID and optional parameters.

   In this document, we define new OIDs for identifying the different
   hash-based signature algorithms.  An additional OID is defined in
   [RFC8708] and repeated here for convenience.  For all of the OIDs,
   the parameters MUST be absent.

3.1.  HSS Public Keys

   The object identifier and public key algorithm identifier for HSS is
   defined in [RFC8708].  The definitions are repeated here for
   reference.

   The object identifier for an HSS public key is id-alg-hss-lms-
   hashsig:

   id-alg-hss-lms-hashsig  OBJECT IDENTIFIER ::= {
      iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)
      smime(16) alg(3) 17 }

   Note that the id-alg-hss-lms-hashsig algorithm identifier is also
   referred to as id-alg-mts-hashsig.  This synonym is based on the
   terminology used in an early draft of the document that became
   [RFC8554].

   The HSS public key identifier is as follows:

   pk-HSS-LMS-HashSig PUBLIC-KEY ::= {
      IDENTIFIER id-alg-hss-lms-hashsig
      KEY HSS-LMS-HashSig-PublicKey
      PARAMS ARE absent
      CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

   The HSS public key is defined as follows:

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   HSS-LMS-HashSig-PublicKey ::= OCTET STRING

   See [RFC8554] for more information on the contents and format of an
   HSS public key.  Note that the single-tree signature scheme LMS is
   instantiated as HSS with level L=1.

3.2.  XMSS Public Keys

   The object identifier for an XMSS public key is id-alg-xmss-hashsig:

   id-alg-xmss-hashsig  OBJECT IDENTIFIER ::= {
      itu-t(0) identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) xmss(13) 0 }

   The XMSS public key identifier is as follows:

   pk-XMSS-HashSig PUBLIC-KEY ::= {
      IDENTIFIER id-alg-xmss-hashsig
      KEY XMSS-HashSig-PublicKey
      PARAMS ARE absent
      CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

   The XMSS public key is defined as follows:

   XMSS-HashSig-PublicKey ::= OCTET STRING

   See [RFC8391] for more information on the contents and format of an
   XMSS public key.

3.3.  XMSS^MT Public Keys

   The object identifier for an XMSS^MT public key is id-alg-xmssmt-
   hashsig:

   id-alg-xmssmt-hashsig  OBJECT IDENTIFIER ::= {
      itu-t(0) identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) xmssmt(14) 0 }

   The XMSS^MT public key identifier is as follows:

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   pk-XMSSMT-HashSig PUBLIC-KEY ::= {
      IDENTIFIER id-alg-xmssmt-hashsig
      KEY XMSSMT-HashSig-PublicKey
      PARAMS ARE absent
      CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

   The XMSS^MT public key is defined as follows:

   XMSSMT-HashSig-PublicKey ::= OCTET STRING

   See [RFC8391] for more information on the contents and format of an
   XMSS^MT public key.

3.4.  SPHINCS+ Public Keys

   The object and public key algorithm identifiers for SPHINCS+ are
   defined in [I-D.ietf-lamps-cms-sphincs-plus].  The definitions are
   repeated here for reference.

   id-alg-sphincs-plus-128 OBJECT IDENTIFIER ::= {
      TBD }

   id-alg-sphincs-plus-192 OBJECT IDENTIFIER ::= {
      TBD }

   id-alg-sphincs-plus-256 OBJECT IDENTIFIER ::= {
      TBD }

   The SPHINCS+ public key identifier is as follows:

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   pk-sphincs-plus-128 PUBLIC-KEY ::= {
      IDENTIFIER id-alg-sphincs-plus-128
      KEY SPHINCS-Plus-PublicKey
      PARAMS ARE absent
      CERT-KEY-USAGE
        { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

   pk-sphincs-plus-192 PUBLIC-KEY ::= {
      IDENTIFIER id-alg-sphincs-plus-192
      KEY SPHINCS-Plus-PublicKey
      PARAMS ARE absent
      CERT-KEY-USAGE
        { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

   pk-sphincs-plus-256 PUBLIC-KEY ::= {
      IDENTIFIER id-alg-sphincs-plus-256
      KEY SPHINCS-Plus-PublicKey
      PARAMS ARE absent
      CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

   The SPHINCS+ public key is defined as follows:

   SPHINCS-Plus-PublicKey ::= OCTET STRING

   See [SP-Sub] for more information on the contents and format of a
   SPHINCS+ public key.

4.  Key Usage Bits

   The intended application for the key is indicated in the keyUsage
   certificate extension.

   If the keyUsage extension is present in an end-entity certificate
   that indicates id-alg-xmss-hashsig or id-alg-xmssmt-hashsig in
   SubjectPublicKeyInfo, then the keyUsage extension MUST contain one or
   both of the following values:

   nonRepudiation; and
   digitalSignature.

   If the keyUsage extension is present in a certification authority
   certificate that indicates id-alg-xmss-hashsig or id-alg-xmssmt-
   hashsig, then the keyUsage extension MUST contain one or more of the
   following values:

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   nonRepudiation;
   digitalSignature;
   keyCertSign; and
   cRLSign.

   [RFC8708] defines the key usage for id-alg-hss-lms-hashsig, which is
   the same as for the keys above.

5.  Signature Algorithms

   This section identifies OIDs for signing using HSS, XMSS, XMSS^MT,
   and SPHINCS+. When these algorithm identifiers appear in the
   algorithm field as an AlgorithmIdentifier, the encoding MUST omit the
   parameters field.  That is, the AlgorithmIdentifier SHALL be a
   SEQUENCE of one component, one of the OIDs defined below.

   The data to be signed is prepared for signing.  For the algorithms
   used in this document, the data is signed directly by the signature
   algorithm, the data is not hashed before processing.  Then, a private
   key operation is performed to generate the signature value.  For HSS,
   the signature value is described in section 6.4 of [RFC8554].  For
   XMSS and XMSS^MT the signature values are described in sections B.2
   and C.2 of [RFC8391], respectively.  For SPHINCS+ the signature
   values are described in [SP-Sub].  The octet string representing the
   signature is encoded directly in the BIT STRING without adding any
   additional ASN.1 wrapping.  For the Certificate and CertificateList
   structures, the signature value is wrapped in the "signatureValue"
   BIT STRING field.

5.1.  HSS Signature Algorithm

   The HSS public key OID is also used to specify that an HSS signature
   was generated on the full message, i.e. the message was not hashed
   before being processed by the HSS signature algorithm.

   id-alg-hss-lms-hashsig OBJECT IDENTIFIER ::= {
      iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)
      smime(16) alg(3) 17 }

   The HSS signature is defined as follows:

   HSS-LMS-HashSig-Signature ::= OCTET STRING

   See [RFC8554] for more information on the contents and format of an
   HSS signature.

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5.2.  XMSS Signature Algorithm

   The XMSS public key OID is also used to specify that an XMSS
   signature was generated on the full message, i.e. the message was not
   hashed before being processed by the XMSS signature algorithm.

   id-alg-xmss-hashsig  OBJECT IDENTIFIER ::= {
      itu-t(0) identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) xmss(13) 0 }

   The XMSS signature is defined as follows:

   XMSS-HashSig-Signature ::= OCTET STRING

   See [RFC8391] for more information on the contents and format of an
   XMSS signature.

5.3.  XMSS^MT Signature Algorithm

   The XMSS^MT public key OID is also used to specify that an XMSS^MT
   signature was generated on the full message, i.e. the message was not
   hashed before being processed by the XMSS^MT signature algorithm.

   id-alg-xmssmt-hashsig  OBJECT IDENTIFIER ::= {
      itu-t(0) identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) xmssmt(14) 0 }

   The XMSS^MT signature is defined as follows:

   XMSSMT-HashSig-Signature ::= OCTET STRING

   See [RFC8391] for more information on the contents and format of an
   XMSS^MT signature.

5.4.  SPHINCS+ Signature Algorithm

   The SPHINCS+ public key OID is also used to specify that a SPHINCS+
   signature was generated on the full message, i.e. the message was not
   hashed before being processed by the SPHINCS+ signature algorithm.

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   id-alg-sphincs-plus-128 OBJECT IDENTIFIER ::= {
      TBD }

   id-alg-sphincs-plus-192 OBJECT IDENTIFIER ::= {
      TBD }

   id-alg-sphincs-plus-256 OBJECT IDENTIFIER ::= {
      TBD }

   The SPHINCS+ signature is defined as follows:

   SPHINCS-Plus-Signature ::= OCTET STRING

   See [SP-Sub] for more information on the contents and format of a
   SPHINCS+ signature.

6.  ASN.1 Module

   For reference purposes, the ASN.1 syntax is presented as an ASN.1
   module here.  This ASN.1 Module builds upon the conventions
   established in [RFC5911].

--
-- ASN.1 Module
--

<CODE STARTS>

Hashsigs-pkix-0 -- TBD - IANA assigned module OID

DEFINITIONS IMPLICIT TAGS ::= BEGIN

EXPORTS ALL;

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

--
-- Object Identifiers
--

-- id-alg-hss-lms-hashsig is defined in [RFC8708]

id-alg-hss-lms-hashsig OBJECT IDENTIFIER ::= { iso(1)
   member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)

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   smime(16) alg(3) 17 }

id-alg-xmss-hashsig  OBJECT IDENTIFIER ::= { itu-t(0)
   identified-organization(4) etsi(0) reserved(127)
   etsi-identified-organization(0) isara(15) algorithms(1)
   asymmetric(1) xmss(13) 0 }

id-alg-xmssmt-hashsig  OBJECT IDENTIFIER ::= { itu-t(0)
   identified-organization(4) etsi(0) reserved(127)
   etsi-identified-organization(0) isara(15) algorithms(1)
   asymmetric(1) xmssmt(14) 0 }

id-alg-sphincs-plus-128 OBJECT IDENTIFIER ::= {
   TBD }

id-alg-sphincs-plus-192 OBJECT IDENTIFIER ::= {
   TBD }

id-alg-sphincs-plus-256 OBJECT IDENTIFIER ::= {
   TBD }

--
-- Signature Algorithms and Public Keys
--

-- sa-HSS-LMS-HashSig is defined in [RFC8708]

sa-HSS-LMS-HashSig SIGNATURE-ALGORITHM ::= {
   IDENTIFIER id-alg-hss-lms-hashsig
   PARAMS ARE absent
   PUBLIC-KEYS { pk-HSS-LMS-HashSig }
   SMIME-CAPS { IDENTIFIED BY id-alg-hss-lms-hashsig } }

sa-XMSS-HashSig SIGNATURE-ALGORITHM ::= {
   IDENTIFIER id-alg-xmss-hashsig
   PARAMS ARE absent
   PUBLIC-KEYS { pk-XMSS-HashSig }
   SMIME-CAPS { IDENTIFIED BY id-alg-xmss-hashsig } }

sa-XMSSMT-HashSig SIGNATURE-ALGORITHM ::= {
   IDENTIFIER id-alg-xmssmt-hashsig
   PARAMS ARE absent
   PUBLIC-KEYS { pk-XMSSMT }
   SMIME-CAPS { IDENTIFIED BY id-alg-xmssmt-hashsig } }

-- sa-sphincs-plus-128 is defined in [I-D.ietf-lamps-cms-sphincs-plus]

sa-sphincs-plus-128 SIGNATURE-ALGORITHM ::= {

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   IDENTIFIER id-alg-sphincs-plus-128
   PARAMS ARE absent
   PUBLIC-KEYS { pk-sphincs-plus-128 }
   SMIME-CAPS { IDENTIFIED BY id-alg-sphincs-plus-128 } }

-- sa-sphincs-plus-192 is defined in [I-D.ietf-lamps-cms-sphincs-plus]

sa-sphincs-plus-192 SIGNATURE-ALGORITHM ::= {
   IDENTIFIER id-alg-sphincs-plus-192
   PARAMS ARE absent
   PUBLIC-KEYS { pk-sphincs-plus-192 }
   SMIME-CAPS { IDENTIFIED BY id-alg-sphincs-plus-192 } }

-- sa-sphincs-plus-256 is defined in [I-D.ietf-lamps-cms-sphincs-plus]

sa-sphincs-plus-256 SIGNATURE-ALGORITHM ::= {
   IDENTIFIER id-alg-sphincs-plus-256
   PARAMS ARE absent
   PUBLIC-KEYS { pk-sphincs-plus-256 }
   SMIME-CAPS { IDENTIFIED BY id-alg-sphincs-plus-256 } }

-- pk-HSS-LMS-HashSig is defined in [RFC8708]

pk-HSS-LMS-HashSig PUBLIC-KEY ::= {
   IDENTIFIER id-alg-hss-lms-hashsig
   KEY HSS-LMS-HashSig-PublicKey
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

HSS-LMS-HashSig-PublicKey ::= OCTET STRING

pk-XMSS-HashSig PUBLIC-KEY ::= {
   IDENTIFIER id-alg-xmss-hashsig
   KEY XMSS-HashSig-PublicKey
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

XMSS-HashSig-PublicKey ::= OCTET STRING

pk-XMSSMT-HashSig PUBLIC-KEY ::= {
   IDENTIFIER id-alg-xmssmt-hashsig
   KEY XMSSMT-PublicKey
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

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XMSSMT-HashSig-PublicKey ::= OCTET STRING

-- pk-sphincs-plus-128 is defined in [I-D.ietf-lamps-cms-sphincs-plus]

pk-sphincs-plus-128 PUBLIC-KEY ::= {
   IDENTIFIER id-alg-sphincs-plus-128
   KEY SPHINCS-Plus-PublicKey
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

-- pk-sphincs-plus-192 is defined in [I-D.ietf-lamps-cms-sphincs-plus]

pk-sphincs-plus-192 PUBLIC-KEY ::= {
   IDENTIFIER id-alg-sphincs-plus-192
   KEY SPHINCS-Plus-PublicKey
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

-- pk-sphincs-plus-256 is defined in [I-D.ietf-lamps-cms-sphincs-plus]

pk-sphincs-plus-256 PUBLIC-KEY ::= {
   IDENTIFIER id-alg-sphincs-plus-256
   KEY SPHINCS-Plus-PublicKey
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

SPHINCS-Plus-PublicKey ::= OCTET STRING

END

<CODE ENDS>

7.  Security Considerations

7.1.  Algorithm Security Considerations

   The cryptographic security of the signatures generated by the
   algorithms mentioned in this document depends only on the hash
   algorithms used within the signature algorithms and the pre-hash
   algorithm used to create an X.509 certificate's message digest.
   Grover's algorithm [Grover96] is a quantum search algorithm which
   gives a quadratic improvement in search time to brute-force pre-image
   attacks.  The results of [BBBV97] show that this improvement is
   optimal, however [Fluhrer17] notes that Grover's algorithm doesn't
   parallelize well.  Thus, given a bounded amount of time to perform

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   the attack and using a conservative estimate of the performance of a
   real quantum computer, the pre-image quantum security of SHA-256 is
   closer to 190 bits.  All parameter sets for the signature algorithms
   in this document currently use SHA-256 internally and thus have at
   least 128 bits of quantum pre-image resistance, or 190 bits using the
   security assumptions in [Fluhrer17].

   [Zhandry15] shows that hash collisions can be found using an
   algorithm with a lower bound on the number of oracle queries on the
   order of 2^(n/3) on the number of bits, however [DJB09] demonstrates
   that the quantum memory requirements would be much greater.
   Therefore a parameter set using SHA-256 would have at least 128 bits
   of quantum collision-resistance as well as the pre-image resistance
   mentioned in the previous paragraph.

   Given the quantum collision and pre-image resistance of SHA-256
   estimated above, the current parameter sets used by id-alg-hss-lms-
   hashsig, id-alg-xmss-hashsig and id-alg-xmssmt-hashsig provide 128
   bits or more of quantum security.  This is believed to be secure
   enough to protect X.509 certificates for well beyond any reasonable
   certificate lifetime.

7.2.  Implementation Security Considerations

   Implementations MUST protect the private keys.  Compromise of the
   private keys may result in the ability to forge signatures.  Along
   with the private key, the implementation MUST keep track of which
   leaf nodes in the tree have been used.  Loss of integrity of this
   tracking data can cause a one-time key to be used more than once.  As
   a result, when a private key and the tracking data are stored on non-
   volatile media or stored in a virtual machine environment, care must
   be taken to preserve confidentiality and integrity.

   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.  [RFC4086] offers important guidance in
   this area.

   The generation of hash-based signatures also depends on random
   numbers.  While the consequences of an inadequate pseudo-random
   number generator (PRNG) to generate these values is much less severe
   than the generation of private keys, the guidance in [RFC4086]
   remains important.

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8.  IANA Considerations

   IANA is requested to assign a module OID from the "SMI for PKIX
   Module Identifier" registry for the ASN.1 module in Section 6.

9.  References

9.1.  Normative References

   [I-D.ietf-lamps-cms-sphincs-plus]
              Housley, R., Fluhrer, S., Kampanakis, P., and B.
              Westerbaan, "Use of the SPHINCS+ Signature Algorithm in
              the Cryptographic Message Syntax (CMS)", Work in Progress,
              Internet-Draft, draft-ietf-lamps-cms-sphincs-plus-01, 21
              November 2022, <https://datatracker.ietf.org/doc/html/
              draft-ietf-lamps-cms-sphincs-plus-01>.

   [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>.

   [RFC5911]  Hoffman, P. and J. Schaad, "New ASN.1 Modules for
              Cryptographic Message Syntax (CMS) and S/MIME", RFC 5911,
              DOI 10.17487/RFC5911, June 2010,
              <https://www.rfc-editor.org/rfc/rfc5911>.

   [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>.

   [RFC8391]  Huelsing, A., Butin, D., Gazdag, S., Rijneveld, J., and A.
              Mohaisen, "XMSS: eXtended Merkle Signature Scheme",
              RFC 8391, DOI 10.17487/RFC8391, May 2018,
              <https://www.rfc-editor.org/rfc/rfc8391>.

   [RFC8554]  McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali
              Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554,
              April 2019, <https://www.rfc-editor.org/rfc/rfc8554>.

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   [SP-Sub]   Aumasson, J., Bernstein, D. J., Beullens, W., Dobraunig,
              C., Eichlseder, M., Fluhrer, S., Gazdag, S., Huelsing, A.,
              Kampanakis, P., Koelb, S., Lange, T., Lauridsen, M. M.,
              Mendel, F., Niederhagen, R., Rechberger, C., Rijneveld,
              J., Schwabe, P., and B. Westerbaan, "SPHINCS+ - Submission
              to the 3rd round of the NIST post-quantum project. v3.1",
              10 June 2021.

9.2.  Informative References

   [RFC3279]  Bassham, L., Polk, W., and R. Housley, "Algorithms and
              Identifiers for the Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", RFC 3279, DOI 10.17487/RFC3279, April
              2002, <https://www.rfc-editor.org/rfc/rfc3279>.

   [RFC4086]  Eastlake 3rd, D., Schiller, J., and S. Crocker,
              "Randomness Requirements for Security", BCP 106, RFC 4086,
              DOI 10.17487/RFC4086, June 2005,
              <https://www.rfc-editor.org/rfc/rfc4086>.

   [RFC4506]  Eisler, M., Ed., "XDR: External Data Representation
              Standard", STD 67, RFC 4506, DOI 10.17487/RFC4506, May
              2006, <https://www.rfc-editor.org/rfc/rfc4506>.

   [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>.

   [RFC8708]  Housley, R., "Use of the HSS/LMS Hash-Based Signature
              Algorithm in the Cryptographic Message Syntax (CMS)",
              RFC 8708, DOI 10.17487/RFC8708, February 2020,
              <https://www.rfc-editor.org/rfc/rfc8708>.

Acknowledgments

   Thanks for Russ Housley and Panos Kampanakis for helpful suggestions.

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   This document uses a lot of text from similar documents ([RFC3279]
   and [RFC8410]) as well as [RFC8708].  Thanks go to the authors of
   those documents.  "Copying always makes things easier and less error
   prone" - [RFC8411].

Authors' Addresses

   Scott Fluhrer
   Cisco Systems
   Email: sfluhrer@cisco.com

   Stefan Gazdag
   genua GmbH
   Email: ietf@gazdag.de

   Daniel Van Geest
   ISARA Corporation
   Email: daniel.vangeest@isara.com

   Stavros Kousidis
   BSI
   Email: stavros.kousidis@bsi.bund.de

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