Imported debug from /usr/lib/site-python/debug.pyc draft-vangeest-x509-hash-sigs-03 - Algorithm Identifiers for HSS and XMSS for Use in the Internet X.509 Public Key Infrastructure
[Docs] [txt|pdf|xml|html] [Tracker] [Email] [Diff1] [Diff2] [Nits]

Versions: 00 01 02 03

Network Working Group                                       D. Van Geest
Internet-Draft                                         ISARA Corporation
Intended status: Standards Track                              S. Fluhrer
Expires: September 12, 2019                                Cisco Systems
                                                          March 11, 2019


  Algorithm Identifiers for HSS and XMSS for Use in the Internet X.509
                       Public Key Infrastructure
                    draft-vangeest-x509-hash-sigs-03

Abstract

   This document specifies algorithm identifiers and ASN.1 encoding
   formats for the Hierarchical Signature System (HSS), eXtended Merkle
   Signature Scheme (XMSS), and XMSS^MT, a multi-tree variant of XMSS.
   This specification applies to the Internet X.509 Public Key
   infrastructure (PKI) when digital signatures are used to sign
   certificates and certificate revocation lists (CRLs).

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on September 12, 2019.

Copyright Notice

   Copyright (c) 2019 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (https://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must



Van Geest & Fluhrer    Expires September 12, 2019               [Page 1]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Subject Public Key Algorithms . . . . . . . . . . . . . . . .   3
     2.1.  HSS Public Keys . . . . . . . . . . . . . . . . . . . . .   3
     2.2.  XMSS Public Keys  . . . . . . . . . . . . . . . . . . . .   4
     2.3.  XMSS^MT Public Keys . . . . . . . . . . . . . . . . . . .   4
   3.  Key Usage Bits  . . . . . . . . . . . . . . . . . . . . . . .   5
   4.  Signature Algorithms  . . . . . . . . . . . . . . . . . . . .   5
     4.1.  HSS Signature Algorithm . . . . . . . . . . . . . . . . .   6
     4.2.  XMSS Signature Algorithm  . . . . . . . . . . . . . . . .   6
     4.3.  XMSS^MT Signature Algorithm . . . . . . . . . . . . . . .   6
   5.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . . . .   7
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
     6.1.  Algorithm Security Considerations . . . . . . . . . . . .   9
     6.2.  Implementation Security Considerations  . . . . . . . . .  10
   7.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  10
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  10
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  10
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  10
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  11
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   The Hierarchical Signature System (HSS) is described in
   [I-D.mcgrew-hash-sigs].

   The eXtended Merkle Signature Scheme (XMSS), and its multi-tree
   variant XMSS^MT, are described in [RFC8391].

   These signature algorithms are based on well-studied Hash Based
   Signature (HBS) schemes, which can withstand known attacks using
   quantum computers.  They combine Merkle Trees with One Time Signature
   (OTS) schemes in order to create signature systems which can sign a
   large but limited number of messages per private key.  The private
   keys are stateful; a key's state must be updated and persisted after
   signing to prevent reuse of OTS keys.  If an OTS key is reused,
   cryptographic security is not guaranteed for that key.

   Due to the 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



Van Geest & Fluhrer    Expires September 12, 2019               [Page 2]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


   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 key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

2.  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
   [I-D.ietf-lamps-cms-hash-sig] and repeated here for convenience.  For
   all of the OIDs, the parameters MUST be absent.

2.1.  HSS Public Keys

   The object identifier and public key algorithm identifier for HSS is
   defined in [I-D.ietf-lamps-cms-hash-sig].  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
   [I-D.mcgrew-hash-sigs].

   The HSS public key's properties are defined as follows:





Van Geest & Fluhrer    Expires September 12, 2019               [Page 3]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


      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

   [I-D.ietf-lamps-cms-hash-sig] contains more information on the
   contents and format of an HSS public key.

2.2.  XMSS Public Keys

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

      id-alg-xmss  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's properties are defined as follows:

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

      XMSS-PublicKey ::= OCTET STRING

   The format of an XMSS public key is is formally defined using XDR
   [RFC4506] and is defined in Appendix B.3 of [RFC8391].  In
   particular, the first 4 bytes represents the big-ending encoding of
   the XMSS algorithm type.

2.3.  XMSS^MT Public Keys

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

      id-alg-xmssmt  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's properties are defined as follows:




Van Geest & Fluhrer    Expires September 12, 2019               [Page 4]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


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

      XMSSMT-PublicKey ::= OCTET STRING

   The format of an XMSS^MT public key is is formally defined using XDR
   [RFC4506] and is defined in Appendix C.3 of [RFC8391].  In
   particular, the first 4 bytes represents the big-ending encoding of
   the XMSS^MT algorithm type.

3.  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 or id-alg-xmssmt 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 or id-alg-xmssmt, then the
   keyUsage extension MUST contain one or more of the following values:

      nonRepudiation;
      digitalSignature;
      keyCertSign; and
      cRLSign.

   [I-D.ietf-lamps-cms-hash-sig] defines the key usage for id-alg-hss-
   lms-hashsig, which is the same as for the keys above.

4.  Signature Algorithms

   This section identifies OIDs for signing using HSS, XMSS, and
   XMSS^MT.  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.





Van Geest & Fluhrer    Expires September 12, 2019               [Page 5]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


   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 3.3 of
   [I-D.mcgrew-hash-sigs].  For XMSS and XMSS^MT the signature values
   are described in sections B.2 and C.2 of [RFC8391] respectively.  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.

4.1.  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 }

   [I-D.ietf-lamps-cms-hash-sig] contains more information on the
   contents and format of an HSS signature.

4.2.  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  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 format of an XMSS signature is is formally defined using XDR
   [RFC4506] and is defined in Appendix B.2 of [RFC8391].

4.3.  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.







Van Geest & Fluhrer    Expires September 12, 2019               [Page 6]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


      id-alg-xmssmt  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 format of an XMSS^MT signature is is formally defined using XDR
   [RFC4506] and is defined in Appendix C.2 of [RFC8391].

5.  ASN.1 Module

   For reference purposes, the ASN.1 syntax is presented as an ASN.1
   module here.

   -- ASN.1 Module

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

   DEFINITIONS EXPLICIT TAGS ::=
   BEGIN

   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 [ietf-lamps-cms-hash-sig]
   --
   -- 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 }

   id-alg-xmss  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  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 }





Van Geest & Fluhrer    Expires September 12, 2019               [Page 7]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


   -- Signature Algorithms and Public Keys

   --
   -- sa-HSS-LMS-HashSig is defined in [ietf-lamps-cms-hash-sig]
   --
   -- 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 } }

   --
   -- pk-HSS-LMS-HashSig is defined in [ietf-lamps-cms-hash-sig]
   --
   -- 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

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

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

   XMSS-PublicKey ::= OCTET STRING

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








Van Geest & Fluhrer    Expires September 12, 2019               [Page 8]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


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

   XMSSMT-PublicKey ::= OCTET STRING

   END

6.  Security Considerations

6.1.  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
   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 and id-alg-xmssmt 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.






Van Geest & Fluhrer    Expires September 12, 2019               [Page 9]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


6.2.  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 (PRNGs) to generate these values is much less severe
   than the generation of private keys, the guidance in [RFC4086]
   remains important.

7.  Acknowledgements

   Thanks for Russ Housley for the helpful suggestions.

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

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 5.

9.  References

9.1.  Normative References








Van Geest & Fluhrer    Expires September 12, 2019              [Page 10]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


   [I-D.ietf-lamps-cms-hash-sig]
              Housley, R., "Use of the HSS/LMS Hash-based Signature
              Algorithm in the Cryptographic Message Syntax (CMS)",
              draft-ietf-lamps-cms-hash-sig-07 (work in progress), March
              2019.

   [I-D.mcgrew-hash-sigs]
              McGrew, D., Curcio, M., and S. Fluhrer, "Hash-Based
              Signatures", draft-mcgrew-hash-sigs-15 (work in progress),
              January 2019.

   [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/info/rfc2119>.

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

   [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/info/rfc5280>.

   [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/info/rfc8391>.

9.2.  Informative References

   [BBBV97]   Bennett, C., Bernstein, E., Brassard, G., and U. Vazirani,
              "Strengths and weaknesses of quantum computing", SIAM J.
              Comput. 26(5), 1510-1523, 1997.

   [DJB09]    Bernstein, D., "Cost analysis of hash collisions: Will
              quantum computers make SHARCS obsolete?", SHARCS 9, p.
              105, 2009.

   [Fluhrer17]
              Fluhrer, S., "Reassessing Grover's Algorithm", Cryptology
              ePrint Archive Report 2017/811, August 2017,
              <https://eprint.iacr.org/2017/811.pdf>.






Van Geest & Fluhrer    Expires September 12, 2019              [Page 11]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


   [Grover96]
              Grover, L., "A fast quantum mechanical algorithm for
              database search", 28th ACM Symposium on the Theory of
              Computing p. 212, 1996.

   [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/info/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/info/rfc4086>.

   [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/info/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/info/rfc8411>.

   [Zhandry15]
              Zhandry, M., "A note on the quantum collision and set
              equality problems", Quantum Information & Computation 15,
              7-8, 557-567, May 2015.

Authors' Addresses

   Daniel Van Geest
   ISARA Corporation
   560 Westmount Rd N
   Waterloo, Ontario  N2L 0A9
   Canada

   Email: daniel.vangeest@isara.com










Van Geest & Fluhrer    Expires September 12, 2019              [Page 12]


Internet-Draft       Hash-Based Signatures for X.509          March 2019


   Scott Fluhrer
   Cisco Systems
   170 West Tasman Drive
   San Jose, CA  95134
   USA

   Email: sfluhrer@cisco.com












































Van Geest & Fluhrer    Expires September 12, 2019              [Page 13]


Html markup produced by rfcmarkup 1.129b, available from https://tools.ietf.org/tools/rfcmarkup/