RFC 8708

Internet Engineering Task Force (IETF)                        R. Housley
Request for Comments: 8708                                Vigil Security
Category: Standards Track                                  February 2020
ISSN: 2070-1721

Use of the HSS/LMS Hash-Based Signature Algorithm in the Cryptographic
                          Message Syntax (CMS)


   This document specifies the conventions for using the Hierarchical
   Signature System (HSS) / Leighton-Micali Signature (LMS) hash-based
   signature algorithm with the Cryptographic Message Syntax (CMS).  In
   addition, the algorithm identifier and public key syntax are
   provided.  The HSS/LMS algorithm is one form of hash-based digital
   signature; it is described in RFC 8554.

Status of This Memo

   This is an Internet Standards Track document.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Further information on
   Internet Standards is available in Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at

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Table of Contents

   1.  Introduction
     1.1.  ASN.1
     1.2.  Terminology
     1.3.  Motivation
   2.  HSS/LMS Hash-Based Signature Algorithm Overview
     2.1.  Hierarchical Signature System (HSS)
     2.2.  Leighton-Micali Signature (LMS)
     2.3.  Leighton-Micali One-Time Signature (LM-OTS) Algorithm
   3.  Algorithm Identifiers and Parameters
   4.  HSS/LMS Public Key Identifier
   5.  Signed-Data Conventions
   6.  Security Considerations
   7.  IANA Considerations
   8.  References
     8.1.  Normative References
     8.2.  Informative References
   Appendix A.  ASN.1 Module

   Author's Address

1.  Introduction

   This document specifies the conventions for using the Hierarchical
   Signature System (HSS) / Leighton-Micali Signature (LMS) hash-based
   signature algorithm with the Cryptographic Message Syntax (CMS) [CMS]
   signed-data content type.  The LMS system provides a one-time digital
   signature that is a variant of Merkle Tree Signatures (MTS).  The HSS
   is built on top of the LMS system to efficiently scale for a larger
   numbers of signatures.  The HSS/LMS algorithm is one form of hash-
   based digital signature, and it is described in [HASHSIG].  The HSS/
   LMS signature algorithm can only be used for a fixed number of
   signing operations with a given private key, and the number of
   signing operations depends upon the size of the tree.  The HSS/LMS
   signature algorithm uses small public keys, and it has low
   computational cost; however, the signatures are quite large.  The
   HSS/LMS private key can be very small when the signer is willing to
   perform additional computation at signing time; alternatively, the
   private key can consume additional memory and provide a faster
   signing time.  The HSS/LMS signatures [HASHSIG] are currently defined
   to exclusively use SHA-256 [SHS].

1.1.  ASN.1

   CMS values are generated using ASN.1 [ASN1-B], using the Basic
   Encoding Rules (BER) and the Distinguished Encoding Rules (DER)

1.2.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "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.

1.3.  Motivation

   Recent advances in cryptanalysis [BH2013] and progress in the
   development of quantum computers [NAS2019] pose a threat to widely
   deployed digital signature algorithms.  As a result, there is a need
   to prepare for a day when cryptosystems such as RSA and DSA that
   depend on discrete logarithms and factoring cannot be depended upon.

   If large-scale quantum computers are ever built, these computers will
   be able to break many of the public key cryptosystems currently in
   use.  A post-quantum cryptosystem [PQC] is a system that is secure
   against quantum computers that have more than a trivial number of
   quantum bits (qubits).  It is open to conjecture when it will be
   feasible to build such computers; however, RSA, DSA, Elliptic Curve
   Digital Signature Algorithm (ECDSA), and Edwards-curve Digital
   Signature Algorithm (EdDSA) are all vulnerable if large-scale quantum
   computers are ever developed.

   Since the HSS/LMS signature algorithm does not depend on the
   difficulty of discrete logarithms or factoring, the HSS/LMS signature
   algorithm is considered to be post-quantum secure.  One use of post-
   quantum-secure signatures is the protection of software updates,
   perhaps using the format described in [FWPROT], to enable deployment
   of software that implements new cryptosystems.

2.  HSS/LMS Hash-Based Signature Algorithm Overview

   Merkle Tree Signatures (MTS) are a method for signing a large but
   fixed number of messages.  An MTS system depends on a one-time
   signature method and a collision-resistant hash function.

   This specification makes use of the hash-based algorithm specified in
   [HASHSIG], which is the Leighton and Micali adaptation [LM] of the
   original Lamport-Diffie-Winternitz-Merkle one-time signature system
   [M1979] [M1987] [M1989a] [M1989b].

   As implied by the name, the hash-based signature algorithm depends on
   a collision-resistant hash function.  The hash-based signature
   algorithm specified in [HASHSIG] uses only the SHA-256 one-way hash
   function [SHS], but it establishes an IANA registry [IANA-LMS] to
   permit the registration of additional one-way hash functions in the

2.1.  Hierarchical Signature System (HSS)

   The MTS system specified in [HASHSIG] uses a hierarchy of trees.  The
   N-time Hierarchical Signature System (HSS) allows subordinate trees
   to be generated when needed by the signer.  Otherwise, generation of
   the entire tree might take weeks or longer.

   An HSS signature as specified in [HASHSIG] carries the number of
   signed public keys (Nspk), followed by that number of signed public
   keys, followed by the LMS signature as described in Section 2.2.  The
   public key for the topmost LMS tree is the public key of the HSS
   system.  The LMS private key in the parent tree signs the LMS public
   key in the child tree, and the LMS private key in the bottom-most
   tree signs the actual message.  The signature over the public key and
   the signature over the actual message are LMS signatures as described
   in Section 2.2.

   The elements of the HSS signature value for a standalone tree (a top
   tree with no children) can be summarized as:

      u32str(0) ||
      lms_signature  /* signature of message */

   where, u32str() and || are used as defined in [HASHSIG].

   The elements of the HSS signature value for a tree with Nspk signed
   public keys can be summarized as:

      u32str(Nspk) ||
      signed_public_key[0] ||
      signed_public_key[1] ||
      signed_public_key[Nspk-2] ||
      signed_public_key[Nspk-1] ||
      lms_signature  /* signature of message */

   where, as defined in Section 3.3 of [HASHSIG], the signed_public_key
   structure contains the lms_signature over the public key, followed by
   the public key itself.  Note that Nspk is the number of levels in the
   hierarchy of trees minus 1.

2.2.  Leighton-Micali Signature (LMS)

   Each tree in the system specified in [HASHSIG] uses the Leighton-
   Micali Signature (LMS) system.  LMS systems have two parameters.  The
   first parameter is the height of the tree, h, which is the number of
   levels in the tree minus one.  The [HASHSIG] specification supports
   five values for this parameter: h=5, h=10, h=15, h=20, and h=25.
   Note that there are 2^h leaves in the tree.  The second parameter, m,
   is the number of bytes output by the hash function, and it is the
   amount of data associated with each node in the tree.  The [HASHSIG]
   specification supports only the SHA-256 hash function [SHS], with
   m=32.  As a result, the [HASHSIG] specification supports five tree
   sizes; they are identified as:

   *  LMS_SHA256_M32_H5

   *  LMS_SHA256_M32_H10

   *  LMS_SHA256_M32_H15

   *  LMS_SHA256_M32_H20

   *  LMS_SHA256_M32_H25

   The [HASHSIG] specification establishes an IANA registry [IANA-LMS]
   to permit the registration of additional hash functions and
   additional tree sizes in the future.

   As specified in [HASHSIG], the LMS public key consists of four
   elements: the lms_algorithm_type from the list above, the otstype to
   identify the Leighton-Micali One-Time Signature (LM-OTS) type as
   discussed in Section 2.3, the private key identifier (I) as described
   in Section 5.3 of [HASHSIG], and the m-byte string associated with
   the root node of the tree (T[1]).

   The LMS public key can be summarized as:

      u32str(lms_algorithm_type) || u32str(otstype) || I || T[1]

   As specified in [HASHSIG], an LMS signature consists of four
   elements: the number of the leaf (q) associated with the LM-OTS
   signature value, an LM-OTS signature value as described in
   Section 2.3, a typecode indicating the particular LMS algorithm, and
   an array of values that is associated with the path through the tree
   from the leaf associated with the LM-OTS signature value to the root.
   The array of values contains the siblings of the nodes on the path
   from the leaf to the root but does not contain the nodes on the path
   itself.  The array for a tree with height h will have h values.  The
   first value is the sibling of the leaf, the next value is the sibling
   of the parent of the leaf, and so on up the path to the root.

   The four elements of the LMS signature value can be summarized as:

      u32str(q) ||
      ots_signature ||
      u32str(type) ||
      path[0] || path[1] || ... || path[h-1]

2.3.  Leighton-Micali One-Time Signature (LM-OTS) Algorithm

   Merkle Tree Signatures (MTS) depend on a one-time signature method,
   and [HASHSIG] specifies the use of the LM-OTS, which has five

   n:   The length in bytes of the hash function output.  [HASHSIG]
        supports only SHA-256 [SHS], with n=32.

   H:   A preimage-resistant hash function that accepts byte strings of
        any length and returns an n-byte string.

   w:   The width in bits of the Winternitz coefficients.  [HASHSIG]
        supports four values for this parameter: w=1, w=2, w=4, and w=8.

   p:   The number of n-byte string elements that make up the LM-OTS
        signature value.

   ls:  The number of bits that are left-shifted in the final step of
        the checksum function, which is defined in Section 4.4 of

   The values of p and ls are dependent on the choices of the parameters
   n and w, as described in Appendix B of [HASHSIG].

   The [HASHSIG] specification supports four LM-OTS variants:

   *  LMOTS_SHA256_N32_W1

   *  LMOTS_SHA256_N32_W2

   *  LMOTS_SHA256_N32_W4

   *  LMOTS_SHA256_N32_W8

   The [HASHSIG] specification establishes an IANA registry [IANA-LMS]
   to permit the registration of additional variants in the future.

   Signing involves the generation of C, an n-byte random value.

   The LM-OTS signature value can be summarized as the identifier of the
   LM-OTS variant, the random value, and a sequence of hash values (y[0]
   through y[p-1]) that correspond to the elements of the public key, as
   described in Section 4.5 of [HASHSIG]:

      u32str(otstype) || C || y[0] || ... || y[p-1]

3.  Algorithm Identifiers and Parameters

   The algorithm identifier for an HSS/LMS hash-based signature is:

      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 }

   When this object identifier is used for an HSS/LMS signature, the
   AlgorithmIdentifier parameters field MUST be absent (that is, the
   parameters are not present, and the parameters are not set to NULL).

   The signature value is a large OCTET STRING, as described in
   Section 2 of this document.  The signature format is designed for
   easy parsing.  The HSS, LMS, and LM-OTS components of the signature
   value each include a counter and a typecode that indirectly provide
   all of the information that is needed to parse the value during
   signature validation.

   The signature value identifies the hash function used in the HSS/LMS
   tree.  [HASHSIG] uses only the SHA-256 hash function [SHS], but it
   establishes an IANA registry [IANA-LMS] to permit the registration of
   additional hash functions in the future.

4.  HSS/LMS Public Key Identifier

   The AlgorithmIdentifier for an HSS/LMS public key uses the id-alg-
   hss-lms-hashsig object identifier, and the parameters field MUST be

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

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

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

   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 version of the document that
   became [HASHSIG].

   The public key value is an OCTET STRING.  Like the signature format,
   it is designed for easy parsing.  The value is the number of levels
   in the public key, L, followed by the LMS public key.

   The HSS/LMS public key value can be described as:

         u32str(L) || lms_public_key

   Note that the public key for the topmost LMS tree is the public key
   of the HSS system.  When L=1, the HSS system is a single tree.

5.  Signed-Data Conventions

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

   When signed attributes are absent, the HSS/LMS signature is computed
   over the content.  When signed attributes are present, a hash is
   computed over the content using the same hash function that is used
   in the HSS/LMS tree, then a message-digest attribute is constructed
   with the hash of the content, and then the HSS/LMS signature is
   computed over the DER-encoded set of signed attributes (which MUST
   include a content-type attribute and a message-digest attribute).  In

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

   When using [HASHSIG], the fields in the SignerInfo are used as

   *  digestAlgorithm MUST contain the one-way hash function used in the
      HSS/LMS tree.  In [HASHSIG], SHA-256 is the only supported hash
      function, but other hash functions might be registered in the
      future.  For convenience, the AlgorithmIdentifier for SHA-256 from
      [PKIXASN1] is repeated here:

            mda-sha256 DIGEST-ALGORITHM ::= {
                IDENTIFIER id-sha256
                PARAMS TYPE NULL ARE preferredAbsent }

            id-sha256 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
                country(16) us(840) organization(1) gov(101) csor(3)
                nistAlgorithms(4) hashalgs(2) 1 }

   *  signatureAlgorithm MUST contain id-alg-hss-lms-hashsig, and the
      algorithm parameters field MUST be absent.

   *  signature contains the single HSS signature value resulting from
      the signing operation as specified in [HASHSIG].

6.  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 in a virtual machine environment, failed writes,
   virtual machine snapshotting or cloning, and other operational
   concerns must be considered to ensure confidentiality and integrity.

   When generating an LMS key pair, an implementation MUST generate each
   key pair independently of all other key pairs in the HSS tree.

   An implementation MUST ensure that an LM-OTS private key is used to
   generate a signature only one time and ensure that it cannot be used
   for any other purpose.

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

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

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

7.  IANA Considerations

   In the "SMI Security for S/MIME Module Identifier
   (1.2.840.113549." registry, IANA has updated the reference
   for value 64 to point to this document.

   In the "SMI Security for S/MIME Algorithms (1.2.840.113549."
   registry, IANA has updated the description for value 17 to "id-alg-
   hss-lms-hashsig" and updated the reference to point to this document.

   IANA has also added the following note to the "SMI Security for
   S/MIME Algorithms (1.2.840.113549." registry:

      Value 17, "id-alg-hss-lms-hashsig", is also referred to as "id-

8.  References

8.1.  Normative References

   [ASN1-B]   ITU-T, "Information technology -- Abstract Syntax Notation
              One (ASN.1): Specification of basic notation",
              ITU-T Recommendation X.680, August 2015.

   [ASN1-E]   ITU-T, "Information technology -- ASN.1 encoding rules:
              Specification of Basic Encoding Rules (BER), Canonical
              Encoding Rules (CER) and Distinguished Encoding Rules
              (DER)", ITU-T Recommendation X.690, August 2015.

   [CMS]      Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
              RFC 5652, DOI 10.17487/RFC5652, September 2009,

   [HASHSIG]  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/info/rfc8554>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,

   [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,

   [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/info/rfc8174>.

   [SHS]      National Institute of Standards and Technology (NIST),
              "Secure Hash Standard (SHS)", FIPS PUB 180-4,
              DOI 10.6028/NIST.FIPS.180-4, August 2015,

8.2.  Informative References

   [BH2013]   Ptacek, T., Ritter, T., Samuel, J., and A. Stamos, "The
              Factoring Dead: Preparing for the Cryptopocalypse", August
              2013, <https://media.blackhat.com/us-13/us-13-Stamos-The-

   [CMSASN1]  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,

   [CMSASN1U] Schaad, J. and S. Turner, "Additional New ASN.1 Modules
              for the Cryptographic Message Syntax (CMS) and the Public
              Key Infrastructure Using X.509 (PKIX)", RFC 6268,
              DOI 10.17487/RFC6268, July 2011,

   [FWPROT]   Housley, R., "Using Cryptographic Message Syntax (CMS) to
              Protect Firmware Packages", RFC 4108,
              DOI 10.17487/RFC4108, August 2005,

   [IANA-LMS] IANA, "Leighton-Micali Signatures (LMS)",

   [LM]       Leighton, T. and S. Micali, "Large provably fast and
              secure digital signature schemes based on secure hash
              functions", U.S. Patent 5,432,852, July 1995.

   [M1979]    Merkle, R., "Secrecy, Authentication, and Public Key
              Systems", Technical Report No. 1979-1, Information Systems
              Laboratory, Stanford University, 1979.

   [M1987]    Merkle, R., "A Digital Signature Based on a Conventional
              Encryption Function", Advances in Cryptology -- CRYPTO '87
              Proceedings, Lecture Notes in Computer Science Vol. 293,
              DOI 10.1007/3-540-48184-2_32, 1988,

   [M1989a]   Merkle, R., "A Certified Digital Signature", Advances in
              Cryptology -- CRYPTO '89 Proceedings, Lecture Notes in
              Computer Science Vol. 435, DOI 10.1007/0-387-34805-0_21,
              1990, <https://doi.org/10.1007/0-387-34805-0_21>.

   [M1989b]   Merkle, R., "One Way Hash Functions and DES", Advances in
              Cryptology -- CRYPTO '89 Proceedings, Lecture Notes in
              Computer Science Vol. 435, DOI 10.1007/0-387-34805-0_40,
              1990, <https://doi.org/10.1007/0-387-34805-0_40>.

   [NAS2019]  National Academies of Sciences, Engineering, and Medicine,
              "Quantum Computing: Progress and Prospects", The National
              Academies Press, DOI 10.17226/25196, 2019,

   [PKIXASN1] 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,

   [PQC]      Bernstein, D., "Introduction to post-quantum
              cryptography", DOI 10.1007/978-3-540-88702-7_1, 2009,

   [RFC4086]  Eastlake 3rd, D., Schiller, J., and S. Crocker,
              "Randomness Requirements for Security", BCP 106, RFC 4086,
              DOI 10.17487/RFC4086, June 2005,

Appendix A.  ASN.1 Module


     { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)
       id-smime(16) id-mod(0) id-mod-mts-hashsig-2013(64) }



       FROM AlgorithmInformation-2009  -- RFC 5911 [CMSASN1]
         { 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 OBJECT IDENTIFIER ::= { iso(1)
       member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)
       smime(16) alg(3) 17 }

   id-alg-mts-hashsig OBJECT IDENTIFIER ::= id-alg-hss-lms-hashsig

   -- Signature Algorithm and Public Key

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

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

   -- Expand the signature algorithm set used by CMS [CMSASN1U]

   SignatureAlgorithmSet SIGNATURE-ALGORITHM ::=
       { sa-HSS-LMS-HashSig, ... }

   -- Expand the S/MIME capabilities set used by CMS [CMSASN1]

   SMimeCaps SMIME-CAPS ::=
       { sa-HSS-LMS-HashSig.&smimeCaps, ... }




   Many thanks to Joe Clarke, Roman Danyliw, Scott Fluhrer, Jonathan
   Hammell, Ben Kaduk, Panos Kampanakis, Barry Leiba, John Mattsson, Jim
   Schaad, Sean Turner, Daniel Van Geest, and Dale Worley for their
   careful review and comments.

Author's Address

   Russ Housley
   Vigil Security, LLC
   516 Dranesville Road
   Herndon, VA 20170
   United States of America

   Email: housley@vigilsec.com