Algorithm Identifiers for HSS and XMSS for Use in the Internet X.509 Public Key Infrastructure
draft-vangeest-x509-hash-sigs-00

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

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Table of Contents

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

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 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.

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 two new OIDs for identifying the different hash-based signature algorithms. A third 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.

   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 object identifier for an HSS public key is id-alg-hss-lms-hashsig: [I-D.mcgrew-hash-sigs].

   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
          

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

[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-xmss:

   id-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 }
          

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

   XMSS-PublicKey ::= OCTET STRING
          

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

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-xmssmt:

   id-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 }
          

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

   XMSSMT-PublicKey ::= OCTET STRING
          

The XMSS^MT public key's properties are defined as follows:

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-xmss or id-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-xmss or id-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

Certificates and CRLs conforming to [RFC5280] may be signed with any public key signature algorithm. The certificate or CRL indicates the algorithm through an algorithm identifier which appears in the signatureAlgorithm field within the Certificate or CertificateList. This algorithm identifier is an OID and has optionally associated parameters. This section identifies algorithm identifiers that MUST be used in the signatureAlgorithm field in a Certificate or CertificateList.

Signature algorithms are always used in conjunction with a one-way hash function.

This section identifies OIDs for 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.

The data to be signed (e.g., the one-way hash function output value) is directly signed by the hash-based signature algorithms without any additional formatting necessary. The signature values is a large OCTET STRING. This signature value is then ASN.1 encoded as a BIT STRING and included in the Certificate or CertificateList in the signature field.

4.1. HSS Signature Algorithm

The ASN.1 OIDs used to specify that an HSS signature was generated on a SHA-256 or SHA-512 hash of an object are, respectively:

   hss-with-SHA256  OBJECT IDENTIFIER ::= { itu-t(0)
      identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) hss(12) 2 }
          

   hss-with-SHA512  OBJECT IDENTIFIER ::= { itu-t(0)
      identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) hss(12) 1 }
          

[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 ASN.1 OIDs used to specify that an XMSS signature was generated on a SHA-256 or SHA-512 hash of an object are, respectively:

   xmss-with-SHA256  OBJECT IDENTIFIER ::= { itu-t(0)
      identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) xmss(13) 2 }
          

   xmss-with-SHA512  OBJECT IDENTIFIER ::= { itu-t(0)
      identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) xmss(13) 1 }
          

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 ASN.1 OIDs used to specify that an XMSS^MT signature was generated on a SHA-256 or SHA-512 hash of an object are, respectively:

   xmssmt-with-SHA256  OBJECT IDENTIFIER ::= { itu-t(0)
      identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) xmssmt(14) 2 }
          

   xmssmt-with-SHA512  OBJECT IDENTIFIER ::= { itu-t(0)
      identified-organization(4) etsi(0) reserved(127)
      etsi-identified-organization(0) isara(15) algorithms(1)
      asymmetric(1) xmssmt(14) 1 }
          

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
  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)}
;
      

--
-- HSS Signatures
--

-- OID for HSS signature generated with SHA-256 hash

hss-with-SHA256  OBJECT IDENTIFIER ::= { itu-t(0)
   identified-organization(4) etsi(0) reserved(127)
   etsi-identified-organization(0) isara(15) algorithms(1)
   asymmetric(1) hss(12) 2 }
      

-- OID for HSS signature generated with SHA-512 hash

hss-with-SHA512  OBJECT IDENTIFIER ::= { itu-t(0)
   identified-organization(4) etsi(0) reserved(127)
   etsi-identified-organization(0) isara(15) algorithms(1)
   asymmetric(1) hss(12) 1 }
      

--
-- XMSS Keys and Signatures
--

-- OID for XMSS public keys

id-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 }
      

-- XMSS Public Keys

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

XMSS-PublicKey ::= OCTET STRING
      

-- OID for XMSS signature generated with SHA-256 hash

xmss-with-SHA256  OBJECT IDENTIFIER ::= { itu-t(0)
   identified-organization(4) etsi(0) reserved(127)
   etsi-identified-organization(0) isara(15) algorithms(1)
   asymmetric(1) xmss(13) 2 }
      

-- OID for XMSS signature generated with SHA-512 hash

xmss-with-SHA512  OBJECT IDENTIFIER ::= { itu-t(0)
   identified-organization(4) etsi(0) reserved(127)
   etsi-identified-organization(0) isara(15) algorithms(1)
   asymmetric(1) xmss(13) 1 }
      

--
-- XMSS^MT Keys and Signatures
--

-- OID for XMSS^MT public keys

id-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 }
      

-- XMSS^MT Public Keys

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

XMSSMT-PublicKey ::= OCTET STRING
      

-- OID for XMSS^MT signature generated with SHA-256 hash

xmssmt-with-SHA256  OBJECT IDENTIFIER ::= { itu-t(0)
   identified-organization(4) etsi(0) reserved(127)
   etsi-identified-organization(0) isara(15) algorithms(1)
   asymmetric(1) xmssmt(14) 2 }
      

-- OID for XMSS^MT signature generated with SHA-512 hash

xmssmt-with-SHA512  OBJECT IDENTIFIER ::= { itu-t(0)
   identified-organization(4) etsi(0) reserved(127)
   etsi-identified-organization(0) isara(15) algorithms(1)
   asymmetric(1) xmssmt(14) 1 }
      

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 pre-hash 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 algorithm identifiers hss-with-SHA256, xmss-with-SHA256 and xmssmt-with-SHA256 defined in this document 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, although the SHA-512 variants could be used if there are any doubts.

The algorithm identifiers hss-with-SHA512, xmss-with-SHA512 and xmssmt-with-SHA512 are defined in order to provide 256 bits of classical security (256 bits of brute-force pre-image resistance with the signature algorithms' SHA-256 and 256 bits of birthday attack collision resistance with the SHA-512 pre-hash).

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 an 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

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

9.2. Informative References

Authors' Addresses