Internet X.509 Public Key Infrastructure: Algorithm Identifiers for HSS and XMSS

Internet-Draft	HSS and XMSS for X.509	February 2024
Bashiri, et al.	Expires 25 August 2024	[Page]

Abstract

This document specifies algorithm identifiers and ASN.1 encoding formats for the Stateful Hash-Based Signature Schemes (S-HBS) 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 those digital signatures are used in Internet X.509 certificates and certificate revocation lists.¶

1. Introduction

Stateful Hash-Based Signature Schemes (S-HBS) such as HSS, XMSS and XMSS^MT combine Merkle trees with One Time Signatures (OTS) in order to provide digital signature schemes that remain secure even when quantum computers become available. Their theoretic 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 S-HBS 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. 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. Due to the statefulness of the private key and the limited number of signatures that can be created, S-HBS might not be appropriate for use in interactive protocols. However, in some use cases the deployment of S-HBS may be appropriate. Such use cases are described and discussed later in Section 4.¶

4. Use Cases of S-HBS in X.509

As many cryptographic algorithms that are considered to be quantum-resistant, S-HBS have several pros and cons regarding their practical usage. On the positive side they are considered to be secure against a classical as well as a quantum adversary, and a secure instantiation of S-HBS may always be built as long as a cryptographically secure hash function exists. Moreover, S-HBS offer small public key sizes, and, in comparison to other post-quantum signature schemes, the S-HBS can offer relatively small signature sizes (for certain parameter sets). While key generation and signature generation may take longer than classical alternatives, fast and minimal verification routines can be built. The major negative aspect is the statefulness. Private keys always have to be handled in a secure manner, S-HBS necessitate a special treatment of the private key in order to avoid security incidents like signature forgery [MCGREW], [SP800208]. Therefore, for S-HBS, a secure environment MUST be used for key generation and key management.¶

Note that, in general, root CAs offer such a secure environment and the number of issued signatures (including signed certificates and CRLs) is often moderate due to the fact that many root CAs delegate OCSP services or the signing of end-entity certificates to other entities (such as subordinate CAs) that use stateless signature schemes. Therefore, many root CAs should be able to handle the required state management, and S-HBS offer a viable solution.¶

As the above reasoning for root CAs usually does not apply for subordinate CAs, it is NOT RECOMMENDED for subordinate CAs to use S-HBS for issuing end-entity certificates. Moreover, S-HBS MUST NOT be used for end-entity certificates.¶

However, S-HBS MAY be used for code signing certificates, since they are suitable and recommended in such non-interactive contexts. For example, see the recommendations for software and firmware signing in [CNSA2.0]. Some manufactures use common and well-established key formats like X.509 for their code signing and update mechanisms. Also there are multi-party IoT ecosystems where publicly trusted code signing certificates are useful.¶

5. 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 stateful 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.¶

5.1. 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:¶

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

See [SP800208] and [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 number of levels being equal to 1.¶

5.2. 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 [SP800208] and [RFC8391] for more information on the contents and format of an XMSS public key.¶

5.3. 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:¶

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 [SP800208] and [RFC8391] for more information on the contents and format of an XMSS^MT public key.¶

6. Key Usage Bits

The intended application for the key is indicated in the keyUsage certificate extension [RFC5280]. If the keyUsage extension is present in a certificate that indicates id-alg-hss-lms-hashsig, id-alg-xmss-hashsig, or id-alg-xmssmt-hashsig, then the following requirements given in this section MUST be fulfilled.¶

If the keyUsage extension is present in a code signing certificate, then it MUST contain at least one of the following values:¶

nonRepudiation; or
digitalSignature.

However, it MUST NOT contain other values.¶

If the keyUsage extension is present in a certification authority certificate, then it MUST contain at least one of the following values:¶

nonRepudiation; or
digitalSignature; or
keyCertSign; or
cRLSign.

However, it MUST NOT contain other values.¶

Note that for certificates that indicate id-alg-hss-lms-hashsig the above definitions are more restrictive than the requirement defined in Section 4 of [RFC8708].¶

7. 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 in the following subsections.¶

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.¶

[EDNOTE: Should we delete the preceding paragraph?]¶

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. The octet string representing the signature is encoded directly in the OCTET STRING without adding any additional ASN.1 wrapping. For the Certificate and CertificateList structures, the signature value is wrapped in the "signatureValue" OCTET STRING field.¶

7.1. 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 [SP800208] and [RFC8554] for more information on the contents and format of an HSS signature.¶

7.2. 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 [SP800208] and [RFC8391] for more information on the contents and format of an XMSS signature.¶

The signature generation MUST be performed according to 7.2 of [SP800208].¶

7.3. 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 [SP800208] and [RFC8391] for more information on the contents and format of an XMSS^MT signature.¶

The signature generation MUST be performed according to 7.2 of [SP800208].¶

9. 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)
   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 }

--
-- 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-HashSig }
   SMIME-CAPS { IDENTIFIED BY id-alg-xmssmt-hashsig } }

-- 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-HashSig-PublicKey
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

XMSSMT-HashSig-PublicKey ::= OCTET STRING

END

<CODE ENDS>

10. Security Considerations

The security requirements of [SP800208] MUST be taken into account.¶

For S-HBS it is crucial to stress the importance of a correct state management. If an attacker were able to obtain signatures for two different messages created using the same OTS key, then it would become computationally feasible for that attacker to create forgeries [BH16]. As noted in [MCGREW] and [ETSI-TR-103-692], extreme care needs to be taken in order to avoid the risk that an OTS key will be reused accidentally. This is a new requirement that most developers will not be familiar with and requires careful handling.¶

Various strategies for a correct state management can be applied:¶

Implement a track record of all signatures generated by a key pair associated to a S-HBS instance. This track record may be stored outside the device which is used to generate the signature. Check the track record to prevent OTS key reuse before a new signature is released. Drop the new signature and hit your PANIC button if you spot OTS key reuse.¶
Use a S-HBS instance only for a moderate number of signatures such that it is always practical to keep a consistent track record and be able to unambiguously trace back all generated signatures.¶
Apply the state reservation strategy described in Section 5 of [MCGREW], where upcoming states are reserved in advance by the signer. In this way the number of state synchronisations between nonvolatile and volatile memory is reduced.¶

13. References

13.1. Normative References

[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>.
[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>.
[SP800208]: National Institute of Standards and Technology (NIST), "Recommendation for Stateful Hash-Based Signature Schemes", 29 October 2020, <https://doi.org/10.6028/NIST.SP.800-208>.

13.2. Informative References

[BH16]: Bruinderink, L. and S. Hülsing, "Oops, I did it again – Security of One-Time Signatures under Two-Message Attacks.", 2016, <https://eprint.iacr.org/2016/1042.pdf>.
[CNSA2.0]: National Security Agency (NSA), "Commercial National Security Algorithm Suite 2.0 (CNSA 2.0) Cybersecurity Advisory (CSA)", 7 September 2022, <https://media.defense.gov/2022/Sep/07/2003071834/-1/-1/0/CSA_CNSA_2.0_ALGORITHMS_.PDF>.
[ETSI-TR-103-692]: European Telecommunications Standards Institute (ETSI), "State management for stateful authentication mechanisms", November 2021, <https://www.etsi.org/deliver/etsi_tr/103600_103699/103692/01.01.01_60/tr_103692v010101p.pdf>.
[MCGREW]: McGrew, D., Kampanakis, P., Fluhrer, S., Gazdag, S., Butin, D., and J. Buchmann, "State Management for Hash-Based Signatures", 2 November 2016, <https://tubiblio.ulb.tu-darmstadt.de/id/eprint/101633>.
[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>.
[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>.

Internet X.509 Public Key Infrastructure: Algorithm Identifiers for HSS and XMSS

Abstract

About This Document

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Table of Contents

1. Introduction

2. Conventions and Definitions

3. Notation