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

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Table of Contents

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 3.¶

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.¶

3. 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.¶

4. Algorithm Identifiers and Parameters

In this document, we define new OIDs for identifying the different stateful hash-based signature algorithms. An additional OID is defined in [I-D.draft-ietf-lamps-rfc8708bis] and repeated here for convenience. For all of the OIDs, the parameters MUST be absent.¶

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 ::= {
   TBD }

id-alg-xmssmt-hashsig  OBJECT IDENTIFIER ::= {
   TBD }

5. Public Key Identifiers

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.¶

[RFC8554] and [RFC8391] define the raw octet string encodings of the public keys used in this document. When used in a SubjectPublicKeyInfo type, the subjectPublicKey BIT STRING contains the raw octet string encodings of the public keys.¶

This document defines ASN.1 OCTET STRING types for encoding the public keys when not used in a SubjectPublicKeyInfo. The OCTET STRING is mapped to a subjectPublicKey (a value of type BIT STRING) as follows: the most significant bit of the OCTET STRING value becomes the most significant bit of the BIT STRING value, and so on; the least significant bit of the OCTET STRING becomes the least significant bit of the BIT STRING.¶

pk-HSS-LMS-HashSig PUBLIC-KEY ::= {
   IDENTIFIER id-alg-hss-lms-hashsig
   -- KEY no ASN.1 wrapping --
   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 no ASN.1 wrapping --
   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 no ASN.1 wrapping --
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

XMSSMT-HashSig-PublicKey ::= OCTET STRING

6. Key Usage Bits

The intended application for the key is indicated in the keyUsage certificate extension [RFC5280]. When one of the AlgorithmIdentifiers specified in this document appears in the SubjectPublicKeyInfo field of a certification authority (CA) X.509 certificate [RFC5280], the certificate key usage extension MUST contain at least one of the following values: digitalSignature, nonRepudiation, keyCertSign, or cRLSign. However, it MUST NOT contain other values.¶

When one of these AlgorithmIdentifiers appears in the SubjectPublicKeyInfo field of an end entity X.509 certificate [RFC5280], the certificate key usage extension MUST contain at least one of the following values: digitalSignature or nonRepudiation. 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 [I-D.draft-ietf-lamps-rfc8708bis].¶

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.¶

When the signature algorithm identifiers described in this document are used to create a signature on a message, no digest algorithm is applied to the message before signing. That is, the full data to be signed is signed rather than a digest of the data.¶

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.¶

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 }

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

id-alg-xmss-hashsig  OBJECT IDENTIFIER ::= {
   TBD }

XMSS-HashSig-Signature ::= OCTET STRING

id-alg-xmssmt-hashsig  OBJECT IDENTIFIER ::= {
   TBD }

XMSSMT-HashSig-Signature ::= OCTET STRING

8. Key Generation

The key generation for XMSS and XMSS^MT 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].¶

X509-SHBS-2024 -- TBD - IANA assigned module OID
  { iso(1) identified-organization(3) dod(6) internet(1) security(5)
    mechanisms(5) pkix(7) id-mod(0) id-mod-x509-shbs-01(TBD) }

DEFINITIONS IMPLICIT TAGS ::= BEGIN

EXPORTS ALL;

IMPORTS
  PUBLIC-KEY, SIGNATURE-ALGORITHM
    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) }

  sa-HSS-LMS-HashSig, pk-HSS-LMS-HashSig
    FROM MTS-HashSig-2013
      { 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) };

--
-- Object Identifiers
--

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

id-alg-xmss-hashsig  OBJECT IDENTIFIER ::= {
   TBD }

id-alg-xmssmt-hashsig  OBJECT IDENTIFIER ::= {
   TBD }

--
-- Signature Algorithms and Public Keys
--

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

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-XMSS-HashSig PUBLIC-KEY ::= {
   IDENTIFIER id-alg-xmss-hashsig
   -- KEY no ASN.1 wrapping --
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

pk-XMSSMT-HashSig PUBLIC-KEY ::= {
   IDENTIFIER id-alg-xmssmt-hashsig
   -- KEY no ASN.1 wrapping --
   PARAMS ARE absent
   CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign } }

--
-- Public Key (pk-) Algorithms
--
PublicKeys PUBLIC-KEY ::= {
   -- This expands PublicKeys from RFC 5912
   pk-HSS-LMS-HashSig |
   pk-XMSS-HashSig |
   pk-XMSSMT-HashSig,
   ...
}

--
-- Signature Algorithms (sa-)
--
SignatureAlgs SIGNATURE-ALGORITHM ::= {
   -- This expands SignatureAlgorithms from RFC 5912
   sa-HSS-LMS-HashSig |
   sa-XMSS-HashSig |
   sa-XMSSMT-HashSig,
   ...
}

END

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.¶

11. Backup and Restore Management

Certificate Authorities have high demands in order to ensure the availability of signature generation throughout the validity period of signing key pairs.¶

Usual backup and restore strategies when using a stateless signature scheme (e.g. SLH-DSA) are to duplicate private keying material and to operate redundant signing devices or to store and safeguard a copy of the private keying material such that it can be used to set up a new signing device in case of technical difficulties.¶

For S-HBS such straightforward backup and restore strategies will lead to OTS reuse with high probability as a correct state management is not guaranteed. Strategies for maintaining availability and keeping a correct state are described in Section 7 of [SP800208].¶

12. 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 9.¶

Acknowledgments

Thanks for Russ Housley and Panos Kampanakis for helpful suggestions.¶

This document uses a lot of text from similar documents [SP800208], ([RFC3279] and [RFC8410]) as well as [I-D.draft-ietf-lamps-rfc8708bis]. Thanks go to the authors of those documents. "Copying always makes things easier and less error prone" - [RFC8411].¶

Authors' Addresses