Use of the SPHINCS+ Signature Algorithm in the Cryptographic Message Syntax (CMS)

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Table of Contents

1. Introduction

NOTICE: This document will be adjusted to match the SPHINCS+ specification that is published by NIST. Until that happens, just about everything in this document is likely to change.¶

This document specifies the conventions for using the SPHINCS+ hash-based signature algorithm (add reference to the NIST document here) with the Cryptographic Message Syntax (CMS) [RFC5652] signed-data content type.¶

SPHINCS+ offers three security levels. The parameters for each of the security levels were chosen to provide 128 bits of security, 192 bits of security, and 256 bits of security. A separate algorithm identifier has been assigned for SPHINCS+ at each of these security levels.¶

SPHINCS+ is a stateless hash-based signature algorithm. Other hash-based signature algorithms are stateful, including HSS/LMS [RFC8554] and XMSS [RFC8391]. Without the need for state kept by the signer, SPHINCS+ is much less fragile.¶

2. SPHINCS+ Hash-based Signature Algorithm Overview

SPHINCS+ is a hash-based signature scheme which consists of a few time signature construction, namely Forest of Random Subsets (FORS) and a hypertree. FORS signs a message with a private key. The corresponding FORS public keys are the leaves in k binary trees. The roots of these trees are hashed together to form a FORS root. SPHINCS+ uses a one-time signature scheme called WOTS+. The FORS tree roots are signed by a WOTS+ one-time signature private key. The corresponding WOTS+ public keys form the leaves in d-layers of Merkle subtrees in the SPHINCS+ hypertree. The bottom layer of that hypertree signs the FORS roots with WOTS+. The root of the bottom Merkle subtrees are then signed with WOTS+ and the corresponding WOTS+ public keys form the leaves of the next level up subtree. Subtree roots are consequently signed by their corresponding subtree layers until we reach the top subtree. The top layer subtree forms the hypertree root which is trusted at the verifier.¶

A SPHINCS+ signature consists of the FORS signature, the WOTS+ signature in each layer, and the path to the root of each subtree until the root of the hypertree is reached.¶

A SPHINCS+ signature is verified by verifying the FORS signature, the WOTS+ signatures and the path to the root of each subtree. When reaching the root of the hypertree, the signature verifies only if it hashes to the pre-trusted root of the SPHINCS+ hypertree.¶

SPHINCS+ is a stateless hash-based signature algorithm. Stateful hash-based signature schemes require that the WOTS+ private key (generated by using a state index) is never reused or the scheme loses it security. Although its security decreases, FORS which is used at the bottom of the SPHINCS+ hypertree does not collapse if the same private key used to sign two or more different messages like in stateful hash-based signature schemes. Without the need for state kept by the signer to ensure it is not reused, SPHINCS+ is much less fragile.¶

SPHINCS+ was designed to sign up to 2^64 messages and offers three security levels. The parameters of the SPHINCS+ hypertree include the security parameter, the hash function, the tree height, the number of layers of subtrees, the Winternitz parameter of WOTS+, the number of FORS trees and leaves in each. The parameters for each of the security levels were chosen to provide 128 bits of security, 192 bits of security, and 256 bits of security.¶

3. SPHINCS+ Public Key Identifier

The AlgorithmIdentifier for a SPHINCS+ public key MUST use one of the id-alg-sphincs-plus object identifiers listed below, based on the security level used to generate the SPHINCS+ hypertree. The parameters field of the AlgorithmIdentifier for the SPHINCS+ public key MUST be absent.¶

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; the certificate key usage extension MUST NOT contain other values.¶

   pk-sphincs-plus-128 PUBLIC-KEY ::= {
       IDENTIFIER id-alg-sphincs-plus-128
       KEY SPHINCS-Plus-PublicKey
       PARAMS ARE absent
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       PRIVATE-KEY SPHINCS-Plus-PrivateKey }

   pk-sphincs-plus-192 PUBLIC-KEY ::= {
       IDENTIFIER id-alg-sphincs-plus-192
       KEY SPHINCS-Plus-PublicKey
       PARAMS ARE absent
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       PRIVATE-KEY SPHINCS-Plus-PrivateKey }

   pk-sphincs-plus-256 PUBLIC-KEY ::= {
       IDENTIFIER id-alg-sphincs-plus-256
       KEY SPHINCS-Plus-PublicKey
       PARAMS ARE absent
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       PRIVATE-KEY SPHINCS-Plus-PrivateKey }

   SPHINCS-Plus-PublicKey ::= OCTET STRING

   SPHINCS-Plus-PrivateKey ::= OCTET STRING

NOTE: The values for these object identifiers will be assigned by NIST. Once assigned, they will be added to a future revision of this document.¶

The SPHINCS+ public key value is an OCTET STRING.¶

The SPHINCS+ private key value is an OCTET STRING.¶

4. Signed-data Conventions

As specified in CMS [RFC5652], 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 SPHINCS+ 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 SPHINCS+ tree, and then a message-digest attribute is constructed to contain the resulting hash value, and then the result of DER encoding the set of signed attributes, which MUST include a content-type attribute and a message-digest attribute, and then the SPHINCS+ signature is computed over the DER-encoded output. In summary:¶

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

When using SPHINCS+, the fields in the SignerInfo are used as follows:¶

digestAlgorithm:

The digestAlgorithm MUST contain the one-way hash function used to in the SPHINCS+ tree. The algorithm identifiers for [FIPS180] and [FIPS202] are repeated below for convenience.¶

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

      mda-shake256 DIGEST-ALGORITHM ::= {
        IDENTIFIER id-shake256
        PARAMS TYPE NULL ARE preferredAbsent }

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

      id-sha256 OBJECT IDENTIFIER ::= { hashalgs 1 }

      id-shake256 OBJECT IDENTIFIER ::= { hashAlgs 12 }

signatureAlgorithm:

The signatureAlgorithm MUST contain one of the the SPHINCS+ algorithm identifiers, and the algorithm parameters field MUST be absent. The algorithm identifier MUST be one of the following: id-alg-sphincs-plus-128, id-alg-sphincs-plus-192, or id-alg-sphincs-plus-256.¶

signature:

The signature contains the signature value resulting from the SPHINCS+ signing operation with the parameters associated with the selected signatureAlgorithm. The SPHINCS+ signing operation and the signature verification operation are specified in TBD.¶

5. Security Considerations

Implementations MUST protect the private keys. Compromise of the private keys may result in the ability to forge signatures.¶

When generating an SPHINCS+ key pair, an implementation MUST generate each key pair independently of all other key pairs in the SPHINCS+ hypertree.¶

A SPHINCS+ tree MUST NOT be used for more than 2^64 signing operations.¶

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, and [RFC4086] offers important guidance in this area.¶

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.¶

When computing signatures, implementations SHOULD include protections against fault injection attacks [CMP2018]. Protections against these attacks include signature verification prior to releasing the signature value to confirm that no error injected and generating the signature a few times to confirm that the same signature value is produced each time.¶

6. IANA Considerations

For the ASN.1 Module in the Appendix of this document, IANA is requested to assign an object identifier (OID) for the module identifier (TBD1). The OID for the module should be allocated in the "SMI Security for PKIX Module Identifier" registry (1.3.6.1.5.5.7.0).¶

7. Acknowledgements

Thanks to Mike Ounsworth for his careful review and constructive comments.¶

Appendix A. Appendix: ASN.1 Module

This ASN.1 Module builds upon the conventions established in [RFC5911].¶

<CODE STARTS>

SPHINCS-Plus-Module-2022
  { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)
    id-smime(16) id-mod(0) id-mod-sphincs-plus-2022(TBD1) }

DEFINITIONS IMPLICIT TAGS ::= BEGIN

EXPORTS ALL;

IMPORTS
  PUBLIC-KEY, SIGNATURE-ALGORITHM, SMIME-CAPS
    FROM AlgorithmInformation-2009  -- RFC 5911
      { 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-sphincs-plus-128 OBJECT IDENTIFIER ::= { TBD }

id-alg-sphincs-plus-192 OBJECT IDENTIFIER ::= { TBD }

id-alg-sphincs-plus-256 OBJECT IDENTIFIER ::= { TBD }

--
-- Signature Algorithm, Public Key, and Private Key
--

sa-sphincs-plus-128 SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-alg-sphincs-plus-128
    PARAMS ARE absent
    PUBLIC-KEYS { pk-sphincs-plus-128 }
    SMIME-CAPS { IDENTIFIED BY id-alg-sphincs-plus-128 } }

sa-sphincs-plus-192 SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-alg-sphincs-plus-192
    PARAMS ARE absent
    PUBLIC-KEYS { pk-sphincs-plus-192 }
    SMIME-CAPS { IDENTIFIED BY id-alg-sphincs-plus-192 } }

sa-sphincs-plus-256 SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-alg-sphincs-plus-256
    PARAMS ARE absent
    PUBLIC-KEYS { pk-sphincs-plus-256 }
    SMIME-CAPS { IDENTIFIED BY id-alg-sphincs-plus-256 } }

pk-sphincs-plus-128 PUBLIC-KEY ::= {
    IDENTIFIER id-alg-sphincs-plus-128
    KEY SPHINCS-Plus-PublicKey
    PARAMS ARE absent
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    PRIVATE-KEY SPHINCS-Plus-PrivateKey }

pk-sphincs-plus-192 PUBLIC-KEY ::= {
    IDENTIFIER id-alg-sphincs-plus-192
    KEY SPHINCS-Plus-PublicKey
    PARAMS ARE absent
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    PRIVATE-KEY SPHINCS-Plus-PrivateKey }

pk-sphincs-plus-256 PUBLIC-KEY ::= {
    IDENTIFIER id-alg-sphincs-plus-256
    KEY SPHINCS-Plus-PublicKey
    PARAMS ARE absent
    CERT-KEY-USAGE
      { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
    PRIVATE-KEY SPHINCS-Plus-PrivateKey }

SPHINCS-Plus-PublicKey ::= OCTET STRING

SPHINCS-Plus-PrivateKey ::= OCTET STRING

--
-- Expand the signature algorithm set used by CMS [RFC5911]
--

SignatureAlgorithmSet SIGNATURE-ALGORITHM ::=
    { sa-sphincs-plus-128 |
      sa-sphincs-plus-192 |
      sa-sphincs-plus-256,
      ... }

--
-- Expand the S/MIME capabilities set used by CMS [RFC5911]
--

SMimeCaps SMIME-CAPS ::=
    { sa-sphincs-plus-128.&smimeCaps |
      sa-sphincs-plus-192.&smimeCaps |
      sa-sphincs-plus-256.&smimeCaps,
      ... }

END

<CODE ENDS>

Authors' Addresses