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Algorithm Identifiers for HSS and XMSS for Use in the Internet X.509 Public Key InfrastructureISARA Corporation560 Westmount Rd NWaterlooOntarioN2L 0A9Canadadaniel.vangeest@isara.comCisco Systems170 West Tasman DriveSan JoseCA95134USAsfluhrer@cisco.comx509HSSXMSSAlgorithmIdentifier
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).
The Hierarchical Signature System (HSS) is described in .
The eXtended Merkle Signature Scheme (XMSS), and its multi-tree variant XMSS^MT, are described in .
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
.
Certificates conforming to 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 and repeated here for convenience. For all of the OIDs, the parameters MUST be absent.
The object identifier and public key algorithm identifier for HSS is defined in . The definitions are repeated here for reference.
The object identifier for an HSS public key is id-alg-hss-lms-hashsig:
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 .
The HSS public key's properties are defined as follows:
contains more information on the contents and format of an HSS public key.
The object identifier for an XMSS public key is id-xmss:
The XMSS public key's properties are defined as follows:
The format of an XMSS public key is is formally defined using XDR and is defined in Appendix B.3 of . In particular, the first 4 bytes represents the big-ending encoding of the XMSS algorithm type.
The object identifier for an XMSS^MT public key is id-xmssmt:
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 and is defined in Appendix C.3 of . In particular, the first 4 bytes represents the big-ending encoding of the XMSS^MT algorithm type.
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; anddigitalSignature.
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; andcRLSign.
[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.
Certificates and CRLs conforming to 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.
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:
contains more information on the contents and format of an HSS signature.
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:
The format of an XMSS signature is is formally defined using XDR and is defined in Appendix B.2 of .
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:
The format of an XMSS^MT signature is is formally defined using XDR and is defined in Appendix C.2 of .
For reference purposes, the ASN.1 syntax is presented as an ASN.1 module here.
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 is a quantum search algorithm which gives a quadratic improvement in search time to brute-force pre-image attacks. The results of show that this improvement is optimal, however 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 .
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 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).
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. 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
remains important.
Thanks for Russ Housley for the helpful suggestions.
This document uses a lot of text from similar documents ( and ) as well as . Thanks go to the authors of those documents. "Copying always makes things easier and less error prone" - .
IANA is requested to assign a module OID from the "SMI for PKIX Module Identifier" registry for the ASN.1 module in Section 5.
&RFC2119;
&RFC8391;
&RFC5280;
&RFC4506;
&I-D.mcgrew-hash-sigs;
&I-D.ietf-lamps-cms-hash-sig;
&RFC4086;
&RFC3279;
&RFC8410;
&RFC8411;
A fast quantum mechanical algorithm for database searchA note on the quantum collision and set equality problemsCost analysis of hash collisions: Will quantum computers make SHARCS obsolete?Strengths and weaknesses of quantum computingReassessing Grover's Algorithm