Internet Engineering Task Force (IETF) R. Housley
Request for Comments: 8708 Vigil Security
Category: Standards Track February 2020
ISSN: 2070-1721
Use of the HSS/LMS Hash-Based Signature Algorithm in the Cryptographic
Message Syntax (CMS)
Abstract
This document specifies the conventions for using the Hierarchical
Signature System (HSS) / Leighton-Micali Signature (LMS) hash-based
signature algorithm with the Cryptographic Message Syntax (CMS). In
addition, the algorithm identifier and public key syntax are
provided. The HSS/LMS algorithm is one form of hash-based digital
signature; it is described in RFC 8554.
Status of This Memo
This is an Internet Standards Track document.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Further information on
Internet Standards is available in Section 2 of RFC 7841.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
https://www.rfc-editor.org/info/rfc8708.
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Table of Contents
1. Introduction
1.1. ASN.1
1.2. Terminology
1.3. Motivation
2. HSS/LMS Hash-Based Signature Algorithm Overview
2.1. Hierarchical Signature System (HSS)
2.2. Leighton-Micali Signature (LMS)
2.3. Leighton-Micali One-Time Signature (LM-OTS) Algorithm
3. Algorithm Identifiers and Parameters
4. HSS/LMS Public Key Identifier
5. Signed-Data Conventions
6. Security Considerations
7. IANA Considerations
8. References
8.1. Normative References
8.2. Informative References
Appendix A. ASN.1 Module
Acknowledgements
Author's Address
1. Introduction
This document specifies the conventions for using the Hierarchical
Signature System (HSS) / Leighton-Micali Signature (LMS) hash-based
signature algorithm with the Cryptographic Message Syntax (CMS) [CMS]
signed-data content type. The LMS system provides a one-time digital
signature that is a variant of Merkle Tree Signatures (MTS). The HSS
is built on top of the LMS system to efficiently scale for a larger
numbers of signatures. The HSS/LMS algorithm is one form of hash-
based digital signature, and it is described in [HASHSIG]. The HSS/
LMS signature algorithm can only be used for a fixed number of
signing operations with a given private key, and the number of
signing operations depends upon the size of the tree. The HSS/LMS
signature algorithm uses small public keys, and it has low
computational cost; however, the signatures are quite large. The
HSS/LMS private key can be very small when the signer is willing to
perform additional computation at signing time; alternatively, the
private key can consume additional memory and provide a faster
signing time. The HSS/LMS signatures [HASHSIG] are currently defined
to exclusively use SHA-256 [SHS].
1.1. ASN.1
CMS values are generated using ASN.1 [ASN1-B], using the Basic
Encoding Rules (BER) and the Distinguished Encoding Rules (DER)
[ASN1-E].
1.2. Terminology
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.
1.3. Motivation
Recent advances in cryptanalysis [BH2013] and progress in the
development of quantum computers [NAS2019] pose a threat to widely
deployed digital signature algorithms. As a result, there is a need
to prepare for a day when cryptosystems such as RSA and DSA that
depend on discrete logarithms and factoring cannot be depended upon.
If large-scale quantum computers are ever built, these computers will
be able to break many of the public key cryptosystems currently in
use. A post-quantum cryptosystem [PQC] is a system that is secure
against quantum computers that have more than a trivial number of
quantum bits (qubits). It is open to conjecture when it will be
feasible to build such computers; however, RSA, DSA, Elliptic Curve
Digital Signature Algorithm (ECDSA), and Edwards-curve Digital
Signature Algorithm (EdDSA) are all vulnerable if large-scale quantum
computers are ever developed.
Since the HSS/LMS signature algorithm does not depend on the
difficulty of discrete logarithms or factoring, the HSS/LMS signature
algorithm is considered to be post-quantum secure. One use of post-
quantum-secure signatures is the protection of software updates,
perhaps using the format described in [FWPROT], to enable deployment
of software that implements new cryptosystems.
2. HSS/LMS Hash-Based Signature Algorithm Overview
Merkle Tree Signatures (MTS) are a method for signing a large but
fixed number of messages. An MTS system depends on a one-time
signature method and a collision-resistant hash function.
This specification makes use of the hash-based algorithm specified in
[HASHSIG], which is the Leighton and Micali adaptation [LM] of the
original Lamport-Diffie-Winternitz-Merkle one-time signature system
[M1979] [M1987] [M1989a] [M1989b].
As implied by the name, the hash-based signature algorithm depends on
a collision-resistant hash function. The hash-based signature
algorithm specified in [HASHSIG] uses only the SHA-256 one-way hash
function [SHS], but it establishes an IANA registry [IANA-LMS] to
permit the registration of additional one-way hash functions in the
future.
2.1. Hierarchical Signature System (HSS)
The MTS system specified in [HASHSIG] uses a hierarchy of trees. The
N-time Hierarchical Signature System (HSS) allows subordinate trees
to be generated when needed by the signer. Otherwise, generation of
the entire tree might take weeks or longer.
An HSS signature as specified in [HASHSIG] carries the number of
signed public keys (Nspk), followed by that number of signed public
keys, followed by the LMS signature as described in Section 2.2. The
public key for the topmost LMS tree is the public key of the HSS
system. The LMS private key in the parent tree signs the LMS public
key in the child tree, and the LMS private key in the bottom-most
tree signs the actual message. The signature over the public key and
the signature over the actual message are LMS signatures as described
in Section 2.2.
The elements of the HSS signature value for a standalone tree (a top
tree with no children) can be summarized as:
u32str(0) ||
lms_signature /* signature of message */
where, u32str() and || are used as defined in [HASHSIG].
The elements of the HSS signature value for a tree with Nspk signed
public keys can be summarized as:
u32str(Nspk) ||
signed_public_key[0] ||
signed_public_key[1] ||
...
signed_public_key[Nspk-2] ||
signed_public_key[Nspk-1] ||
lms_signature /* signature of message */
where, as defined in Section 3.3 of [HASHSIG], the signed_public_key
structure contains the lms_signature over the public key, followed by
the public key itself. Note that Nspk is the number of levels in the
hierarchy of trees minus 1.
2.2. Leighton-Micali Signature (LMS)
Each tree in the system specified in [HASHSIG] uses the Leighton-
Micali Signature (LMS) system. LMS systems have two parameters. The
first parameter is the height of the tree, h, which is the number of
levels in the tree minus one. The [HASHSIG] specification supports
five values for this parameter: h=5, h=10, h=15, h=20, and h=25.
Note that there are 2^h leaves in the tree. The second parameter, m,
is the number of bytes output by the hash function, and it is the
amount of data associated with each node in the tree. The [HASHSIG]
specification supports only the SHA-256 hash function [SHS], with
m=32. As a result, the [HASHSIG] specification supports five tree
sizes; they are identified as:
* LMS_SHA256_M32_H5
* LMS_SHA256_M32_H10
* LMS_SHA256_M32_H15
* LMS_SHA256_M32_H20
* LMS_SHA256_M32_H25
The [HASHSIG] specification establishes an IANA registry [IANA-LMS]
to permit the registration of additional hash functions and
additional tree sizes in the future.
As specified in [HASHSIG], the LMS public key consists of four
elements: the lms_algorithm_type from the list above, the otstype to
identify the Leighton-Micali One-Time Signature (LM-OTS) type as
discussed in Section 2.3, the private key identifier (I) as described
in Section 5.3 of [HASHSIG], and the m-byte string associated with
the root node of the tree (T[1]).
The LMS public key can be summarized as:
u32str(lms_algorithm_type) || u32str(otstype) || I || T[1]
As specified in [HASHSIG], an LMS signature consists of four
elements: the number of the leaf (q) associated with the LM-OTS
signature value, an LM-OTS signature value as described in
Section 2.3, a typecode indicating the particular LMS algorithm, and
an array of values that is associated with the path through the tree
from the leaf associated with the LM-OTS signature value to the root.
The array of values contains the siblings of the nodes on the path
from the leaf to the root but does not contain the nodes on the path
itself. The array for a tree with height h will have h values. The
first value is the sibling of the leaf, the next value is the sibling
of the parent of the leaf, and so on up the path to the root.
The four elements of the LMS signature value can be summarized as:
u32str(q) ||
ots_signature ||
u32str(type) ||
path[0] || path[1] || ... || path[h-1]
2.3. Leighton-Micali One-Time Signature (LM-OTS) Algorithm
Merkle Tree Signatures (MTS) depend on a one-time signature method,
and [HASHSIG] specifies the use of the LM-OTS, which has five
parameters:
n: The length in bytes of the hash function output. [HASHSIG]
supports only SHA-256 [SHS], with n=32.
H: A preimage-resistant hash function that accepts byte strings of
any length and returns an n-byte string.
w: The width in bits of the Winternitz coefficients. [HASHSIG]
supports four values for this parameter: w=1, w=2, w=4, and w=8.
p: The number of n-byte string elements that make up the LM-OTS
signature value.
ls: The number of bits that are left-shifted in the final step of
the checksum function, which is defined in Section 4.4 of
[HASHSIG].
The values of p and ls are dependent on the choices of the parameters
n and w, as described in Appendix B of [HASHSIG].
The [HASHSIG] specification supports four LM-OTS variants:
* LMOTS_SHA256_N32_W1
* LMOTS_SHA256_N32_W2
* LMOTS_SHA256_N32_W4
* LMOTS_SHA256_N32_W8
The [HASHSIG] specification establishes an IANA registry [IANA-LMS]
to permit the registration of additional variants in the future.
Signing involves the generation of C, an n-byte random value.
The LM-OTS signature value can be summarized as the identifier of the
LM-OTS variant, the random value, and a sequence of hash values (y[0]
through y[p-1]) that correspond to the elements of the public key, as
described in Section 4.5 of [HASHSIG]:
u32str(otstype) || C || y[0] || ... || y[p-1]
3. Algorithm Identifiers and Parameters
The algorithm identifier for an HSS/LMS hash-based signature is:
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 }
When this object identifier is used for an HSS/LMS signature, the
AlgorithmIdentifier parameters field MUST be absent (that is, the
parameters are not present, and the parameters are not set to NULL).
The signature value is a large OCTET STRING, as described in
Section 2 of this document. The signature format is designed for
easy parsing. The HSS, LMS, and LM-OTS components of the signature
value each include a counter and a typecode that indirectly provide
all of the information that is needed to parse the value during
signature validation.
The signature value identifies the hash function used in the HSS/LMS
tree. [HASHSIG] uses only the SHA-256 hash function [SHS], but it
establishes an IANA registry [IANA-LMS] to permit the registration of
additional hash functions in the future.
4. HSS/LMS Public Key Identifier
The AlgorithmIdentifier for an HSS/LMS public key uses the id-alg-
hss-lms-hashsig object identifier, and the parameters field 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; however, it MUST NOT contain other values.
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
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 version of the document that
became [HASHSIG].
The public key value is an OCTET STRING. Like the signature format,
it is designed for easy parsing. The value is the number of levels
in the public key, L, followed by the LMS public key.
The HSS/LMS public key value can be described as:
u32str(L) || lms_public_key
Note that the public key for the topmost LMS tree is the public key
of the HSS system. When L=1, the HSS system is a single tree.
5. Signed-Data Conventions
As specified in [CMS], 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 HSS/LMS 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 HSS/LMS tree, then a message-digest attribute is constructed
with the hash of the content, and then the HSS/LMS signature is
computed over the DER-encoded set of signed attributes (which MUST
include a content-type attribute and a message-digest attribute). In
summary:
IF (signed attributes are absent)
THEN HSS_LMS_Sign(content)
ELSE message-digest attribute = Hash(content);
HSS_LMS_Sign(DER(SignedAttributes))
When using [HASHSIG], the fields in the SignerInfo are used as
follows:
* digestAlgorithm MUST contain the one-way hash function used in the
HSS/LMS tree. In [HASHSIG], SHA-256 is the only supported hash
function, but other hash functions might be registered in the
future. For convenience, the AlgorithmIdentifier for SHA-256 from
[PKIXASN1] is repeated here:
mda-sha256 DIGEST-ALGORITHM ::= {
IDENTIFIER id-sha256
PARAMS TYPE NULL ARE preferredAbsent }
id-sha256 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithms(4) hashalgs(2) 1 }
* signatureAlgorithm MUST contain id-alg-hss-lms-hashsig, and the
algorithm parameters field MUST be absent.
* signature contains the single HSS signature value resulting from
the signing operation as specified in [HASHSIG].
6. 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 a 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 in a virtual machine environment, failed writes,
virtual machine snapshotting or cloning, and other operational
concerns must be considered to ensure confidentiality and integrity.
When generating an LMS key pair, an implementation MUST generate each
key pair independently of all other key pairs in the HSS tree.
An implementation MUST ensure that an LM-OTS private key is used to
generate a signature only one time and ensure that it cannot be used
for any other purpose.
The generation of private keys relies on random numbers. The use of
inadequate pseudorandom 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.
The generation of hash-based signatures also depends on random
numbers. While the consequences of an inadequate pseudorandom number
generator (PRNG) to generate these values is much less severe than in
the generation of private keys, the guidance in [RFC4086] remains
important.
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.
7. IANA Considerations
In the "SMI Security for S/MIME Module Identifier
(1.2.840.113549.1.9.16.0)" registry, IANA has updated the reference
for value 64 to point to this document.
In the "SMI Security for S/MIME Algorithms (1.2.840.113549.1.9.16.3)"
registry, IANA has updated the description for value 17 to "id-alg-
hss-lms-hashsig" and updated the reference to point to this document.
IANA has also added the following note to the "SMI Security for
S/MIME Algorithms (1.2.840.113549.1.9.16.3)" registry:
Value 17, "id-alg-hss-lms-hashsig", is also referred to as "id-
alg-mts-hashsig".
8. References
8.1. Normative References
[ASN1-B] ITU-T, "Information technology -- Abstract Syntax Notation
One (ASN.1): Specification of basic notation",
ITU-T Recommendation X.680, August 2015.
[ASN1-E] ITU-T, "Information technology -- ASN.1 encoding rules:
Specification of Basic Encoding Rules (BER), Canonical
Encoding Rules (CER) and Distinguished Encoding Rules
(DER)", ITU-T Recommendation X.690, August 2015.
[CMS] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
RFC 5652, DOI 10.17487/RFC5652, September 2009,
.
[HASHSIG] McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali
Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554,
April 2019, .
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
[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,
.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, .
[SHS] National Institute of Standards and Technology (NIST),
"Secure Hash Standard (SHS)", FIPS PUB 180-4,
DOI 10.6028/NIST.FIPS.180-4, August 2015,
.
8.2. Informative References
[BH2013] Ptacek, T., Ritter, T., Samuel, J., and A. Stamos, "The
Factoring Dead: Preparing for the Cryptopocalypse", August
2013, .
[CMSASN1] 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,
.
[CMSASN1U] Schaad, J. and S. Turner, "Additional New ASN.1 Modules
for the Cryptographic Message Syntax (CMS) and the Public
Key Infrastructure Using X.509 (PKIX)", RFC 6268,
DOI 10.17487/RFC6268, July 2011,
.
[FWPROT] Housley, R., "Using Cryptographic Message Syntax (CMS) to
Protect Firmware Packages", RFC 4108,
DOI 10.17487/RFC4108, August 2005,
.
[IANA-LMS] IANA, "Leighton-Micali Signatures (LMS)",
.
[LM] Leighton, T. and S. Micali, "Large provably fast and
secure digital signature schemes based on secure hash
functions", U.S. Patent 5,432,852, July 1995.
[M1979] Merkle, R., "Secrecy, Authentication, and Public Key
Systems", Technical Report No. 1979-1, Information Systems
Laboratory, Stanford University, 1979.
[M1987] Merkle, R., "A Digital Signature Based on a Conventional
Encryption Function", Advances in Cryptology -- CRYPTO '87
Proceedings, Lecture Notes in Computer Science Vol. 293,
DOI 10.1007/3-540-48184-2_32, 1988,
.
[M1989a] Merkle, R., "A Certified Digital Signature", Advances in
Cryptology -- CRYPTO '89 Proceedings, Lecture Notes in
Computer Science Vol. 435, DOI 10.1007/0-387-34805-0_21,
1990, .
[M1989b] Merkle, R., "One Way Hash Functions and DES", Advances in
Cryptology -- CRYPTO '89 Proceedings, Lecture Notes in
Computer Science Vol. 435, DOI 10.1007/0-387-34805-0_40,
1990, .
[NAS2019] National Academies of Sciences, Engineering, and Medicine,
"Quantum Computing: Progress and Prospects", The National
Academies Press, DOI 10.17226/25196, 2019,
.
[PKIXASN1] Hoffman, P. and J. Schaad, "New ASN.1 Modules for the
Public Key Infrastructure Using X.509 (PKIX)", RFC 5912,
DOI 10.17487/RFC5912, June 2010,
.
[PQC] Bernstein, D., "Introduction to post-quantum
cryptography", DOI 10.1007/978-3-540-88702-7_1, 2009,
.
[RFC4086] Eastlake 3rd, D., Schiller, J., and S. Crocker,
"Randomness Requirements for Security", BCP 106, RFC 4086,
DOI 10.17487/RFC4086, June 2005,
.
Appendix A. ASN.1 Module
```
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) }
DEFINITIONS IMPLICIT TAGS ::= BEGIN
EXPORTS ALL;
IMPORTS
PUBLIC-KEY, SIGNATURE-ALGORITHM, SMIME-CAPS
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) } ;
--
-- Object Identifiers
--
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-mts-hashsig OBJECT IDENTIFIER ::= id-alg-hss-lms-hashsig
--
-- Signature Algorithm and Public Key
--
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 } }
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
--
-- Expand the signature algorithm set used by CMS [CMSASN1U]
--
SignatureAlgorithmSet SIGNATURE-ALGORITHM ::=
{ sa-HSS-LMS-HashSig, ... }
--
-- Expand the S/MIME capabilities set used by CMS [CMSASN1]
--
SMimeCaps SMIME-CAPS ::=
{ sa-HSS-LMS-HashSig.&smimeCaps, ... }
END
``````
Acknowledgements
Many thanks to Joe Clarke, Roman Danyliw, Scott Fluhrer, Jonathan
Hammell, Ben Kaduk, Panos Kampanakis, Barry Leiba, John Mattsson, Jim
Schaad, Sean Turner, Daniel Van Geest, and Dale Worley for their
careful review and comments.
Author's Address
Russ Housley
Vigil Security, LLC
516 Dranesville Road
Herndon, VA 20170
United States of America
Email: housley@vigilsec.com
```