INTERNET-DRAFT R. Housley
Intended Status: Proposed Standard Vigil Security
Expires: 24 June 2019 24 December 2018
Use of the Hash-based Signature Algorithm with
CBOR Object Signing and Encryption (COSE)
Abstract
This document specifies the conventions for using the Leighton-Micali
Signature (LMS) algorithm for digital signatures with the CBOR Object
Signing and Encryption (COSE) syntax.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. LMS Digital Signature Algorithm Overview . . . . . . . . . . . 3
3.1. Hierarchical Signature System (HSS) . . . . . . . . . . . 4
3.2. Leighton-Micali Signature (LMS) . . . . . . . . . . . . . 5
3.3. Leighton-Micali One-time Signature Algorithm (LM-OTS) . . 6
4. Hash-based Signature Algorithm Identifiers . . . . . . . . . . 7
5. Security Considerations . . . . . . . . . . . . . . . . . . . 7
5.1. Implementation Security Considerations . . . . . . . . . . 7
5.2. Algorithm Security Considerations . . . . . . . . . . . . 8
6. Operational Considerations . . . . . . . . . . . . . . . . . . 8
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 9
7.1. COSE Algorithms Registry Entry . . . . . . . . . . . . . . 9
7.2. COSE Key Types Registry Entry . . . . . . . . . . . . . . 9
8. References . . . . . . . . . . . . . . . . . . . . . . . . . . 10
8.1. Normative References . . . . . . . . . . . . . . . . . . . 10
8.2. Informative References . . . . . . . . . . . . . . . . . . 10
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . 11
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 11
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1. Introduction
Today, RSA is often used to digitally sign software updates. In
preparation for a day when RSA, DSA, and ECDSA cannot be depended
upon, a digital signature algorithm is needed that will remain secure
even if there are significant cryptoanalytic advances or a large-
scale quantum computer is invented. The hash-based digital signature
algorithm specified in [HASHSIG] is one such algorithm. The use of
hash-based signatures to protect software update distribution will
allow the deployment of software that implements new cryptosystems
even if such advances break current digital signature mechanisms.
This document specifies the conventions for using the Leighton-Micali
Signature (LMS) algorithm [HASHSIG] for digital signatures with the
CBOR Object Signing and Encryption (COSE) [RFC8152] syntax. The LMS
algorithm is one form of hash-based digital signature; it can only be
used for a fixed number of signatures. The LMS algorithm uses small
private and public keys, and it has low computational cost; however,
the signatures are quite large.
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.
3. LMS Digital Signature Algorithm Overview
This specification makes use of the hash-based signature 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].
The hash-based signature algorithm has three major components:
o Hierarchical Signature System (HSS) -- see Section 3.1;
o Leighton-Micali Signature (LMS) -- see Section 3.2; and
o Leighton-Micali One-time Signature Algorithm (LM-OTS) -- see
Section 3.3.
As implied by the name, the hash-based signature algorithm depends on
a collision-resistant hash function. The the hash-based signature
algorithm specified in [HASHSIG] currently makes use of the SHA-256
one-way hash function [SHS], but it also establishes an IANA registry
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to permit the registration of additional one-way hash functions in
the future.
3.1. Hierarchical Signature System (HSS)
The hash-based signature algorithm specified in [HASHSIG] uses a
hierarchy of trees. The Hierarchical Signature System (HSS) allows
subordinate trees to be generated when needed by the signer. By
using trees-of-trees, a very large number of nodes can be
accommodated, where each node enables a single digital signature.
Without the HSS, the generation of such a large 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 3.2.
Each signed public key is represented by the hash value at the root
of the tree, and it also contains information about the tree
structure. The signature over the public key is an LMS signature as
described in Section 3.2.
The elements of the HSS signature value for a stand-alone tree can be
summarized as:
u32str(0) ||
lms_signature /* signature of message */
The elements of the HSS signature value for a tree with Nspk levels
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], a signed_public_key is
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.
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3.2. Leighton-Micali Signature (LMS)
Each tree in the hash-based signature algorithm 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 hash-based signature algorithm 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 is the number of bytes
output by the hash function, m, which is the amount of data
associated with each node in the tree. This specification supports
only SHA-256, with m=32.
Currently, the hash-based signature algorithm supports five tree
sizes:
LMS_SHA256_M32_H5;
LMS_SHA256_M32_H10;
LMS_SHA256_M32_H15;
LMS_SHA256_M32_H20; and
LMS_SHA256_M32_H25.
The [HASHSIG] specification establishes an IANA registry to permit
the registration of additional tree sizes in the future.
An LMS signature consists of four elements: the number of the leaf
associated with the LM-OTS signature, an LM-OTS signature as
described in Section 3.3, 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
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]
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3.3. Leighton-Micali One-time Signature Algorithm (LM-OTS)
The hash-based signature algorithm depends on a one-time signature
method. This specification makes use of the Leighton-Micali One-time
Signature Algorithm (LM-OTS) [HASHSIG]. An LM-OTS has five
parameters:
n - The number of bytes output by the hash function. This
specification 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. This
specification supports only SHA-256 [SHS].
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.
ls - The number of left-shift bits used in the checksum function,
which is defined in Section 4.5 of [HASHSIG].
The values of p and ls are dependent on the choices of the parameters
n and w, as described in Appendix A of [HASHSIG].
Currently, the hash-based signature algorithm supports four LM-OTS
variants:
LMOTS_SHA256_N32_W1;
LMOTS_SHA256_N32_W2;
LMOTS_SHA256_N32_W4; and
LMOTS_SHA256_N32_W8.
The [HASHSIG] specification establishes an IANA registry to permit
the registration of additional variants in the future.
Signing involves the generation of C, which is an n-byte random
value.
The LM-OTS signature value can be summarized as:
u32str(otstype) || C || y[0] || ... || y[p-1]
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4. Hash-based Signature Algorithm Identifiers
The CBOR Object Signing and Encryption (COSE) [RFC8152] supports two
signature algorithm schemes. This specification makes use of the
signature with appendix scheme for hash-based signatures.
The signature value is a large byte string. The byte string is
designed for easy parsing, and it includes a counter and type codes
that indirectly provide all of the information that is needed to
parse the byte string during signature validation.
When using a COSE key for this algorithm, the following checks are
made:
o The 'kty' field MUST be present, and it MUST be 'HSS-LMS'.
o If the 'alg' field is present, and it MUST be 'HSS-LMS'.
o If the 'key_ops' field is present, it MUST include 'sign' when
creating a hash-based signature.
o If the 'key_ops' field is present, it MUST include 'verify'
when verifying a hash-based signature.
o If the 'kid' field is present, it MAY be used to identify the
top of the HSS tree. In [HASHSIG], this identifier is called
'I', and it is the 16-byte identifier of the LMS public key
for the tree.
5. Security Considerations
5.1. Implementation Security Considerations
Implementations must protect the private keys. Use of a hardware
security module (HSM) is one way to 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 stored in a virtual machine
environment, care must be taken to preserve confidentiality and
integrity.
When a LMS key pair is generating a LMS key pair, an implementation
must must generate the key pair and the corresponding identifier
independently of all other key pairs in the HSS tree.
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An implementation must ensure that a 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 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. [RFC4086] 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 [RFC4086]
remains important.
5.2. Algorithm Security Considerations
At Black Hat USA 2013, some researchers gave a presentation on the
current sate of public key cryptography. They said: "Current
cryptosystems depend on discrete logarithm and factoring which has
seen some major new developments in the past 6 months" [BH2013].
They encouraged preparation for a day when RSA and DSA cannot be
depended upon.
A post-quantum cryptosystem is a system that is secure against
quantum computers that have more than a trivial number of quantum
bits. It is open to conjecture when it will be feasible to build
such a machine. RSA, DSA, and ECDSA are not post-quantum secure.
The LM-OTP one-time signature, LMS, and HSS do not depend on discrete
logarithm or factoring, as a result these algorithms are considered
to be post-quantum secure.
Today, RSA is often used to digitally sign software updates. This
means that the distribution of software updates could be compromised
if a significant advance is made in factoring or a quantum computer
is invented. The use of hash-based signatures to protect software
update distribution will allow the deployment of software that
implements new cryptosystems.
6. Operational Considerations
The public key for the hash-based signature is the key at the root of
Hierarchical Signature System (HSS). In the absence of a public key
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infrastructure [RFC5280], this public key is a trust anchor, and the
number of signatures that can be generated is bounded by the size of
the overall HSS set of trees. When all of the LM-OTS signatures have
been used to produce a signature, then the establishment of a new
trust anchor is required.
To ensure that none of tree nodes are used to generate more than one
signature, the signer maintains state across different invocations of
the signing algorithm. Section 12.2 of [HASHSIG] offers some
practical implementation approaches around this statefulness. In
some of these approaches, nodes are sacrificed to ensure that none
are used more than once. As a result, the total number of signatures
that can be generated might be less than the overall HSS set of
trees.
7. IANA Considerations
IANA is requested to add entries for hash-based signatures in the
"COSE Algorithms" registry and hash-based public keys in the "COSE
Key Types" registry.
7.1. COSE Algorithms Registry Entry
The new entry in the "COSE Algorithms" registry has the following
columns:
Name: HASHSIG-HSS-LMS
Value: TBD (Value to be assigned by IANA)
Description: Hash-based digital signatures using HSS/LMS
Reference: This document (Number to be assigned by RFC Editor)
Recommended: Yes
7.2. COSE Key Types Registry Entry
The new entry in the "COSE Key Types" registry has the following
columns:
Name: HASHSIG-HSS-LMS
Value: TBD (Value to be assigned by IANA)
Description: Public key for hash-based digital signature using HSS/LMS
Reference: This document (Number to be assigned by RFC Editor)
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8. References
8.1. Normative References
[HASHSIG] McGrew, D., M. Curcio, and S. Fluhrer, "Hash-Based
Signatures", Work in progress.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, DOI
10.17487/RFC2119, March 1997, .
[RFC8152] Schaad, J., "CBOR Object Signing and Encryption (COSE)",
RFC 8152, DOI 10.17487/RFC8152, July 2017,
.
[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),
FIPS Publication 180-3: Secure Hash Standard, October
2008.
8.2. Informative References
[BH2013] Ptacek, T., T. Ritter, J. Samuel, and A. Stamos, "The
Factoring Dead: Preparing for the Cryptopocalypse", August
2013.
[LM] Leighton, T. and S. Micali, "Large provably fast and
secure digital signature schemes from secure hash
functions", U.S. Patent 5,432,852, July 1995.
[M1979] Merkle, R., "Secrecy, Authentication, and Public Key
Systems", Stanford University Information Systems
Laboratory Technical Report 1979-1, 1979.
[M1987] Merkle, R., "A Digital Signature Based on a Conventional
Encryption Function", Lecture Notes in Computer Science
crypto87, 1988.
[M1989a] Merkle, R., "A Certified Digital Signature", Lecture Notes
in Computer Science crypto89, 1990.
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[M1989b] Merkle, R., "One Way Hash Functions and DES", Lecture Notes
in Computer Science crypto89, 1990.
[PQC] Bernstein, D., "Introduction to post-quantum
cryptography", 2009.
[RFC4086] Eastlake 3rd, D., Schiller, J., and S. Crocker,
"Randomness Requirements for Security", BCP 106, RFC 4086,
DOI 10.17487/RFC4086, June 2005, .
[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,
.
Acknowledgements
Thanks to Jim Schaad and Tony Putman for their valuable review and
insights.
Author's Address
Russ Housley
Vigil Security, LLC
516 Dranesville Road
Herndon, VA 20170
USA
EMail: housley@vigilsec.com
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