Crypto Forum Research Group S. Fluhrer
Internet-Draft Cisco Systems
Intended status: Informational Q. Dang
Expires: September 20, 2020 NIST
March 19, 2020
Additional Parameter sets for LMS Hash-Based Signatures
draft-fluhrer-lms-more-parm-sets-01
Abstract
This note extends LMS (RFC 8554) by defining parameter sets by
including additional hash functions. Hese include hash functions
that result in signatures with significantly smaller than the
signatures using the current parameter sets, and should have
sufficient security.
This document is a product of the Crypto Forum Research Group (CFRG)
in the IRTF.
Status of This Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Disclaimer . . . . . . . . . . . . . . . . . . . . . . . 2
2. Conventions Used In This Document . . . . . . . . . . . . . . 3
3. Additional Hash Function Definitions . . . . . . . . . . . . 3
3.1. 192 bit Hash Function based on SHA256 . . . . . . . . . . 3
3.2. 256 bit Hash Function based on SHAKE256 . . . . . . . . . 3
3.3. 192 bit Hash Function based on SHAKE256 . . . . . . . . . 4
4. Additional LM-OTS Parameter Sets . . . . . . . . . . . . . . 4
5. Additional LM Parameter Sets . . . . . . . . . . . . . . . . 5
6. Comparisons of 192 bit and 256 bit parameter sets . . . . . . 6
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 7
8. Security Considerations . . . . . . . . . . . . . . . . . . . 9
8.1. Note on the version of SHAKE . . . . . . . . . . . . . . 10
9. References . . . . . . . . . . . . . . . . . . . . . . . . . 10
9.1. Normative References . . . . . . . . . . . . . . . . . . 10
9.2. Informative References . . . . . . . . . . . . . . . . . 11
Appendix A. Test Cases . . . . . . . . . . . . . . . . . . . . . 11
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 11
1. Introduction
Stateful hash based signatures have small private and public keys,
are efficient to compute, and are believed to have excellent
security. One disadvantage is that the signatures they produce tend
to be somewhat large (possibly 1k - 4kbytes). What this draft
explores are a set of parameter sets to the LMS (RFC8554) stateful
hash based signature method that reduce the size of the signature
significantly.
1.1. Disclaimer
This document is not intended as legal advice. Readers are advised
to consult with their own legal advisers if they would like a legal
interpretation of their rights.
The IETF policies and processes regarding intellectual property and
patents are outlined in [RFC3979] and [RFC4879] and at
https://datatracker.ietf.org/ipr/about.
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2. Conventions Used In This Document
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 [RFC2119].
3. Additional Hash Function Definitions
3.1. 192 bit Hash Function based on SHA256
This document defines a SHA-2 based hash function with a 192 bit
output. As such, we define SHA256/192 as a truncated version of
SHA-256 [FIPS180]. That is, it is the result of performing a SHA-256
operation to a message, and then omitting the final 64 bits of the
output. It is the same procedure used to define SHA-224, except that
we use the SHA-256 IV (rather than using one dedicated to
SHA256/192), and you truncate 64 bits, rather than 32.
The following test vector may illustrate this:
SHA256("abc") = ba7816bf 8f01cfea 414140de 5dae2223
b00361a3 96177a9c b410ff61 f20015ad
SHA256/192("abc") = ba7816bf 8f01cfea 414140de 5dae2223
b00361a3 96177a9c
We use the same IV as the untruncated SHA-256, rather than defining a
distinct one, so that we can use a standard SHA-256 hash
implementation without modification. In addition, the fact that you
get partial knowledge of the SHA-256 hash of a message by examining
the SHA256/192 hash of the same message is not a concern for this
application. Each message that is hashed is randomized. Any message
being signed includes the C randomizer which varies per message; in
addition, all hashes include the I identifier, which varies depending
on the public key. Therefore, signing the same message by SHA256 and
by SHA256/192 will not result in the same value being hashed, and so
the latter hash value is not a prefix of the former one.
3.2. 256 bit Hash Function based on SHAKE256
This document defines a SHAKE-based hash function with a 256 bit
output. As such, we define SHAKE256-256 as a hash where you submit
the preimage to the SHAKE256 XOF, with the output being 256 bits, see
FIPS 202 [FIPS202] for more detail.
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3.3. 192 bit Hash Function based on SHAKE256
This document defines a SHAKE-based hash function with a 192 bit
output. As such, we define SHAKE256-192 as a hash where you submit
the preimage to the SHAKE-256 XOF, with the output being 192 bits,
see FIPS 202 [FIPS202] for more detail.
4. Additional LM-OTS Parameter Sets
Here is a table with the LM-OTS parameters defined that use the above
hashes:
+---------------------+--------------+----+---+-----+----+-------+
| Parameter Set Name | H | n | w | p | ls | id |
+---------------------+--------------+----+---+-----+----+-------+
| LMOTS_SHA256_N24_W1 | SHA256/192 | 24 | 1 | 200 | 8 | TBD1 |
| | | | | | | |
| LMOTS_SHA256_N24_W2 | SHA256/192 | 24 | 2 | 101 | 6 | TBD2 |
| | | | | | | |
| LMOTS_SHA256_N24_W4 | SHA256/192 | 24 | 4 | 51 | 4 | TBD3 |
| | | | | | | |
| LMOTS_SHA256_N24_W8 | SHA256/192 | 24 | 8 | 26 | 0 | TBD4 |
| | | | | | | |
| LMOTS_SHAKE_N32_W1 | SHAKE256-256 | 32 | 1 | 265 | 7 | TBD5 |
| | | | | | | |
| LMOTS_SHAKE_N32_W2 | SHAKE256-256 | 32 | 2 | 133 | 6 | TBD6 |
| | | | | | | |
| LMOTS_SHAKE_N32_W4 | SHAKE256-256 | 32 | 4 | 67 | 4 | TBD7 |
| | | | | | | |
| LMOTS_SHAKE_N32_W8 | SHAKE256-256 | 32 | 8 | 34 | 0 | TBD8 |
| | | | | | | |
| LMOTS_SHAKE_N24_W1 | SHAKE256-192 | 24 | 1 | 200 | 8 | TBD9 |
| | | | | | | |
| LMOTS_SHAKE_N24_W2 | SHAKE256-192 | 24 | 2 | 101 | 6 | TBD10 |
| | | | | | | |
| LMOTS_SHAKE_N24_W4 | SHAKE256-192 | 24 | 4 | 51 | 4 | TBD11 |
| | | | | | | |
| LMOTS_SHAKE_N24_W8 | SHAKE256-192 | 24 | 8 | 26 | 0 | TBD12 |
+---------------------+--------------+----+---+-----+----+-------+
Table 1
The id is the IANA-defined identifier used to denote this specific
parameter set, and which appears in both public keys and signatures.
The SHA256_N24, SHAKE_N32, SHAKE_N24 in the parameter set name denote
the SHA256/192, SHAKE256-256 and SHAKE256-192 hash functions defined
in Section 3.
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Remember that the C message randomizer (which is included in the
signature) is the size of the hash n, and so it shrinks from 32 bytes
to 24 bytes for those the parameter sets that use either SHA256/192
or SHAKE256-192.
5. Additional LM Parameter Sets
Here is a table with the LM parameters defined that use SHA259/192,
SHAKE256-256 and SHAKE256-192 hash functions:
+--------------------+--------------+----+----+-------+
| Parameter Set Name | H | m | h | id |
+--------------------+--------------+----+----+-------+
| LMS_SHA256_M24_H5 | SHA256/192 | 24 | 5 | TBD13 |
| | | | | |
| LMS_SHA256_M24_H10 | SHA256/192 | 24 | 10 | TBD14 |
| | | | | |
| LMS_SHA256_M24_H15 | SHA256/192 | 24 | 15 | TBD15 |
| | | | | |
| LMS_SHA256_M24_H20 | SHA256/192 | 24 | 20 | TBD16 |
| | | | | |
| LMS_SHA256_M24_H25 | SHA256/192 | 24 | 25 | TBD17 |
| | | | | |
| LMS_SHAKE_M32_H5 | SHAKE256-256 | 32 | 5 | TBD18 |
| | | | | |
| LMS_SHAKE_M32_H10 | SHAKE256-256 | 32 | 10 | TBD19 |
| | | | | |
| LMS_SHAKE_M32_H15 | SHAKE256-256 | 32 | 15 | TBD20 |
| | | | | |
| LMS_SHAKE_M32_H20 | SHAKE256-256 | 32 | 20 | TBD21 |
| | | | | |
| LMS_SHAKE_M32_H25 | SHAKE256-256 | 32 | 25 | TBD22 |
| | | | | |
| LMS_SHAKE_M24_H5 | SHAKE256-192 | 24 | 5 | TBD23 |
| | | | | |
| LMS_SHAKE_M24_H10 | SHAKE256-192 | 24 | 10 | TBD24 |
| | | | | |
| LMS_SHAKE_M24_H15 | SHAKE256-192 | 24 | 15 | TBD25 |
| | | | | |
| LMS_SHAKE_M24_H20 | SHAKE256-192 | 24 | 20 | TBD26 |
| | | | | |
| LMS_SHAKE_M24_H25 | SHAKE256-192 | 24 | 25 | TBD27 |
+--------------------+--------------+----+----+-------+
Table 2
The id is the IANA-defined identifier used to denote this specific
parameter set, and which appears in both public keys and signatures.
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The SHA256_M24, SHAKE_M32, SHAKE_M24 in the parameter set name denote
the SHA256/192, SHAKE256-256 and SHAKE256-192 hash functions defined
in Section 3.
6. Comparisons of 192 bit and 256 bit parameter sets
Switching to a 192 bit hash affects the signature size, the
computation time, and the security strength.
The major reason for considering these truncated parameter sets is
that they cause the signatures to shrink considerably.
Here is a table that gives the space used by both the 256 bit
parameter sets and the 192 bit parameter sets, for a range of
plausible Winternitz parameters and tree heights
+---------+------------+--------------+--------------+
| ParmSet | Winternitz | 256 bit hash | 192 bit hash |
+---------+------------+--------------+--------------+
| 15 | 4 | 2672 | 1624 |
| | | | |
| 15 | 8 | 1616 | 1024 |
| | | | |
| 20 | 4 | 2832 | 1744 |
| | | | |
| 20 | 8 | 1776 | 1144 |
| | | | |
| 15/10 | 4 | 5236 | 3172 |
| | | | |
| 15/10 | 8 | 3124 | 1972 |
| | | | |
| 15/15 | 4 | 5396 | 3292 |
| | | | |
| 15/15 | 8 | 3284 | 2092 |
| | | | |
| 20/10 | 4 | 5396 | 3292 |
| | | | |
| 20/10 | 8 | 3284 | 2092 |
| | | | |
| 20/15 | 4 | 5556 | 3412 |
| | | | |
| 20/15 | 8 | 3444 | 2212 |
+---------+------------+--------------+--------------+
Table 3
ParmSet: this is the height of the Merkle tree(s); parameter sets
listed as a single integer have L=1, and consist a single Merkle tree
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of that height; parameter sets with L=2 are listed as x/y, with x
being the height of the top level Merkle tree, and y being the bottom
level.
Winternitz: this is the Winternitz parameter used (for the tests that
use multiple trees, this applies to all of them).
256 bit hash: the size in bytes of a signature, assuming that a 256
bit hash is used in the signature (either SHA256 or SHAKE256/256).
192 bit hash: the size in bytes of a signature, assuming that a 192
bit hash is used in the signature (either SHA256/192 or
SHAKE256/192).
An examination of the signature sizes show that the 192 bit
parameters consistently give a 35% - 40% reduction in the size of the
signature in comparison with the 256 bit parameters.
In addition, for SHA256-192, there is a smaller (circa 20%) reduction
in the amount of computation required for a signature operation with
a 192 bit hash. The SHAKE256-192 signatures may have either a faster
or slower computation, depending on the implementation speed of SHAKE
versus SHA-256 hashes.
The SHAKE256-256 based parameter sets give no space advantage (or
disadvantage) over the existing SHA256-based parameter sets; any
performance delta would depend solely on the implementation and
whether they can generate SHAKE hashes faster than SHA-256 ones.
7. IANA Considerations
[TO BE REMOVED: The entries from Section 4, namely
LMOTS_SHA256_N24_W1 through LMOTS_SHAKE_N24_W8 , should be inserted
into https://www.iana.org/assignments/leighton-micali-signatures/
leighton-micali-signatures.xhtml#lm-ots-signatures ]
[TO BE REMOVED: The entries from Section 5, namely LMS_SHA256_M24_H5
through LMS_SHAKE_M24_H25 should be inserted into
https://www.iana.org/assignments/leighton-micali-signatures/leighton-
micali-signatures.xhtml#leighton-micali-signatures-1 ]
Until IANA assigns the codepoints, we will (for testing purposes
only) use the following private use code points to do any necessary
interoperability testing. Such an implementation must change to the
IANA-assigned code points when they become available.
+---------------------+---------------------+
| Parameter Set Name | Temporary Codepoint |
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+---------------------+---------------------+
| LMOTS_SHA256_N24_W1 | 0xE0000001 |
| | |
| LMOTS_SHA256_N24_W2 | 0xE0000002 |
| | |
| LMOTS_SHA256_N24_W4 | 0xE0000003 |
| | |
| LMOTS_SHA256_N24_W8 | 0xE0000004 |
| | |
| LMOTS_SHAKE_N32_W1 | 0xE0000005 |
| | |
| LMOTS_SHAKE_N32_W2 | 0xE0000006 |
| | |
| LMOTS_SHAKE_N32_W4 | 0xE0000007 |
| | |
| LMOTS_SHAKE_N32_W8 | 0xE0000008 |
| | |
| LMOTS_SHAKE_N24_W1 | 0xE0000009 |
| | |
| LMOTS_SHAKE_N24_W2 | 0xE000000A |
| | |
| LMOTS_SHAKE_N24_W4 | 0xE000000B |
| | |
| LMOTS_SHAKE_N24_W8 | 0xE000000C |
| | |
| LMS_SHA256_M24_H5 | 0xE0000001 |
| | |
| LMS_SHA256_M24_H10 | 0xE0000002 |
| | |
| LMS_SHA256_M24_H15 | 0xE0000003 |
| | |
| LMS_SHA256_M24_H20 | 0xE0000004 |
| | |
| LMS_SHA256_M24_H25 | 0xE0000005 |
| | |
| LMS_SHAKE_M32_H5 | 0xE0000006 |
| | |
| LMS_SHAKE_M32_H10 | 0xE0000007 |
| | |
| LMS_SHAKE_M32_H15 | 0xE0000008 |
| | |
| LMS_SHAKE_M32_H20 | 0xE0000009 |
| | |
| LMS_SHAKE_M32_H25 | 0xE000000A |
| | |
| LMS_SHAKE_M24_H5 | 0xE000000B |
| | |
| LMS_SHAKE_M24_H10 | 0xE000000C |
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| | |
| LMS_SHAKE_M24_H15 | 0xE000000D |
| | |
| LMS_SHAKE_M24_H20 | 0xE000000E |
| | |
| LMS_SHAKE_M24_H25 | 0xE000000F |
+---------------------+---------------------+
Table 4
8. Security Considerations
The strength of a signature that uses the SHA256/192, SHAKE256-256
and SHAKE256-192 hash functions is based on the difficultly in
finding preimages or second preimages to those hash functions.
The case of SHAKE256-256 is essentially the same as the existing
SHA-256 based signatures; the difficultly of finding preimages is
essentially the same, and so they have (barring unexpected
cryptographical advances) essentially the same level of security.
The case of SHA256/192 and SHAKE256-192 requires closer analysis.
For a classical (nonquantum) computer, they have no known attack
better than performing hashes of a large number of distinct
preimages; as a successful attack has a high probability of requiring
nearly 2**192 hash computations (for either SHA256/192 or
SHAKE256-192). These can be taken as the expected work effort, and
would appear to be completely infeasible in practice.
For a Quantum Computer, they could in theory use a Grover's algorithm
to reduce the expected complexity required to circa 2**96 hash
computations (for N=24). On the other hand, to implement Grover's
algorithm with this number of hash computations would require
performing circa 2**96 hash computations in succession, which will
take more time than is likely to be acceptable to any attacker. To
speed this up, the attacker would need to run a number of instances
of Grover's algorithm in parallel. This would necessarily increase
the total work effort required, and to an extent that makes it likely
to be infeasible.
Hence, we expect that LMS based on these hash functions is secure
against both classical and quantum computers, even though, in both
cases, the expected work effort is less (for the N=24 case) than
against either SHA256 or SHAKE256-256.
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8.1. Note on the version of SHAKE
FIPS 202 defines both SHAKE-128 and SHAKE-256. This specification
selects SHAKE-256, even though it is, for large messages, less
efficient. The reason is that SHAKE-128 has a low upper bound on the
difficulty of finding preimages (due to the invertibility of its
internal permutation), which would limit the strength of LMS (whose
strength is based on the difficulty of finding preimages). Hence, we
specify the use of SHAKE-256, which has a considerably stronger
preimage resistance.
9. References
9.1. Normative References
[FIPS180] National Institute of Standards and Technology, "Secure
Hash Standard (SHS)", FIPS 180-4, March 2012.
[FIPS202] National Institute of Standards and Technology, "SHA-3
Standard: Permutation-Based Hash and Extendable-Output
Functions", FIPS 202, August 2015.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC3979] Bradner, S., Ed., "Intellectual Property Rights in IETF
Technology", RFC 3979, DOI 10.17487/RFC3979, March 2005,
<https://www.rfc-editor.org/info/rfc3979>.
[RFC4879] Narten, T., "Clarification of the Third Party Disclosure
Procedure in RFC 3979", RFC 4879, DOI 10.17487/RFC4879,
April 2007, <https://www.rfc-editor.org/info/rfc4879>.
[RFC5226] Narten, T. and H. Alvestrand, "Guidelines for Writing an
IANA Considerations Section in RFCs", RFC 5226,
DOI 10.17487/RFC5226, May 2008,
<https://www.rfc-editor.org/info/rfc5226>.
[RFC8554] McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali
Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554,
April 2019, <https://www.rfc-editor.org/info/rfc8554>.
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9.2. Informative References
[Grover96]
Grover, L., "A fast quantum mechanical algorithm for
database search", 28th ACM Symposium on the Theory of
Computing p. 212, 1996.
Appendix A. Test Cases
In the future, this section will include an example test vector that
uses the new hash functions
Authors' Addresses
Scott Fluhrer
Cisco Systems
170 West Tasman Drive
San Jose, CA
USA
Email: sfluhrer@cisco.com
Quynh Dang
NIST
100 Bureau Drive
Gaithersburg, MD
USA
Email: quynh.dang@nist.gov
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