rfc9858v1.txt   rfc9858.txt 
Internet Research Task Force (IRTF) S. Fluhrer Internet Research Task Force (IRTF) S. Fluhrer
Request for Comments: 9858 Cisco Systems Request for Comments: 9858 Cisco Systems
Category: Informational Q. Dang Category: Informational Q. Dang
ISSN: 2070-1721 NIST ISSN: 2070-1721 NIST
September 2025 October 2025
Additional Parameter Sets for HSS/LMS Hash-Based Signatures Additional Parameter Sets for HSS/LMS Hash-Based Signatures
Abstract Abstract
This document extends HSS/LMS (RFC 8554) by defining parameter sets This document extends HSS/LMS (RFC 8554) by defining parameter sets
by including additional hash functions. These include hash functions that use alternative hash functions. These include hash functions
that result in signatures with significantly smaller sizes than the that result in signatures with significantly smaller sizes than the
signatures using the current parameter sets and should have signatures that use the RFC 8554 parameter sets and should have
sufficient security. sufficient security.
This document is a product of the Crypto Forum Research Group (CFRG) This document is a product of the Internet Research Task Force
in the IRTF. (IRTF). The IRTF publishes the results of Internet-related research
and development activities. These results might not be suitable for
deployment. This RFC represents the consensus of the Crypto Forum
Research Group of the Internet Research Task Force (IRTF). Documents
approved for publication by the IRSG are not candidates for any level
of Internet Standard; see Section 2 of RFC 7841.
Status of This Memo Status of This Memo
This document is not an Internet Standards Track specification; it is This document is not an Internet Standards Track specification; it is
published for informational purposes. published for informational purposes.
This document is a product of the Internet Research Task Force This document is a product of the Internet Research Task Force
(IRTF). The IRTF publishes the results of Internet-related research (IRTF). The IRTF publishes the results of Internet-related research
and development activities. These results might not be suitable for and development activities. These results might not be suitable for
deployment. This RFC represents the consensus of the Crypto Forum deployment. This RFC represents the consensus of the Crypto Forum
skipping to change at line 58 skipping to change at line 63
to this document. to this document.
Table of Contents Table of Contents
1. Introduction 1. Introduction
2. Additional Hash Function Definitions 2. Additional Hash Function Definitions
2.1. 192-Bit Hash Function Based on SHA-256 2.1. 192-Bit Hash Function Based on SHA-256
2.2. 256-Bit Hash Function Based on SHAKE256 2.2. 256-Bit Hash Function Based on SHAKE256
2.3. 192-Bit Hash Function Based on SHAKE256 2.3. 192-Bit Hash Function Based on SHAKE256
3. Additional LM-OTS Parameter Sets 3. Additional LM-OTS Parameter Sets
4. Additional LM Parameter Sets 4. Additional LMS Parameter Sets
5. Usage for These Additional Hash Functions within HSS 5. Usage for These Additional Hash Functions within HSS
6. Parameter Set Selection 6. Parameter Set Selection
7. Comparisons of 192-Bit and 256-Bit Parameter Sets 7. Comparisons of 192-Bit and 256-Bit Parameter Sets
8. Security Considerations 8. Security Considerations
8.1. Note on the Version of SHAKE 8.1. Note on the Version of SHAKE
9. IANA Considerations 9. IANA Considerations
10. References 10. References
10.1. Normative References 10.1. Normative References
10.2. Informative References 10.2. Informative References
Appendix A. Test Cases Appendix A. Test Cases
A.1. Test Case 1 - SHA-256/192
A.2. Test vector for SHAKE256/192
A.3. Test vector for SHA-256/256
A.4. Test vector for SHA-256/192, W=4
Acknowledgements Acknowledgements
Authors' Addresses Authors' Addresses
1. Introduction 1. Introduction
Stateful hash-based signatures have small private and public keys, Stateful hash-based signatures have small private and public keys,
are efficient to compute, and are believed to have excellent are efficient to compute, and are believed to have excellent
security. One disadvantage is that the signatures they produce tend security. One disadvantage is that the signatures they produce tend
to be somewhat large (possibly 1-4 kilobytes). This document to be somewhat large (possibly 1-4 kilobytes). This document defines
explores a set of parameter sets for the HSS/LMS stateful hash-based a set of parameter sets for the HSS/LMS stateful hash-based signature
signature method [RFC8554] that reduce the size of the signature method [RFC8554] that reduce the size of the signature significantly
significantly or rely on a hash function other than SHA-256 (to or rely on a hash function other than SHA-256 (to increase
increase cryptodiversity). cryptodiversity).
This document represents the consensus of the Crypto Forum Research This document represents the consensus of the Crypto Forum Research
Group (CFRG) in the IRTF. It is not an IETF product and is not a Group (CFRG) in the IRTF. It is not an IETF product and is not a
standard. standard.
According to official definitions and common usage, a Leighton-Micali According to official definitions and common usage, a Leighton-Micali
Signature (LMS) is a stateful hash-based signature scheme that is Signature (LMS) is a stateful hash-based signature scheme that is
based on a single-level Merkle tree. The Hierarchical Signature based on a single-level Merkle tree. The Hierarchical Signature
System (HSS) is a way of binding several LMS signatures together in a System (HSS) is a way of binding several LMS signatures together in a
hierarchical manner to increase the number of signatures available. hierarchical manner to increase the number of signatures available.
skipping to change at line 103 skipping to change at line 112
HSS signatures (even if the HSS signature consists of a single LMS HSS signatures (even if the HSS signature consists of a single LMS
signature). However, it is common to refer to these signatures as signature). However, it is common to refer to these signatures as
"LMS signatures". This document uses the term "HSS/LMS" to cover "LMS signatures". This document uses the term "HSS/LMS" to cover
both the pedantic and the common meanings. both the pedantic and the common meanings.
This document is intended to be compatible with the NIST document This document is intended to be compatible with the NIST document
[NIST_SP_800-208]. [NIST_SP_800-208].
2. Additional Hash Function Definitions 2. Additional Hash Function Definitions
This section defines three hash functions that are used in Sections 3 This section defines three hash functions that are used with the
and 4. These hash functions are used where SHA-256 is used in the parameter sets defined in Sections 3 and 4. These hash functions are
original parameter sets from [RFC8554]. The hash function used is used where SHA-256 is used in the original parameter sets from
specified by the parameter set that is selected. [RFC8554]. The hash function used is specified by the parameter set
that is selected.
2.1. 192-Bit Hash Function Based on SHA-256 2.1. 192-Bit Hash Function Based on SHA-256
This document defines a SHA-2-based hash function with a 192-bit This document defines a SHA-2-based hash function with a 192-bit
output. As such, we define SHA-256/192 as a truncated version of output. As such, we define SHA-256/192 as a truncated version of
SHA-256 [FIPS180]. That is, it is the result of performing a SHA-256 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 operation to a message and then omitting the final 64 bits of the
output. This procedure for truncating the hash output to 192 bits is output. This procedure for truncating the hash output to 192 bits is
described in Section 7 of [FIPS180]. described in Section 7 of [FIPS180].
The following test vector illustrates this: The following test vector illustrates this:
SHA-256("abc") = ba7816bf 8f01cfea 414140de 5dae2223 SHA-256("abc") = ba7816bf 8f01cfea 414140de 5dae2223
b00361a3 96177a9c b410ff61 f20015ad b00361a3 96177a9c b410ff61 f20015ad
SHA-256/192("abc") = ba7816bf 8f01cfea 414140de 5dae2223 SHA-256/192("abc") = ba7816bf 8f01cfea 414140de 5dae2223
b00361a3 96177a9c b00361a3 96177a9c
We use the same IV as the untruncated SHA-256, rather than defining a We use the same initial hash value (initialization vector) as the
distinct one, so that we can use a standard SHA-256 hash untruncated SHA-256, rather than defining a distinct one, so that we
implementation without modification. In addition, the fact that can use a standard SHA-256 hash implementation without modification.
anyone gets partial knowledge of the SHA-256 hash of a message by In addition, the fact that anyone gets partial knowledge of the
examining the SHA-256/192 hash of the same message is not a concern SHA-256 hash of a message by examining the SHA-256/192 hash of the
for this application. Each message that is hashed is randomized. same message is not a concern for this application. Each message
Any message being signed includes the C randomizer (a value that is that is hashed is randomized. Any message being signed includes the
selected by the signer and is included in the hash), which varies per C randomizer (a value that is selected by the signer and is included
message. Therefore, signing the same message by SHA-256 and by SHA- in the hash), which varies per message. Therefore, signing the same
256/192 will not result in the same value being hashed, and so the message by SHA-256 and by SHA-256/192 will not result in the same
latter hash value is not a prefix of the former one. In addition, value being hashed, and so the latter hash value is not a prefix of
all hashes include the I identifier, which is included as a part of the former one. In addition, all hashes include the I identifier,
the signature process in [RFC8554]. This I identifier is selected which is included as a part of the signature process in [RFC8554].
randomly for each private key (and hence two keys will have different This I identifier is selected randomly for each private key (and
I values with high probability), and so two intermediate hashes hence two keys will have different I values with high probability),
computed as a part of signing with two HSS private keys (one with a and so two intermediate hashes computed as a part of signing with two
SHA-256 parameter set and one with a SHA-256/192 parameter set) will HSS private keys (one with a SHA-256 parameter set and one with a
also be distinct with high probability. SHA-256/192 parameter set) will also be distinct with high
probability.
2.2. 256-Bit Hash Function Based on SHAKE256 2.2. 256-Bit Hash Function Based on SHAKE256
This document defines a SHAKE-based hash function with a 256-bit This document defines a SHAKE-based hash function with a 256-bit
output. As such, we define SHAKE256/256 to be the first 256 bits of output. As such, we define SHAKE256/256 to be the first 256 bits of
the SHAKE256 extendable-output function (XOF). That is, it is the the SHAKE256 extendable-output function (XOF). That is, it is the
result of performing a SHAKE-256 operation to a message and then result of performing a SHAKE-256 operation to a message and then
using the first 256 bits of output. See [FIPS202] for more detail. using the first 256 bits of output. See [FIPS202] for more detail.
2.3. 192-Bit Hash Function Based on SHAKE256 2.3. 192-Bit Hash Function Based on SHAKE256
This document defines a SHAKE-based hash function with a 192-bit This document defines a SHAKE-based hash function with a 192-bit
output. As such, we define SHAKE256/192 to be the first 192 bits of output. As such, we define SHAKE256/192 to be the first 192 bits of
the SHAKE256 XOF. That is, it is the result of performing a the SHAKE256 XOF. That is, it is the result of performing a
SHAKE-256 operation to a message and then using the first 192 bits of SHAKE-256 operation to a message and then using the first 192 bits of
output. See [FIPS202] for more detail. output. See [FIPS202] for more detail.
3. Additional LM-OTS Parameter Sets 3. Additional LM-OTS Parameter Sets
Here is a table with the Leighton-Micali One-Time Signature (LM-OTS) The table below defines the Leighton-Micali One-Time Signature (LM-
parameters defined that use the above hashes: OTS) parameters that use the hashes defined in Section 2:
+=====================+==============+====+===+=====+====+========+ +=====================+==============+==+=+=====+====+============+
| Parameter Set Name | H | n | w | p | ls | id | | Parameter Set Name | H | n|w| p | ls | id |
+=====================+==============+====+===+=====+====+========+ +=====================+==============+==+=+=====+====+============+
| LMOTS_SHA256_N24_W1 | SHA-256/192 | 24 | 1 | 200 | 8 | 0x0005 | | LMOTS_SHA256_N24_W1 | SHA-256/192 |24|1| 200 | 8 | 0x00000005 |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHA256_N24_W2 | SHA-256/192 | 24 | 2 | 101 | 6 | 0x0006 | | LMOTS_SHA256_N24_W2 | SHA-256/192 |24|2| 101 | 6 | 0x00000006 |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHA256_N24_W4 | SHA-256/192 | 24 | 4 | 51 | 4 | 0x0007 | | LMOTS_SHA256_N24_W4 | SHA-256/192 |24|4| 51 | 4 | 0x00000007 |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHA256_N24_W8 | SHA-256/192 | 24 | 8 | 26 | 0 | 0x0008 | | LMOTS_SHA256_N24_W8 | SHA-256/192 |24|8| 26 | 0 | 0x00000008 |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHAKE_N32_W1 | SHAKE256/256 | 32 | 1 | 265 | 7 | 0x0009 | | LMOTS_SHAKE_N32_W1 | SHAKE256/256 |32|1| 265 | 7 | 0x00000009 |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHAKE_N32_W2 | SHAKE256/256 | 32 | 2 | 133 | 6 | 0x000a | | LMOTS_SHAKE_N32_W2 | SHAKE256/256 |32|2| 133 | 6 | 0x0000000A |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHAKE_N32_W4 | SHAKE256/256 | 32 | 4 | 67 | 4 | 0x000b | | LMOTS_SHAKE_N32_W4 | SHAKE256/256 |32|4| 67 | 4 | 0x0000000B |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHAKE_N32_W8 | SHAKE256/256 | 32 | 8 | 34 | 0 | 0x000c | | LMOTS_SHAKE_N32_W8 | SHAKE256/256 |32|8| 34 | 0 | 0x0000000C |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHAKE_N24_W1 | SHAKE256/192 | 24 | 1 | 200 | 8 | 0x000d | | LMOTS_SHAKE_N24_W1 | SHAKE256/192 |24|1| 200 | 8 | 0x0000000D |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHAKE_N24_W2 | SHAKE256/192 | 24 | 2 | 101 | 6 | 0x000e | | LMOTS_SHAKE_N24_W2 | SHAKE256/192 |24|2| 101 | 6 | 0x0000000E |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHAKE_N24_W4 | SHAKE256/192 | 24 | 4 | 51 | 4 | 0x000f | | LMOTS_SHAKE_N24_W4 | SHAKE256/192 |24|4| 51 | 4 | 0x0000000F |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
| LMOTS_SHAKE_N24_W8 | SHAKE256/192 | 24 | 8 | 26 | 0 | 0x0010 | | LMOTS_SHAKE_N24_W8 | SHAKE256/192 |24|8| 26 | 0 | 0x00000010 |
+---------------------+--------------+----+---+-----+----+--------+ +---------------------+--------------+--+-+-----+----+------------+
Table 1 Table 1
Parameter Set Name: The human-readable name of the parameter set. Parameter Set Name: The human-readable name of the parameter set.
H: The second-preimage-resistant cryptographic hash function used H: The second-preimage-resistant cryptographic hash function used
within this parameter set. within this parameter set.
n: The number of bytes of the output of the hash function. n: The number of bytes of the output of the hash function.
skipping to change at line 226 skipping to change at line 237
The SHA256_N24, SHAKE_N32, and SHAKE_N24 in the parameter set names The SHA256_N24, SHAKE_N32, and SHAKE_N24 in the parameter set names
denote the SHA-256/192, SHAKE256/256, and SHAKE256/192 hash functions denote the SHA-256/192, SHAKE256/256, and SHAKE256/192 hash functions
defined in Section 2. defined in Section 2.
Remember that the C message randomizer (which is included in the Remember that the C message randomizer (which is included in the
signature) has the same size (n bytes) as the hash output, and so it signature) has the same size (n bytes) as the hash output, and so it
shrinks from 32 bytes to 24 bytes for the parameter sets that use shrinks from 32 bytes to 24 bytes for the parameter sets that use
either SHA-256/192 or SHAKE256/192. either SHA-256/192 or SHAKE256/192.
4. Additional LM Parameter Sets 4. Additional LMS Parameter Sets
Here is a table with the Leighton-Micali (LM) parameters defined that The table below defines several many-time signature parameters called
use SHA-256/192, SHAKE256/256, and SHAKE256/192 hash functions: Leighton-Micali Signature (LMS) parameters, using the SHA-256/192,
SHAKE256/256, and SHAKE256/192 hash functions:
+====================+==============+====+====+========+ +====================+==============+====+====+============+
| Parameter Set Name | H | m | h | id | | Parameter Set Name | H | m | h | id |
+====================+==============+====+====+========+ +====================+==============+====+====+============+
| LMS_SHA256_M24_H5 | SHA-256/192 | 24 | 5 | 0x000a | | LMS_SHA256_M24_H5 | SHA-256/192 | 24 | 5 | 0x0000000A |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHA256_M24_H10 | SHA-256/192 | 24 | 10 | 0x000b | | LMS_SHA256_M24_H10 | SHA-256/192 | 24 | 10 | 0x0000000B |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHA256_M24_H15 | SHA-256/192 | 24 | 15 | 0x000c | | LMS_SHA256_M24_H15 | SHA-256/192 | 24 | 15 | 0x0000000C |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHA256_M24_H20 | SHA-256/192 | 24 | 20 | 0x000d | | LMS_SHA256_M24_H20 | SHA-256/192 | 24 | 20 | 0x0000000D |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHA256_M24_H25 | SHA-256/192 | 24 | 25 | 0x000e | | LMS_SHA256_M24_H25 | SHA-256/192 | 24 | 25 | 0x0000000E |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M32_H5 | SHAKE256/256 | 32 | 5 | 0x000f | | LMS_SHAKE_M32_H5 | SHAKE256/256 | 32 | 5 | 0x0000000F |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M32_H10 | SHAKE256/256 | 32 | 10 | 0x0010 | | LMS_SHAKE_M32_H10 | SHAKE256/256 | 32 | 10 | 0x00000010 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M32_H15 | SHAKE256/256 | 32 | 15 | 0x0011 | | LMS_SHAKE_M32_H15 | SHAKE256/256 | 32 | 15 | 0x00000011 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M32_H20 | SHAKE256/256 | 32 | 20 | 0x0012 | | LMS_SHAKE_M32_H20 | SHAKE256/256 | 32 | 20 | 0x00000012 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M32_H25 | SHAKE256/256 | 32 | 25 | 0x0013 | | LMS_SHAKE_M32_H25 | SHAKE256/256 | 32 | 25 | 0x00000013 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M24_H5 | SHAKE256/192 | 24 | 5 | 0x0014 | | LMS_SHAKE_M24_H5 | SHAKE256/192 | 24 | 5 | 0x00000014 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M24_H10 | SHAKE256/192 | 24 | 10 | 0x0015 | | LMS_SHAKE_M24_H10 | SHAKE256/192 | 24 | 10 | 0x00000015 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M24_H15 | SHAKE256/192 | 24 | 15 | 0x0016 | | LMS_SHAKE_M24_H15 | SHAKE256/192 | 24 | 15 | 0x00000016 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M24_H20 | SHAKE256/192 | 24 | 20 | 0x0017 | | LMS_SHAKE_M24_H20 | SHAKE256/192 | 24 | 20 | 0x00000017 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
| LMS_SHAKE_M24_H25 | SHAKE256/192 | 24 | 25 | 0x0018 | | LMS_SHAKE_M24_H25 | SHAKE256/192 | 24 | 25 | 0x00000018 |
+--------------------+--------------+----+----+--------+ +--------------------+--------------+----+----+------------+
Table 2 Table 2
Parameter Set Name: The human-readable name of the parameter set. Parameter Set Name: The human-readable name of the parameter set.
H: The second-preimage-resistant cryptographic hash function used H: The second-preimage-resistant cryptographic hash function used
within this parameter set. within this parameter set.
m: The size in bytes of the hash function output. m: The size in bytes of the hash function output.
skipping to change at line 288 skipping to change at line 300
These values are additions to the entries in Table 2 of [RFC8554]. These values are additions to the entries in Table 2 of [RFC8554].
The SHA256_M24, SHAKE_M32, and SHAKE_M24 in the parameter set names The SHA256_M24, SHAKE_M32, and SHAKE_M24 in the parameter set names
denote the SHA-256/192, SHAKE256/256, and SHAKE256/192 hash functions denote the SHA-256/192, SHAKE256/256, and SHAKE256/192 hash functions
defined in Section 2. defined in Section 2.
5. Usage for These Additional Hash Functions within HSS 5. Usage for These Additional Hash Functions within HSS
To use the additional hash functions within HSS, one would use the To use the additional hash functions within HSS, one would use the
appropriate LMOTS id from Table 1 and the appropriate LMS id from appropriate LM-OTS id from Table 1 and the appropriate LMS id from
Table 2 and use that additional hash function when computing the Table 2 and use that additional hash function when computing the
hashes for key generation, signature generation, and signature hashes for key generation, signature generation, and signature
verification. verification.
Note that the size of the I Merkle tree identifier remains 16 bytes, Note that the size of the I Merkle tree identifier remains 16 bytes,
independent of what hash function is used. independent of what hash function is used.
6. Parameter Set Selection 6. Parameter Set Selection
This document, along with [RFC8554], defines four hash functions for This document, along with [RFC8554], defines four hash functions for
skipping to change at line 329 skipping to change at line 341
the security strength. the security strength.
The impact on signature size and computation time is based on two The impact on signature size and computation time is based on two
effects: effects:
1. Each hash that appears in the signature is shorter. 1. Each hash that appears in the signature is shorter.
2. We need fewer Winternitz chains (because LM-OTS signs a shorter 2. We need fewer Winternitz chains (because LM-OTS signs a shorter
value). value).
For signature length, both effects are relevant (because the For signature length, both effects are relevant. The first is
signature consists of a series of hashes and each hash is shorter, relevant because the signature consists of a series of hashes and
and because we need fewer Winternitz chains, we need fewer hashes in each hash is shorter. The second is relevant because when we need
each LM-OTS signature). fewer Winternitz chains, we need fewer hashes in each LM-OTS
signature.
For computation time (for both signature generation and For computation time (for both signature generation and
verification), effect 1 is irrelevant (we still need to perform verification), effect 1 is irrelevant (we still need to perform
essentially the same hash computation), but effect 2 still applies. essentially the same hash computation), but effect 2 still applies.
For example, with W=8, SHA-256 requires 34 Winternitz chains per LM- For example, with W=8, SHA-256 requires 34 Winternitz chains per LM-
OTS signature, but SHA-256/192 requires only 26. Since the vast OTS signature, but SHA-256/192 requires only 26. Since the vast
majority of time (for both signature generation and verification) is majority of time (for both signature generation and verification) is
spent computing these Winternitz chains, this reduction in the number spent computing these Winternitz chains, this reduction in the number
of chains gives us some performance improvement. of chains gives us some performance improvement.
Here is a table that gives the space used by both the 256-bit and The table below gives the space used by both the 256-bit and 192-bit
192-bit parameter sets for a range of plausible Winternitz parameters parameter sets for a range of commonly used Winternitz parameters and
and tree heights: tree heights:
+=========+============+==============+==============+ +=========+============+==============+==============+
| ParmSet | Winternitz | 256-bit hash | 192-bit hash | | ParmSet | Winternitz | 256-bit hash | 192-bit hash |
+=========+============+==============+==============+ +=========+============+==============+==============+
| 15 | 4 | 2672 | 1624 | | 15 | 4 | 2672 | 1624 |
+---------+------------+--------------+--------------+ +---------+------------+--------------+--------------+
| 15 | 8 | 1616 | 1024 | | 15 | 8 | 1616 | 1024 |
+---------+------------+--------------+--------------+ +---------+------------+--------------+--------------+
| 20 | 4 | 2832 | 1744 | | 20 | 4 | 2832 | 1744 |
+---------+------------+--------------+--------------+ +---------+------------+--------------+--------------+
skipping to change at line 401 skipping to change at line 414
192-bit hash: The size in bytes of a signature, assuming that a 192-bit hash: The size in bytes of a signature, assuming that a
192-bit hash is used in the signature (either SHA-256/192 or 192-bit hash is used in the signature (either SHA-256/192 or
SHAKE256/192). SHAKE256/192).
An examination of the signature sizes shows that the 192-bit An examination of the signature sizes shows that the 192-bit
parameters consistently give a 35-40% reduction in the size of the parameters consistently give a 35-40% reduction in the size of the
signature in comparison with the 256-bit parameters. signature in comparison with the 256-bit parameters.
For SHA-256/192, there is a smaller (circa 20%) reduction in the For SHA-256/192, there is a smaller (circa 20%) reduction in the
amount of computation required for a signature operation with a amount of computation required for a signature operation with a
192-bit hash (for reason 2 listed above). The SHAKE256/192 192-bit hash, because fewer Winternitz chains would need to be
signatures may have either a faster or slower computation, depending computed. The SHAKE256/192 signatures may have either a faster or
on the implementation speed of SHAKE versus SHA-256 hashes. slower computation, depending on the implementation speed of SHAKE
versus SHA-256 hashes.
The SHAKE256/256-based parameter sets give no space advantage (or The SHAKE256/256-based parameter sets give no space advantage (or
disadvantage) over the existing SHA-256-based parameter sets; any disadvantage) over the existing SHA-256-based parameter sets; any
performance delta would depend solely on the implementation and performance delta would depend solely on the implementation and
whether they can generate SHAKE hashes faster than SHA-256 ones. whether they can generate SHAKE hashes faster than SHA-256 ones.
8. Security Considerations 8. Security Considerations
The strength of a signature that uses the SHA-256/192, SHAKE256/256, The strength of a signature that uses the SHA-256/192, SHAKE256/256,
and SHAKE256/192 hash functions is based on the difficulty in finding and SHAKE256/192 hash functions is based on the difficulty in finding
skipping to change at line 441 skipping to change at line 455
The case of SHA-256/192 and SHAKE256/192 requires closer analysis. The case of SHA-256/192 and SHAKE256/192 requires closer analysis.
For a classical (non-quantum) computer, there is no known attack For a classical (non-quantum) computer, there is no known attack
better than performing hashes of a large number of distinct better than performing hashes of a large number of distinct
preimages. Therefore, a successful attack has a high probability of preimages. Therefore, a successful attack has a high probability of
requiring nearly 2^192 hash computations (for either SHA-256/192 or requiring nearly 2^192 hash computations (for either SHA-256/192 or
SHAKE256/192). These can be taken as the expected work effort and SHAKE256/192). These can be taken as the expected work effort and
would appear to be completely infeasible in practice. would appear to be completely infeasible in practice.
In theory, an attacker with a quantum computer could use Grover's In theory, an attacker with a quantum computer could use Grover's
algorithm [Grover96] to reduce the expected complexity to circa 2**96 algorithm [Grover96] to reduce the expected complexity to circa 2^96
hash computations (for N=24). On the other hand, implementing hash computations (for N=24). On the other hand, implementing
Grover's algorithm with this number of hash computations would Grover's algorithm with this number of hash computations would
require performing circa 2**96 hash computations in succession, which require performing circa 2^96 hash computations in succession, which
will take more time than is likely to be acceptable to any attacker. 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 To speed this up, the attacker would need to run a number of
instances of Grover's algorithm in parallel. This would necessarily instances of Grover's algorithm in parallel. This would necessarily
increase the total work effort required, and to an extent, that makes increase the total work effort required, and to an extent, that makes
it likely infeasible. This is because if we limit the time taken by it likely infeasible. This is because if we limit the time taken by
Grover's algorithm to 2**t steps (for t <= 96), then to attack a hash Grover's algorithm to 2^t steps (for t <= 96), then to attack a hash
preimage problem of 192 bits, it requires a total of 2**(192-t) hash preimage problem of 192 bits, it requires a total of 2^(192-t) hash
computations, rather than the 2**(192/2) hash computations it would computations, rather than the 2^(192/2) hash computations it would
require if we did not limit the time taken. In other words, the hash require if we did not limit the time taken. In other words, the hash
preimage can be found in 2**t steps by using 2**(192-2t) quantum preimage can be found in 2^t steps by using 2^(192-2t) quantum
computers (for t <= 96), with one of the quantum computers finding computers (for t <= 96), with one of the quantum computers finding
the preimage. For example, if the adversary is willing to wait for the preimage. For example, if the adversary is willing to wait for
2**64 times the time taken by a hash computation (which is over 50 2^64 times the time taken by a hash computation (which is over 50
years if a quantum computer can compute a hash in 0.1 nanoseconds), years if a quantum computer can compute a hash in 0.1 nanoseconds),
this implies that a total of 2**(192-64) = 2**128 hash computations this implies that a total of 2^(192-64) = 2^128 hash computations
will need to be performed, performing the computations on 2**64 (18 will need to be performed, on 2^64 (18 quintillion) separate quantum
quintillion) separate quantum computers, each of which computes 2**64 computers, each of which computes 2^64 hash evaluations.
hash evaluations.
Hence, we expect that HSS/LMS based on these hash functions is secure Hence, we expect that HSS/LMS based on these hash functions is secure
against both classical and quantum computers, even though, in both against both classical and quantum computers, even though, in both
cases, the expected work effort is less (for the N=24 case) than cases, the expected work effort is less (for the N=24 case) than
against either SHA-256 or SHAKE256/256. against either SHA-256 or SHAKE256/256.
SHA-256 is subject to a length extension attack. In this attack, if SHA-256 is subject to a length extension attack. In this attack, if
the attacker is given the hash value of an unknown message (and the the attacker is given the hash value of an unknown message (and the
message length), then the attacker can compute the hash of the message length), then the attacker can compute the hash of the
message appended with certain strings (even though the attacker does message appended with certain strings (even though the attacker does
skipping to change at line 486 skipping to change at line 499
* For the initial message hash, the hash is entirely on public data. * For the initial message hash, the hash is entirely on public data.
Hence, this attack is irrelevant, because the attacker could Hence, this attack is irrelevant, because the attacker could
compute the hash of the message with appended data anyways. compute the hash of the message with appended data anyways.
* The rest of the hashes within HSS are fixed length. Hence, there * The rest of the hashes within HSS are fixed length. Hence, there
is no opportunity to perform length extension attacks. is no opportunity to perform length extension attacks.
In addition, to perform a length extension attack on SHA-256/192, the In addition, to perform a length extension attack on SHA-256/192, the
attacker has to guess the 64 omitted bits (because the attack attacker has to guess the 64 omitted bits (because the attack
requires all 256 bits of the hash value); hence, that is even less of requires all 256 bits of the hash value); hence, that is even less of
a concern than it is for the standard SHA256. a concern than it is for the standard SHA-256.
There is one corner case for which the security strength is reduced: There is one corner case for which the security strength is reduced:
if we need to assume that the signer will never deliberately generate if we need to assume that the signer will never deliberately generate
a signature that is valid for two different messages. HSS uses a signature that is valid for two different messages. HSS uses
randomized hashing when signing a message. That is, when a message randomized hashing when signing a message. That is, when a message
is being presented to be signed, the signer generates a random value is being presented to be signed, the signer generates a random value
C and includes that in what is prepended to the message. Because the C and includes that in what is prepended to the message. Because the
attacker cannot predict this value, it is infeasible for anyone other attacker cannot predict this value, it is infeasible for anyone other
than the signer to find a generic collision. That is, practically than the signer to find a generic collision. That is, practically
speaking, a signature that is valid for two colliding messages is speaking, a signature that is valid for two colliding messages is
skipping to change at line 508 skipping to change at line 521
happen, a signer (that is, the one with the private key and who picks happen, a signer (that is, the one with the private key and who picks
the random C value) would have to break the collision resistance of the random C value) would have to break the collision resistance of
the hash function to generate those two colliding messages. Note the hash function to generate those two colliding messages. Note
that this does not apply to someone who submits the messages for that this does not apply to someone who submits the messages for
signing; only the signer could perform this. This would result in a signing; only the signer could perform this. This would result in a
signature that would be valid for two different selected messages. signature that would be valid for two different selected messages.
This is a nonstandard assumption for signature schemes and is usually This is a nonstandard assumption for signature schemes and is usually
not a concern, as we assume that the signer is trusted to generate not a concern, as we assume that the signer is trusted to generate
signatures for any message. However, if the application needs to signatures for any message. However, if the application needs to
assume that it is infeasible for the signer to generate such a assume that it is infeasible for the signer to generate such a
signature, then the security strength assumptions are reduced; 128 signature, then the security strength assumptions are reduced (128
bits for SHAKE256/256 and 96 bits for SHA-256/192 and SHAKE256/192. bits for SHAKE256/256 and 96 bits for SHA-256/192 and SHAKE256/192).
Some cryptographers have raised the possibility of a multi-target Some cryptographers have raised the possibility of a multi-target
attack (where the attacker has signatures from a large number of attack (where the attacker has signatures from a large number of
public keys and succeeds if they can generate a forgery against any public keys and succeeds if they can generate a forgery against any
one of those public keys). While no such method of attack has been one of those public keys). While no such method of attack has been
proposed, the possibility cannot be excluded; if there are a large proposed, the possibility cannot be excluded; if there are a large
number of public keys, it might be prudent to consider the number of public keys, it might be prudent to consider the
possibility of some security loss with N=24. If there are 2**K possibility of some security loss with N=24. If there are 2^K public
public keys, this security loss cannot be more than K bits of keys, this security loss cannot be more than K bits of security.
security.
8.1. Note on the Version of SHAKE 8.1. Note on the Version of SHAKE
[FIPS202] defines both SHAKE128 and SHAKE256. This specification [FIPS202] defines both SHAKE128 and SHAKE256. This specification
selects SHAKE256, even though it is less efficient for large selects SHAKE256, even though it is less efficient for large
messages. The reason is that SHAKE128 has a low upper bound on the messages. The reason is that SHAKE128 has a low upper bound on the
difficulty of finding preimages (due to the invertibility of its difficulty of finding preimages (due to the invertibility of its
internal permutation), which would limit the strength of HSS/LMS internal permutation), which would limit the strength of HSS/LMS
(whose strength is based on the difficulty of finding preimages). (whose strength is based on the difficulty of finding preimages).
Hence, we specify the use of SHAKE256, which has a considerably Hence, we specify the use of SHAKE256, which has a considerably
skipping to change at line 590 skipping to change at line 602
Appendix A. Test Cases Appendix A. Test Cases
This appendix provides four test cases that can be used to verify or This appendix provides four test cases that can be used to verify or
debug an implementation. This data is formatted with the name of the debug an implementation. This data is formatted with the name of the
elements on the left and the value of the elements on the right, in elements on the left and the value of the elements on the right, in
hexadecimal. The concatenation of all of the values within a public hexadecimal. The concatenation of all of the values within a public
key or signature produces that public key or signature, and values key or signature produces that public key or signature, and values
that do not fit within a single line are listed across successive that do not fit within a single line are listed across successive
lines. lines.
A.1. Test Case 1 - SHA-256/192
-------------------------------------------- --------------------------------------------
(note: procedure in Appendix A of [RFC8554] is used) (note: procedure in Appendix A of [RFC8554] is used)
SEED 000102030405060708090a0b0c0d0e0f SEED 000102030405060708090a0b0c0d0e0f
1011121314151617 1011121314151617
I 202122232425262728292a2b2c2d2e2f I 202122232425262728292a2b2c2d2e2f
-------------------------------------------- --------------------------------------------
--------------------------------------------
Figure 1: Test Case 1 - Private Key for SHA-256/192 Figure 1: Private Key for SHA-256/192
-------------------------------------------- --------------------------------------------
HSS public key HSS public key
levels 00000001 levels 00000001
-------------------------------------------- --------------------------------------------
LMS type 0000000a # LMS_SHA256_M24_H5 LMS type 0000000a # LMS_SHA256_M24_H5
LMOTS type 00000008 # LMOTS_SHA256_N24_W8 LM-OTS type 00000008 # LMOTS_SHA256_N24_W8
I 202122232425262728292a2b2c2d2e2f I 202122232425262728292a2b2c2d2e2f
K 2c571450aed99cfb4f4ac285da148827 K 2c571450aed99cfb4f4ac285da148827
96618314508b12d2 96618314508b12d2
-------------------------------------------- --------------------------------------------
--------------------------------------------
Figure 2: Test Case 1 - Public Key for SHA-256/192 Figure 2: Public Key for SHA-256/192
-------------------------------------------- --------------------------------------------
Message 54657374206d65737361676520666f72 |Test message for| Message 54657374206d65737361676520666f72 |Test message for|
205348413235362d3139320a | SHA-256/192.| 205348413235362d3139320a | SHA-256/192.|
-------------------------------------------- --------------------------------------------
Figure 3: Test Case 1 - Message for SHA-256/192 Figure 3: Message for SHA-256/192
-------------------------------------------- --------------------------------------------
HSS signature HSS signature
Nspk 00000000 Nspk 00000000
sig[0]: sig[0]:
-------------------------------------------- --------------------------------------------
LMS signature LMS signature
q 00000005 q 00000005
-------------------------------------------- --------------------------------------------
LMOTS signature LM-OTS signature
LMOTS type 00000008 # LMOTS_SHA256_N24_W8 LM-OTS type 00000008 # LMOTS_SHA256_N24_W8
C 0b5040a18c1b5cabcbc85b047402ec62 C 0b5040a18c1b5cabcbc85b047402ec62
94a30dd8da8fc3da 94a30dd8da8fc3da
y[0] e13b9f0875f09361dc77fcc4481ea463 y[0] e13b9f0875f09361dc77fcc4481ea463
c073716249719193 c073716249719193
y[1] 614b835b4694c059f12d3aedd34f3db9 y[1] 614b835b4694c059f12d3aedd34f3db9
3f3580fb88743b8b 3f3580fb88743b8b
y[2] 3d0648c0537b7a50e433d7ea9d6672ff y[2] 3d0648c0537b7a50e433d7ea9d6672ff
fc5f42770feab4f9 fc5f42770feab4f9
y[3] 8eb3f3b23fd2061e4d0b38f832860ae7 y[3] 8eb3f3b23fd2061e4d0b38f832860ae7
6673ad1a1a52a900 6673ad1a1a52a900
skipping to change at line 698 skipping to change at line 710
4ea64209942fbae3 4ea64209942fbae3
path[1] 38d19f152182c807d3c40b189d3fcbea path[1] 38d19f152182c807d3c40b189d3fcbea
942f44682439b191 942f44682439b191
path[2] 332d33ae0b761a2a8f984b56b2ac2fd4 path[2] 332d33ae0b761a2a8f984b56b2ac2fd4
ab08223a69ed1f77 ab08223a69ed1f77
path[3] 19c7aa7e9eee96504b0e60c6bb5c942d path[3] 19c7aa7e9eee96504b0e60c6bb5c942d
695f0493eb25f80a 695f0493eb25f80a
path[4] 5871cffd131d0e04ffe5065bc7875e82 path[4] 5871cffd131d0e04ffe5065bc7875e82
d34b40b69dd9f3c1 d34b40b69dd9f3c1
Figure 4: Test Case 1 - Signature for SHA-256/192 Figure 4: Signature for SHA-256/192
A.2. Test vector for SHAKE256/192
-------------------------------------------- --------------------------------------------
(note: procedure in Appendix A of [RFC8554] is used) (note: procedure in Appendix A of [RFC8554] is used)
SEED 303132333435363738393a3b3c3d3e3f SEED 303132333435363738393a3b3c3d3e3f
4041424344454647 4041424344454647
I 505152535455565758595a5b5c5d5e5f I 505152535455565758595a5b5c5d5e5f
-------------------------------------------- --------------------------------------------
--------------------------------------------
Figure 5: Test Case 2 - Private Key for SHAKE256/192 Figure 5: Private Key for SHAKE256/192
--------------------------------------------- ---------------------------------------------
HSS public key HSS public key
levels 00000001 levels 00000001
-------------------------------------------- --------------------------------------------
LMS type 00000014 # LMS_SHAKE256_N24_H5 LMS type 00000014 # LMS_SHAKE_N24_H5
LMOTS type 00000010 # LMOTS_SHAKE256_N24_W8 LM-OTS type 00000010 # LMOTS_SHAKE_N24_W8
I 505152535455565758595a5b5c5d5e5f I 505152535455565758595a5b5c5d5e5f
K db54a4509901051c01e26d9990e55034 K db54a4509901051c01e26d9990e55034
7986da87924ff0b1 7986da87924ff0b1
-------------------------------------------- --------------------------------------------
--------------------------------------------
Figure 6: Test Case 2 - Public Key for SHAKE256/192 Figure 6: Public Key for SHAKE256/192
-------------------------------------------- --------------------------------------------
Message 54657374206d65737361676520666f72 |Test message for| Message 54657374206d65737361676520666f72 |Test message for|
205348414b453235362d3139320a | SHAKE256/192.| 205348414b453235362d3139320a | SHAKE256/192.|
-------------------------------------------- --------------------------------------------
Figure 7: Test Case 2 - Message for SHAKE256/192 Figure 7: Message for SHAKE256/192
-------------------------------------------- --------------------------------------------
HSS signature HSS signature
Nspk 00000000 Nspk 00000000
sig[0]: sig[0]:
-------------------------------------------- --------------------------------------------
LMS signature LMS signature
q 00000006 q 00000006
-------------------------------------------- --------------------------------------------
LMOTS signature LM-OTS signature
LMOTS type 00000010 # LMOTS_SHAKE256_N24_W8 LM-OTS type 00000010 # LMOTS_SHAKE_N24_W8
C 84219da9ce9fffb16edb94527c6d1056 C 84219da9ce9fffb16edb94527c6d1056
5587db28062deac4 5587db28062deac4
y[0] 208e62fc4fbe9d85deb3c6bd2c01640a y[0] 208e62fc4fbe9d85deb3c6bd2c01640a
ccb387d8a6093d68 ccb387d8a6093d68
y[1] 511234a6a1a50108091c034cb1777e02 y[1] 511234a6a1a50108091c034cb1777e02
b5df466149a66969 b5df466149a66969
y[2] a498e4200c0a0c1bf5d100cdb97d2dd4 y[2] a498e4200c0a0c1bf5d100cdb97d2dd4
0efd3cada278acc5 0efd3cada278acc5
y[3] a570071a043956112c6deebd1eb3a7b5 y[3] a570071a043956112c6deebd1eb3a7b5
6f5f6791515a7b5f 6f5f6791515a7b5f
skipping to change at line 796 skipping to change at line 808
fd020fe789477a93 fd020fe789477a93
y[22] afff9a3e636dbba864a5bffa3e28d13d y[22] afff9a3e636dbba864a5bffa3e28d13d
49bb597d94865bde 49bb597d94865bde
y[23] 88c4627f206ab2b465084d6b780666e9 y[23] 88c4627f206ab2b465084d6b780666e9
52f8710efd748bd0 52f8710efd748bd0
y[24] f1ae8f1035087f5028f14affcc5fffe3 y[24] f1ae8f1035087f5028f14affcc5fffe3
32121ae4f87ac5f1 32121ae4f87ac5f1
y[25] eac9062608c7d87708f1723f38b23237 y[25] eac9062608c7d87708f1723f38b23237
a4edf4b49a5cd3d7 a4edf4b49a5cd3d7
-------------------------------------------- --------------------------------------------
LMS type 00000014 # LMS_SHAKE256_N24_H5 LMS type 00000014 # LMS_SHAKE_N24_H5
path[0] dd4bdc8f928fb526f6fb7cdb944a7eba path[0] dd4bdc8f928fb526f6fb7cdb944a7eba
a7fb05d995b5721a a7fb05d995b5721a
path[1] 27096a5007d82f79d063acd434a04e97 path[1] 27096a5007d82f79d063acd434a04e97
f61552f7f81a9317 f61552f7f81a9317
path[2] b4ec7c87a5ed10c881928fc6ebce6dfc path[2] b4ec7c87a5ed10c881928fc6ebce6dfc
e9daae9cc9dba690 e9daae9cc9dba690
path[3] 7ca9a9dd5f9f573704d5e6cf22a43b04 path[3] 7ca9a9dd5f9f573704d5e6cf22a43b04
e64c1ffc7e1c442e e64c1ffc7e1c442e
path[4] cb495ba265f465c56291a902e62a461f path[4] cb495ba265f465c56291a902e62a461f
6dfda232457fad14 6dfda232457fad14
Figure 8: Test Case 2 - Signature for SHAKE256/192 Figure 8: Signature for SHAKE256/192
A.3. Test vector for SHA-256/256
-------------------------------------------- --------------------------------------------
(note: procedure in Appendix A of [RFC8554] is used) (note: procedure in Appendix A of [RFC8554] is used)
SEED 606162636465666768696a6b6c6d6e6f SEED 606162636465666768696a6b6c6d6e6f
707172737475767778797a7b7c7d7e7f 707172737475767778797a7b7c7d7e7f
I 808182838485868788898a8b8c8d8e8f I 808182838485868788898a8b8c8d8e8f
-------------------------------------------- --------------------------------------------
--------------------------------------------
Figure 9: Test Case 3 - Private Key for SHAKE256/256 Figure 9: Private Key for SHAKE256/256
-------------------------------------------- --------------------------------------------
HSS public key HSS public key
levels 00000001 levels 00000001
-------------------------------------------- --------------------------------------------
LMS type 0000000f # LMS_SHAKE256_N32_H5 LMS type 0000000f # LMS_SHAKE_N32_H5
LMOTS type 0000000c # LMOTS_SHAKE256_N32_W8 LM-OTS type 0000000c # LMOTS_SHAKE_N32_W8
I 808182838485868788898a8b8c8d8e8f I 808182838485868788898a8b8c8d8e8f
K 9bb7faee411cae806c16a466c3191a8b K 9bb7faee411cae806c16a466c3191a8b
65d0ac31932bbf0c2d07c7a4a36379fe 65d0ac31932bbf0c2d07c7a4a36379fe
-------------------------------------------- --------------------------------------------
--------------------------------------------
Figure 10: Test Case 3 - Public Key for SHAKE256/256 Figure 10: Public Key for SHAKE256/256
-------------------------------------------- --------------------------------------------
Message 54657374206d657361676520666f7220 |Test message for| Message 54657374206d657361676520666f7220 |Test message for|
5348414b453235362d3235360a |SHAKE256/256.| 5348414b453235362d3235360a |SHAKE256/256.|
-------------------------------------------- --------------------------------------------
Figure 11: Test Case 3 - Message for SHAKE256/256 Figure 11: Message for SHAKE256/256
-------------------------------------------- --------------------------------------------
HSS signature HSS signature
Nspk 00000000 Nspk 00000000
sig[0]: sig[0]:
-------------------------------------------- --------------------------------------------
LMS signature LMS signature
q 00000007 q 00000007
-------------------------------------------- --------------------------------------------
LMOTS signature LM-OTS signature
LMOTS type 0000000c # LMOTS_SHAKE256_N32_W8 LM-OTS type 0000000c # LMOTS_SHAKE_N32_W8
C b82709f0f00e83759190996233d1ee4f C b82709f0f00e83759190996233d1ee4f
4ec50534473c02ffa145e8ca2874e32b 4ec50534473c02ffa145e8ca2874e32b
y[0] 16b228118c62b96c9c77678b33183730 y[0] 16b228118c62b96c9c77678b33183730
debaade8fe607f05c6697bc971519a34 debaade8fe607f05c6697bc971519a34
y[1] 1d69c00129680b67e75b3bd7d8aa5c8b y[1] 1d69c00129680b67e75b3bd7d8aa5c8b
71f02669d177a2a0eea896dcd1660f16 71f02669d177a2a0eea896dcd1660f16
y[2] 864b302ff321f9c4b8354408d0676050 y[2] 864b302ff321f9c4b8354408d0676050
4f768ebd4e545a9b0ac058c575078e6c 4f768ebd4e545a9b0ac058c575078e6c
y[3] 1403160fb45450d61a9c8c81f6bd69bd y[3] 1403160fb45450d61a9c8c81f6bd69bd
fa26a16e12a265baf79e9e233eb71af6 fa26a16e12a265baf79e9e233eb71af6
skipping to change at line 922 skipping to change at line 934
477e8316947ca725d141135202a9442e 477e8316947ca725d141135202a9442e
y[30] 1db33bbd390d2c04401c39b253b78ce2 y[30] 1db33bbd390d2c04401c39b253b78ce2
97b0e14755e46ec08a146d279c67af70 97b0e14755e46ec08a146d279c67af70
y[31] de256890804d83d6ec5ca3286f1fca9c y[31] de256890804d83d6ec5ca3286f1fca9c
72abf6ef868e7f6eb0fddda1b040ecec 72abf6ef868e7f6eb0fddda1b040ecec
y[32] 9bbc69e2fd8618e9db3bdb0af13dda06 y[32] 9bbc69e2fd8618e9db3bdb0af13dda06
c6617e95afa522d6a2552de15324d991 c6617e95afa522d6a2552de15324d991
y[33] 19f55e9af11ae3d5614b564c642dbfec y[33] 19f55e9af11ae3d5614b564c642dbfec
6c644198ce80d2433ac8ee738f9d825e 6c644198ce80d2433ac8ee738f9d825e
-------------------------------------------- --------------------------------------------
LMS type 0000000f # LMS_SHAKE256_N32_H5 LMS type 0000000f # LMS_SHAKE_N32_H5
path[0] 71d585a35c3a908379f4072d070311db path[0] 71d585a35c3a908379f4072d070311db
5d65b242b714bc5a756ba5e228abfa0d 5d65b242b714bc5a756ba5e228abfa0d
path[1] 1329978a05d5e815cf4d74c1e547ec4a path[1] 1329978a05d5e815cf4d74c1e547ec4a
a3ca956ae927df8b29fb9fab3917a7a4 a3ca956ae927df8b29fb9fab3917a7a4
path[2] ae61ba57e5342e9db12caf6f6dbc5253 path[2] ae61ba57e5342e9db12caf6f6dbc5253
de5268d4b0c4ce4ebe6852f012b162fc de5268d4b0c4ce4ebe6852f012b162fc
path[3] 1c12b9ffc3bcb1d3ac8589777655e22c path[3] 1c12b9ffc3bcb1d3ac8589777655e22c
d9b99ff1e4346fd0efeaa1da044692e7 d9b99ff1e4346fd0efeaa1da044692e7
path[4] ad6bfc337db69849e54411df8920c228 path[4] ad6bfc337db69849e54411df8920c228
a2b7762c11e4b1c49efb74486d3931ea a2b7762c11e4b1c49efb74486d3931ea
Figure 12: Test Case 3 - Signature for SHAKE256/256 Figure 12: Signature for SHAKE256/256
A.4. Test vector for SHA-256/192, W=4
-------------------------------------------- --------------------------------------------
(note: procedure in Appendix A of [RFC8554] is used) (note: procedure in Appendix A of [RFC8554] is used)
SEED 202122232425262728292a2b2c2d2e2f SEED 202122232425262728292a2b2c2d2e2f
3031323334353637 3031323334353637
I 404142434445464748494a4b4c4d4e4f I 404142434445464748494a4b4c4d4e4f
-------------------------------------------- --------------------------------------------
--------------------------------------------
Figure 13: Test Case 4 - Private Key for SHA256/192 with W=4 Figure 13: Private Key for SHA256/192 with W=4
-------------------------------------------- --------------------------------------------
HSS public key HSS public key
levels 00000001 levels 00000001
-------------------------------------------- --------------------------------------------
LMS type 0000000d # LMS_SHA256_M24_H20 LMS type 0000000d # LMS_SHA256_M24_H20
LMOTS type 00000007 # LMOTS_SHA256_N24_W4 LM-OTS type 00000007 # LMOTS_SHA256_N24_W4
I 404142434445464748494a4b4c4d4e4f I 404142434445464748494a4b4c4d4e4f
K 9c08a50d170406869892802ee4142fcd K 9c08a50d170406869892802ee4142fcd
eac990f110c2460c eac990f110c2460c
-------------------------------------------- --------------------------------------------
--------------------------------------------
Figure 14: Test Case 4 - Public Key for SHA256/192 with W=4 Figure 14: Public Key for SHA256/192 with W=4
-------------------------------------------- --------------------------------------------
Message 54657374206d65737361676520666f72 |Test message for| Message 54657374206d65737361676520666f72 |Test message for|
205348413235362f31393220773d34 | SHA256/192 w=4| 205348413235362f31393220773d34 | SHA256/192 w=4|
-------------------------------------------- --------------------------------------------
Figure 15: Test Case 4 - Message for SHA256/192 with W=4 Figure 15: Message for SHA256/192 with W=4
-------------------------------------------- --------------------------------------------
HSS signature HSS signature
Nspk 00000000 Nspk 00000000
sig[0]: sig[0]:
-------------------------------------------- --------------------------------------------
LMS signature LMS signature
q 00000064 q 00000064
-------------------------------------------- --------------------------------------------
LMOTS signature LM-OTS signature
LMOTS type 00000007 # LMOTS_SHA256_N24_W4 LM-OTS type 00000007 # LMOTS_SHA256_N24_W4
C 853fa6e1a65fef076acd2485505b93be C 853fa6e1a65fef076acd2485505b93be
9aeb2641e3d3805c 9aeb2641e3d3805c
y[0] 1887f26f4bcdb6ac0337b76fa5d66038 y[0] 1887f26f4bcdb6ac0337b76fa5d66038
34287e010b20516f 34287e010b20516f
y[1] 7c336df2134c0a981f1ec2bb7baee516 y[1] 7c336df2134c0a981f1ec2bb7baee516
e91e67d3bd16c8d9 e91e67d3bd16c8d9
y[2] 45a7f2be4fd84a604ae3743efc609ee0 y[2] 45a7f2be4fd84a604ae3743efc609ee0
e69572e9c6d4a682 e69572e9c6d4a682
y[3] 50e877b75d3cae63e9d5c15a32bb3cd1 y[3] 50e877b75d3cae63e9d5c15a32bb3cd1
7045f6b3e195284f 7045f6b3e195284f
skipping to change at line 1124 skipping to change at line 1136
071e572fd032c780 071e572fd032c780
path[16] f44c9503a4c03c37417dc96422ba0849 path[16] f44c9503a4c03c37417dc96422ba0849
c37956f9fd5d33ea c37956f9fd5d33ea
path[17] 4fcab84276effec652ca77d7d47ac93c path[17] 4fcab84276effec652ca77d7d47ac93c
633d99e0a236f03d 633d99e0a236f03d
path[18] 5587d1990ffaef737fced1f5cdd8f373 path[18] 5587d1990ffaef737fced1f5cdd8f373
844e9f316aad41a0 844e9f316aad41a0
path[19] b12302639f83a2d74c9fe30d305a942b path[19] b12302639f83a2d74c9fe30d305a942b
c0c30352a5e44dfb c0c30352a5e44dfb
Figure 16: Test Case 4 - Signature for SHA256/192 with W=4 Figure 16: Signature for SHA256/192 with W=4
Acknowledgements Acknowledgements
We would like to thank Carsten Bormann, Russ Housley, Andrey Jivsov, We would like to thank Carsten Bormann, Russ Housley, Andrey Jivsov,
Mallory Knodel, Virendra Kumar, Thomas Pornin, and Stanislav Mallory Knodel, Virendra Kumar, Thomas Pornin, and Stanislav
Smyshlyaev for their insightful and helpful reviews. Smyshlyaev for their insightful and helpful reviews.
Authors' Addresses Authors' Addresses
Scott Fluhrer Scott Fluhrer
 End of changes. 62 change blocks. 
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