| Internet-Draft | Additional LMS Signatures | November 2020 |
| Fluhrer & Dang | Expires 6 May 2021 | [Page] |
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.¶
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Copyright (c) 2020 IETF Trust and the persons identified as the document authors. All rights reserved.¶
This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.¶
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.¶
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.¶
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].¶
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.¶
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.¶
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.¶
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 |
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.¶
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.¶
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 |
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_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.¶
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 |
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 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.¶
[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 |
|---|---|
| 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 |
| LMS_SHAKE_M24_H15 | 0xE000000D |
| LMS_SHAKE_M24_H20 | 0xE000000E |
| LMS_SHAKE_M24_H25 | 0xE000000F |
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.¶
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.¶
This section provides three test cases that can be used to verify or debug an implementation, one for each hash function. This data is formatted with the name of the 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 key or signature produces that public key or signature, and values that do not fit within a single line are listed across successive lines.¶
Test Case 1 Private Key for SHA259/192¶
--------------------------------------------
(note: procedure in Appendix A of RFC8554 is used)
SEED 000102030405060708090a0b0c0d0e0f
1011121314151617
I 202122232425262728292a2b2c2d2e2f
--------------------------------------------
--------------------------------------------
¶
Test Case 1 Public Key for SHA256/192¶
--------------------------------------------
HSS public key
levels 00000001
--------------------------------------------
LMS type 0e000001 # LMS_SHA256_M24_H5
LMOTS type 0e000004 # LMOTS_SHA256_N24_W8
I 202122232425262728292a2b2c2d2e2f
K 2c571450aed99cfb4f4ac285da148827
96618314508b12d2
--------------------------------------------
--------------------------------------------
¶
Test Case 1 Message for SHA256/192¶
--------------------------------------------
Message 54657374206d657361676520666f7220 |Test mesage for |
5348413235362f3139320a |SHA256/192.|
--------------------------------------------
¶
Test Case 1 Signature for SHA256/192¶
--------------------------------------------
HSS signature
Nspk 00000000
sig[0]:
--------------------------------------------
LMS signature
q 00000005
--------------------------------------------
LMOTS signature
LMOTS type e0000004 # LMOTS_SHA256_N24_W8
C 0b5040a18c1b5cabcbc85b047402ec62
94a30dd8da8fc3da
y[0] dcc7fa8c8d2d2a8cb41b4fb080443d82
302d75edf5e1ab2a
y[1] 6dfc604ac2510910dd8e289eb0b43986
f44f72156c6f5829
y[2] 25a6220a0b38dc3e518afe5b1b9b2525
e25364c02cea0298
y[3] 1a1136b7c7263f5c64babe117bf808e4
5299716d291b9cd7
y[4] 134667b731876d2b36170f4b4bf1dae8
d68d46da97b4e68b
y[5] d17d25948a09526225e1a40a55212fac
d8e9ddbef3efe9a0
y[6] 13f4edcb07e401ba4fd42625b573e2b1
5515769e6fc3511d
y[7] ffbc1e12acfb9bf0c2fac322bbfaf292
46254cfd4d497213
y[8] 1e9ad5bc6fac2e2f3c3dbd92a46c6187
725f518b744cb9c6
y[9] cfea0868d59cf329d0633ba5b5ae3202
f12cedf224a656c1
y[10] b8d9ec380b05f629ae878e6265de29bc
171f2b0128b1da0c
y[11] 29ba727d4ec2e2fade202fc84737a9d8
d97f52fb70dde6e2
y[12] 6eaccbfb4d5f2faacd4066aa93818533
587e2eccedb42e41
y[13] c9bfa602e3e973fe08c8ee35713d8580
b10102170f207ca7
y[14] e937f14d3ae25f6f99c307bb66d2b0da
88ed13130bf2b89f
y[15] 696ed00415b5437628f76d11040b061f
837c4b42900aff2f
y[16] 06d19d6870145e9b1a746673de15a02c
74744f42db18c194
y[17] 9dccadd828483b74251d571ddec71585
59036c5cf6709df4
y[18] 420641e1a7793544e48cab9818fb6156
89ae83b32468093b
y[19] f1247ed1da9ee87da408fffa366b4f2c
6b55b5787ed14e8f
y[20] e9c9626aedebd1c3f8d6a2c5a9e514f7
cbf2385bbc703af3
y[21] ecae4ad57b9de6cc58df826552bdd9d8
6bda1e3d845786fd
y[22] e7bb777d2cf0fedf0c31e7aee973fe18
95ff74244193761b
y[23] d41802eece0e8d583ab0ae1729913a1a
d5c4837a564075ca
y[24] d562dc2abcc212ab163bd29a2c13dae8
2f5e966f29963eb2
y[25] b85121440c1a6993ee2396eff407e50e
11a98fb723b1fda7
--------------------------------------------
LMS type e0000001 # LMS_SHA256_M24_H5
path[0] e9ca10eaa811b22ae07fb195e3590a33
4ea64209942fbae3
path[1] 38d19f152182c807d3c40b189d3fcbea
942f44682439b191
path[2] 332d33ae0b761a2a8f984b56b2ac2fd4
ab08223a69ed1f77
path[3] 19c7aa7e9eee96504b0e60c6bb5c942d
695f0493eb25f80a
path[4] 5871cffd131d0e04ffe5065bc7875e82
d34b40b69dd9f3c1
¶
Test Case 2 Private Key for SHAKE256-192¶
--------------------------------------------
(note: procedure in Appendix A of RFC8554 is used)
SEED 303132333435363738393a3b3c3d3e3f
4041424344454647
I 505152535455565758595a5b5c5d5e5f
--------------------------------------------
--------------------------------------------
¶
Test Case 2 Public Key for SHAKE256-192¶
--------------------------------------------
HSS public key
levels 00000001
--------------------------------------------
LMS type 0e00000b # LMS_SHAKE_M24_H5
LMOTS type 0e00000c # LMOTS_SHAKE_N24_W8
I 505152535455565758595a5b5c5d5e5f
K db54a4509901051c01e26d9990e55034
7986da87924ff0b1
--------------------------------------------
--------------------------------------------
¶
Test Case 2 Message for SHAKE256-192¶
--------------------------------------------
Message 54657374206d657361676520666f7220 |Test mesage for |
5348414b453235362d3139320a |SHAKE256-192.|
--------------------------------------------
¶
Test Case 2 Signature for SHAKE256-192¶
--------------------------------------------
HSS signature
Nspk 00000000
sig[0]:
--------------------------------------------
LMS signature
q 00000006
--------------------------------------------
LMOTS signature
LMOTS type e000000c # LMOTS_SHAKE_N24_W8
C bbf8b68bac9e1d2fa970a094bc4fedb7
3ea78940cdd522ff
y[0] 124f566f03b8949c17d8bb078b16c8cf
8b56f23f67b07cea
y[1] 98d8ee389efd08795a2864c51e267e7f
14fed4e894e0121d
y[2] 0490e090b0295f97faa80f322a77d839
2d8d307421f3e968
y[3] ec8bbe764563d7099be23bc155a809de
5b6ad6f2cb56c417
y[4] b5f07e1c7b389f0eb0e26d6b61c4228e
fdbf00b631e27ae4
y[5] 76c45c4f9e0c10adf0af1f54715c8254
e92cd8abae422020
y[6] e7c17c1455e55754f32e7bebf6b17a18
1c67b57c97b84ec9
y[7] fa3dc68df1b3ae000a30722ced785e53
866c68a359a964dd
y[8] 37afbf185f61cf86bb688965c736e359
bad70d8e9e594679
y[9] 0017a5ae6f891b59f41c94e5b217b621
8172e8db59f224b8
y[10] 1ecb389899d17ee22b2e5112846855db
e955e6e8fc4f4c4b
y[11] bb36d30da85bcbfd25b6d45d6820cbff
054abe31db02604e
y[12] 3340cbcf9ccf1dd756f75c250460467a
daa18d60a994455b
y[13] 20172d8ebab81ee66c415dc9d226f193
2f4e049628d89a1a
y[14] 154cbea8e3bb0e37f0cee83e8a1a4492
a99633496f59694f
y[15] 54b48a63c8f1c8ae9460039423942e10
8e977c415087674e
y[16] 59baabff86aa9d26e361da998b0924cc
8b78912aeb54e83f
y[17] 11d1843b74c7a8151c32125f46bd61d5
635bab6154c67fce
y[18] 3b7e82c150a738cffdb6a537ba60fcd5
6eb1d8a69f52b1bf
y[19] d8726006e96fb89c429e975129870650
4040e1ee5bbd0a53
y[20] 3dfea6e2f369b79fa746ac77d09c54e6
c249d3864b7af264
y[21] fe58d8442eba0ae8a9b3bd5d4c6a564e
aed2506e68c2c44a
y[22] 2c2dd72df1144b8b1ceff9f6ff84a547
1552a090c86cfaef
y[23] 78d309c632432e1f7f16a6cd15057327
1e4c76c638af0562
y[24] 82825de35a40e9aa8711b305306fc3ce
c2eff373c8013b7a
y[25] eaabd5ebf6edbe5bf50978507489d66d
6ef6e3601be84bab
--------------------------------------------
LMS type e000000b # MS_SHAKE_M24_H5
path[0] f756d0b3277dbcecfa7c007eaef9c068
83b987845492c384
path[1] 478f397cf71f7859d406aa93129d6448
04ffd60ffe9a2917
path[2] 5589b9893128c82ad6d2299eebfdb038
d2e6b64780f5119b
path[3] 29e03883c0df124495ac5ede5d53da77
541abebaee9dbc93
path[4] 6b8892b7556f7ab3831f528e80bf6b95
41e6d5099c7006e4
¶
Test Case 3 Private Key for SHAKE256-256¶
--------------------------------------------
(note: procedure in Appendix A of RFC8554 is used)
SEED 606162636465666768696a6b6c6d6e6f
707172737475767778797a7b7c7d7e7f
I 808182838485868788898a8b8c8d8e8f
--------------------------------------------
--------------------------------------------
¶
Test Case 3 Public Key for SHAKE256-256¶
--------------------------------------------
HSS public key
levels 00000001
--------------------------------------------
LMS type 0e000006 # LMS_SHAKE_M32_H5
LMOTS type 0e000008 # LMOTS_SHAKE_N32_W8
I 808182838485868788898a8b8c8d8e8f
K 9bb7faee411cae806c16a466c3191a8b
65d0ac31932bbf0c2d07c7a4a36379fe
--------------------------------------------
--------------------------------------------
¶
Test Case 3 Message for SHAKE256-256¶
--------------------------------------------
Message 54657374206d657361676520666f7220 |Test mesage for |
5348414b453235362d3235360a |SHAKE256-256.|
--------------------------------------------
¶
Test Case 2 Signature for SHAKE256-256¶
--------------------------------------------
HSS signature
Nspk 00000000
sig[0]:
--------------------------------------------
LMS signature
q 00000007
--------------------------------------------
LMOTS signature
LMOTS type e0000008 # LMOTS_SHAKE_N32_W8
C b82709f0f00e83759190996233d1ee4f
4ec50534473c02ffa145e8ca2874e32b
y[0] 16b228118c62b96c9c77678b33183730
debaade8fe607f05c6697bc971519a34
y[1] 1d69c00129680b67e75b3bd7d8aa5c8b
71f02669d177a2a0eea896dcd1660f16
y[2] 864b302ff321f9c4b8354408d0676050
4f768ebd4e545a9b0ac058c575078e6c
y[3] 1403160fb45450d61a9c8c81f6bd69bd
fa26a16e12a265baf79e9e233eb71af6
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y[33] 19f55e9af11ae3d5614b564c642dbfec
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--------------------------------------------
LMS type e0000006 # MS_SHAKE_M32_H5
path[0] 71d585a35c3a908379f4072d070311db
5d65b242b714bc5a756ba5e228abfa0d
path[1] 1329978a05d5e815cf4d74c1e547ec4a
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path[2] ae61ba57e5342e9db12caf6f6dbc5253
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path[3] 1c12b9ffc3bcb1d3ac8589777655e22c
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path[4] ad6bfc337db69849e54411df8920c228
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¶