Hawkynt

PERK

Digital signature scheme submitted to the NIST additional signatures project, proving knowledge of a permutation that solves an instance of the Permuted Kernel Problem over F_1021. The proof is MPC-in-the-Head: each round splits the secret permutation into N shares, commits to all of them and opens all but one. Version 2.0.0, all twelve parameter sets, verified against the submission Known Answer Tests.

Properties

Property	Value
Category	Asymmetric Ciphers
Sub-category	Post-Quantum Digital Signature
Security status	🧪 Experimental
Complexity	Expert
Inventor	Najwa Aaraj, Slim Bettaieb, Loic Bidoux, Alessandro Budroni, Victor Dyseryn, Andre Esser, Thibauld Feneuil, Philippe Gaborit, Mukul Kulkarni, Victor Mateu, Marco Palumbi, Lucas Perin, Matthieu Rivain, Jean-Pierre Tillich, Keita Xagawa
Year	2023
Origin	🌐 International
Source	`algorithms/asymmetric/perk.js`

Parameters

Parameter	Supported values
Key sizes	164 bytes (1312 bits); 257 bytes (2056 bits)

Security

Status: 🧪 Experimental

No vulnerabilities are recorded for this implementation.

Documentation

References

Test vectors

20 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — PERK PQCsignKAT_164.rsp record 0: drawn seeds to public key (perk-128-fast-3)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-128-fast-3
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add91282214654cb55e7c2cacd53919604d`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add ab066e720db3a9df62ad80c8f24bfe90 40aca485c56c4a0b4e71733c44bd4782 887d601d57de29d6c8a8f7c7caf17707 7a11bb3f14024390b448632bafaa0f1f 86aebda57b7a703c83260265118735e7 9dab33649e9199b5d187c02435c69db3 6918ef7de373c0a5451c86b901b88464 8010499d95b9802d7acb2e53cef16e7c fe7db001`

Vector 2 — PERK PQCsignKAT_164.rsp record 0: drawn seeds to private key (perk-128-fast-3)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-128-fast-3
`keyGenerationOutput`	privateKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add91282214654cb55e7c2cacd53919604d`
`expected`	`91282214654cb55e7c2cacd53919604d 7c9935a0b07694aa0c6d10e4db6b1add ab066e720db3a9df62ad80c8f24bfe90 40aca485c56c4a0b4e71733c44bd4782 887d601d57de29d6c8a8f7c7caf17707 7a11bb3f14024390b448632bafaa0f1f 86aebda57b7a703c83260265118735e7 9dab33649e9199b5d187c02435c69db3 6918ef7de373c0a5451c86b901b88464 8010499d95b9802d7acb2e53cef16e7c fe7db001`

Vector 3 — PERK PQCsignKAT_164.rsp record 0: the published signed message (perk-128-fast-3)

Field	Value
`parameterSet`	perk-128-fast-3
`privateKey`	`91282214654cb55e7c2cacd53919604d 7c9935a0b07694aa0c6d10e4db6b1add ab066e720db3a9df62ad80c8f24bfe90 40aca485c56c4a0b4e71733c44bd4782 887d601d57de29d6c8a8f7c7caf17707 7a11bb3f14024390b448632bafaa0f1f 86aebda57b7a703c83260265118735e7 9dab33649e9199b5d187c02435c69db3 6918ef7de373c0a5451c86b901b88464 8010499d95b9802d7acb2e53cef16e7c fe7db001`
`signingRandomness`	`4249e0458b874d2cf0ee707de4068e75 f217bb8e877219832dfcedf6ab029ae7 d0b4e078d60d8467d1884563ccfd66d8`
`input`	`d81c4d8d734fcbfbeade3d3f8a039faa 2a2c9957e835ad55b22e75bf57bb556a c8`
`expected`	`f217bb8e877219832dfcedf6ab029ae7 d0b4e078d60d8467d1884563ccfd66d8 c09c9219a82fa6f896d0e9ddeb0d7e27 6418a3bd9af3d904cd8f520023b040a5 …` (8378 bytes; the full value is in the source)

Vector 4 — PERK PQCsignKAT_164.rsp record 0: the published signature verifies (perk-128-fast-3)

Field	Value
`parameterSet`	perk-128-fast-3
`publicKey`	`7c9935a0b07694aa0c6d10e4db6b1add ab066e720db3a9df62ad80c8f24bfe90 40aca485c56c4a0b4e71733c44bd4782 887d601d57de29d6c8a8f7c7caf17707 7a11bb3f14024390b448632bafaa0f1f 86aebda57b7a703c83260265118735e7 9dab33649e9199b5d187c02435c69db3 6918ef7de373c0a5451c86b901b88464 8010499d95b9802d7acb2e53cef16e7c fe7db001`
`signature`	`f217bb8e877219832dfcedf6ab029ae7 d0b4e078d60d8467d1884563ccfd66d8 c09c9219a82fa6f896d0e9ddeb0d7e27 6418a3bd9af3d904cd8f520023b040a5 …` (8345 bytes; the full value is in the source)
`input`	`d81c4d8d734fcbfbeade3d3f8a039faa 2a2c9957e835ad55b22e75bf57bb556a c8`
`expected`	`01`

Vector 5 — PERK PQCsignKAT_164.rsp record 0: one bit of the message flipped must not verify

Field	Value
`parameterSet`	perk-128-fast-3
`publicKey`	`7c9935a0b07694aa0c6d10e4db6b1add ab066e720db3a9df62ad80c8f24bfe90 40aca485c56c4a0b4e71733c44bd4782 887d601d57de29d6c8a8f7c7caf17707 7a11bb3f14024390b448632bafaa0f1f 86aebda57b7a703c83260265118735e7 9dab33649e9199b5d187c02435c69db3 6918ef7de373c0a5451c86b901b88464 8010499d95b9802d7acb2e53cef16e7c fe7db001`
`signature`	`f217bb8e877219832dfcedf6ab029ae7 d0b4e078d60d8467d1884563ccfd66d8 c09c9219a82fa6f896d0e9ddeb0d7e27 6418a3bd9af3d904cd8f520023b040a5 …` (8345 bytes; the full value is in the source)
`input`	`d81c4d8d734fcbfaeade3d3f8a039faa 2a2c9957e835ad55b22e75bf57bb556a c8`
`expected`	`00`

Vector 6 — PERK PQCsignKAT_164.rsp record 0: one bit of the opened share must not verify

Field	Value
`parameterSet`	perk-128-fast-3
`publicKey`	`7c9935a0b07694aa0c6d10e4db6b1add ab066e720db3a9df62ad80c8f24bfe90 40aca485c56c4a0b4e71733c44bd4782 887d601d57de29d6c8a8f7c7caf17707 7a11bb3f14024390b448632bafaa0f1f 86aebda57b7a703c83260265118735e7 9dab33649e9199b5d187c02435c69db3 6918ef7de373c0a5451c86b901b88464 8010499d95b9802d7acb2e53cef16e7c fe7db001`
`signature`	`f217bb8e877219832dfcedf6ab029ae7 d0b4e078d60d8467d1884563ccfd66d8 c09c9219a82fa6f896d0e9ddeb0d7e27 6418a3bd9af3d904cd8f520023b040a5 …` (8345 bytes; the full value is in the source)
`input`	`d81c4d8d734fcbfbeade3d3f8a039faa 2a2c9957e835ad55b22e75bf57bb556a c8`
`expected`	`00`

Vector 7 — PERK PQCsignKAT_164.rsp: record 0’s signature must not verify under record 1’s public key

Field	Value
`parameterSet`	perk-128-fast-3
`publicKey`	`4b622de1350119c45a9f2e2ef3dc5df5 07f763d0e573cc275a30483c17ad2ef9 692b40593b0d87e2931812832c223c7f 0cd53b798c4d98e0c12a12e54129c8b0 ab4405ed448b1a5c1eae2d351281fe0a 8584da5ef8a06de853e472384c8e5916 cdcd17e2b966d18711cc3f5b55a960d7 180bb86f9f3525b2506a549f73377086 a097c8049851f1c0bc6b1b0d121506cc 10085c02`
`signature`	`f217bb8e877219832dfcedf6ab029ae7 d0b4e078d60d8467d1884563ccfd66d8 c09c9219a82fa6f896d0e9ddeb0d7e27 6418a3bd9af3d904cd8f520023b040a5 …` (8345 bytes; the full value is in the source)
`input`	`d81c4d8d734fcbfbeade3d3f8a039faa 2a2c9957e835ad55b22e75bf57bb556a c8`
`expected`	`00`

Vector 8 — PERK PQCsignKAT_257.rsp record 0: drawn seeds to public key (perk-128-fast-5)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-128-fast-5
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add91282214654cb55e7c2cacd53919604d`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 59bcff353c091f9c56165035e67cba7a 9a175c360357d2450bbbf2ce13133992 a2e8f6db40255fd97d0b5a4115cc6a1b 36b26b63afb32b4a1f97c996a920f163 3ded3d856c33b4378547545ff86264e6 f81d123dc49218367edf45d76f933a60 2df68cda3ff13fbc58ad246746c03cda b06ac518b22260e5f79f2ed12b3f39ea 4df8946a53ce4184f970bf66fbfd7824 574ee4090634a30126064b4858ef3773 438381ef847b61cf1717b2a326c50361 7c940e80f016995b04b7cb42351f4db7 df5a5dd655dc3cd90930bdee008f2293 c5a7c116f7d2e1b3785bc6383661ede8 b8`

Vector 9 — PERK PQCsignKAT_257.rsp record 0: the published signature verifies (perk-128-fast-5)

Field	Value
`parameterSet`	perk-128-fast-5
`publicKey`	`7c9935a0b07694aa0c6d10e4db6b1add 59bcff353c091f9c56165035e67cba7a 9a175c360357d2450bbbf2ce13133992 a2e8f6db40255fd97d0b5a4115cc6a1b 36b26b63afb32b4a1f97c996a920f163 3ded3d856c33b4378547545ff86264e6 f81d123dc49218367edf45d76f933a60 2df68cda3ff13fbc58ad246746c03cda b06ac518b22260e5f79f2ed12b3f39ea 4df8946a53ce4184f970bf66fbfd7824 574ee4090634a30126064b4858ef3773 438381ef847b61cf1717b2a326c50361 7c940e80f016995b04b7cb42351f4db7 df5a5dd655dc3cd90930bdee008f2293 c5a7c116f7d2e1b3785bc6383661ede8 b8`
`signature`	`f217bb8e877219832dfcedf6ab029ae7 d0b4e078d60d8467d1884563ccfd66d8 a8f57a24fe26180f7a4b690f7c381555 85a5a94ba7a7c1dcf738b9ed9c24d8d2 …` (8026 bytes; the full value is in the source)
`input`	`d81c4d8d734fcbfbeade3d3f8a039faa 2a2c9957e835ad55b22e75bf57bb556a c8`
`expected`	`01`

Vector 10 — PERK PQCsignKAT_164.rsp record 0: drawn seeds to public key (perk-128-short-3)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-128-short-3
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add91282214654cb55e7c2cacd53919604d`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add ab066e720db3a9df62ad80c8f24bfe90 40aca485c56c4a0b4e71733c44bd4782 887d601d57de29d6c8a8f7c7caf17707 7a11bb3f14024390b448632bafaa0f1f 86aebda57b7a703c83260265118735e7 9dab33649e9199b5d187c02435c69db3 6918ef7de373c0a5451c86b901b88464 8010499d95b9802d7acb2e53cef16e7c fe7db001`

Vector 11 — PERK PQCsignKAT_164.rsp record 0: the published signature verifies (perk-128-short-3)

Field	Value
`parameterSet`	perk-128-short-3
`publicKey`	`7c9935a0b07694aa0c6d10e4db6b1add ab066e720db3a9df62ad80c8f24bfe90 40aca485c56c4a0b4e71733c44bd4782 887d601d57de29d6c8a8f7c7caf17707 7a11bb3f14024390b448632bafaa0f1f 86aebda57b7a703c83260265118735e7 9dab33649e9199b5d187c02435c69db3 6918ef7de373c0a5451c86b901b88464 8010499d95b9802d7acb2e53cef16e7c fe7db001`
`signature`	`f217bb8e877219832dfcedf6ab029ae7 d0b4e078d60d8467d1884563ccfd66d8 d80641754000787f27fc012140d5f870 5bc52514f6e33554a9c522a7bbc0b778 …` (6251 bytes; the full value is in the source)
`input`	`d81c4d8d734fcbfbeade3d3f8a039faa 2a2c9957e835ad55b22e75bf57bb556a c8`
`expected`	`01`

Vector 12 — PERK PQCsignKAT_257.rsp record 0: drawn seeds to public key (perk-128-short-5)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-128-short-5
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add91282214654cb55e7c2cacd53919604d`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 59bcff353c091f9c56165035e67cba7a 9a175c360357d2450bbbf2ce13133992 a2e8f6db40255fd97d0b5a4115cc6a1b 36b26b63afb32b4a1f97c996a920f163 3ded3d856c33b4378547545ff86264e6 f81d123dc49218367edf45d76f933a60 2df68cda3ff13fbc58ad246746c03cda b06ac518b22260e5f79f2ed12b3f39ea 4df8946a53ce4184f970bf66fbfd7824 574ee4090634a30126064b4858ef3773 438381ef847b61cf1717b2a326c50361 7c940e80f016995b04b7cb42351f4db7 df5a5dd655dc3cd90930bdee008f2293 c5a7c116f7d2e1b3785bc6383661ede8 b8`

Vector 13 — PERK PQCsignKAT_251.rsp record 0: drawn seeds to public key (perk-192-fast-3)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-192-fast-3
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148038626ed79d4511408 00e03b59b956f8210e556067407d13dc`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb14803e92380f3dc00284e 8067c4bb0a24fd733cbf502f9b338a4a 8c1ea4dee6924452b526b061e87ecc0c 0a8c8a67627f319b536ded4051cf5308 319c8d5df3149306d5f77d7defc48633 02ce71685bc990c92ef73df7009794f3 63188b23967715d29ac7aa2902dcfa12 e496ac605ca8f9e1f8543a472eada917 e9b30d5d3dc12093d1296b258e499bc2 4730526efa138a30d73fe3e817319ee6 8fbfad4f878dc9f776b3b6026c3909f0 7ed186ab2545e890afa492a0ef1e5ddd 8f2e267bc105021d083332c1de51af6f c8770c`

Vector 14 — PERK PQCsignKAT_392.rsp record 0: drawn seeds to public key (perk-192-fast-5)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-192-fast-5
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148038626ed79d4511408 00e03b59b956f8210e556067407d13dc`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb14803f73f0ebaca010920 2ec4211bd22c6c6f84c6b1c28b523113 afbbc29e7abd514fce33572eb295e0f4 …` (368 bytes; the full value is in the source)

Vector 15 — PERK PQCsignKAT_251.rsp record 0: drawn seeds to public key (perk-192-short-3)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-192-short-3
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148038626ed79d4511408 00e03b59b956f8210e556067407d13dc`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb14803e92380f3dc00284e 8067c4bb0a24fd733cbf502f9b338a4a 8c1ea4dee6924452b526b061e87ecc0c 0a8c8a67627f319b536ded4051cf5308 319c8d5df3149306d5f77d7defc48633 02ce71685bc990c92ef73df7009794f3 63188b23967715d29ac7aa2902dcfa12 e496ac605ca8f9e1f8543a472eada917 e9b30d5d3dc12093d1296b258e499bc2 4730526efa138a30d73fe3e817319ee6 8fbfad4f878dc9f776b3b6026c3909f0 7ed186ab2545e890afa492a0ef1e5ddd 8f2e267bc105021d083332c1de51af6f c8770c`

Vector 16 — PERK PQCsignKAT_392.rsp record 0: drawn seeds to public key (perk-192-short-5)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-192-short-5
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148038626ed79d4511408 00e03b59b956f8210e556067407d13dc`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb14803f73f0ebaca010920 2ec4211bd22c6c6f84c6b1c28b523113 afbbc29e7abd514fce33572eb295e0f4 …` (368 bytes; the full value is in the source)

Vector 17 — PERK PQCsignKAT_346.rsp record 0: drawn seeds to public key (perk-256-fast-3)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-256-fast-3
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d 8626ed79d451140800e03b59b956f821 0e556067407d13dc90fa9e8b872bfb8f`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d 8a8e11fa43a9e54dc3a97b684df755ec a1fb75e272cf97bf5a663a8c961af7ef …` (314 bytes; the full value is in the source)

Vector 18 — PERK PQCsignKAT_539.rsp record 0: drawn seeds to public key (perk-256-fast-5)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-256-fast-5
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d 8626ed79d451140800e03b59b956f821 0e556067407d13dc90fa9e8b872bfb8f`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d 52983c39c13e764e56329d2894e1b44e be4c20364e34a0e80aafb13ec47dd37c …` (507 bytes; the full value is in the source)

Vector 19 — PERK PQCsignKAT_346.rsp record 0: drawn seeds to public key (perk-256-short-3)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-256-short-3
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d 8626ed79d451140800e03b59b956f821 0e556067407d13dc90fa9e8b872bfb8f`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d 8a8e11fa43a9e54dc3a97b684df755ec a1fb75e272cf97bf5a663a8c961af7ef …` (314 bytes; the full value is in the source)

Vector 20 — PERK PQCsignKAT_539.rsp record 0: drawn seeds to public key (perk-256-short-5)

Field	Value
`keyGeneration`	Yes
`parameterSet`	perk-256-short-5
`keyGenerationOutput`	publicKey
`input`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d 8626ed79d451140800e03b59b956f821 0e556067407d13dc90fa9e8b872bfb8f`
`expected`	`7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d 52983c39c13e764e56329d2894e1b44e be4c20364e34a0e80aafb13ec47dd37c …` (507 bytes; the full value is in the source)

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