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zeekay
a466c21334
ring's lsagVerify halted the chain from calldata. A scalar of 0 or >= N makes ScalarMult return a nil point and curve.Add dereferences it; geth's dispatch has no recover, so one transaction stops every validator. Its parser also left scalars unvalidated, and the two builds disagree about them -- cgo refuses an out-of-range scalar, pure-Go reduces it silently -- so the same calldata produced different verdicts depending on how the node was compiled. frost's Schnorr check was a total forgery. An unliftable x-only key fell through to the identity, collapsing z*G == R + c*Y to z*G == R, so choosing any z and publishing R = z*G verifies under every off-curve x. cggmp21 forges the same way if either coordinate comparison is dropped: one coordinate does not identify a secp256k1 point, since (P, -P) share x and (P, lambda*P, lambda^2*P) share y through the GLV endomorphism. pulsar returned the full supplied gas on four exits -- work done, nothing billed -- and ring had three arms returning zero. Corona quoted base + n*10000 with n an unbounded uint32 off the wire, up to 4.29e13 gas. Capping the charger alone would have left the exported EstimateGas disagreeing with the fee, so quote and charge are now one function. corona's deserializePoly ignored the count from bytes.Reader.Read, which returns a short read with a nil error, so a truncated blob was zero-filled and fabricated coefficients were accepted as signed material. Its exported ExpectedSignatureSize said 4096 against a real 163840 -- it omitted the A matrix and bTilde that its own parser reads -- so any caller sizing calldata by it built a call that could only be rejected. Per-party gas prices nothing: corona's verifier never referenced t or n (dead parameters, now gone), and frost and cggmp21 use totalSigners only for a structural check. All three charge a variable fee for constant work. The cap contains it; the schedule is consensus-visible and left alone. Vectors are frozen hex with the generators deleted, because a fresh-key round trip passes when signer and verifier are uniformly wrong together. Each carries a genuine signature by the same key over the same message under a sibling slot's context, which must be refused -- domain separation tested against a real signature rather than corrupted bytes. 189 mutations, one at a time with restore-and-reverify. Five survivors, each proven equivalent by a downstream check reaching the identical verdict.
39 lines
41 KiB
Go
39 lines
41 KiB
Go
// Copyright (C) 2025-2026, Lux Industries, Inc. All rights reserved.
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// See the file LICENSE for licensing terms.
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package p3q
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// Frozen FIPS 204 known-answer vectors for the remaining two P3Q
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// parameter sets. The ML-DSA-44 vector lives in kat_test.go; these
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// extend the same discipline to ML-DSA-65 (the Lux production target)
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// and ML-DSA-87, so no parameter set is covered only by a round trip
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// that checks the implementation against itself.
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//
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// Each set carries THREE blobs. katNNPub and katNNSig are a signature
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// over katExtMsg under this precompile's own context, PrecompileCtx
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// ("lux-evm-precompile-p3q-v1"), and must verify. katNNForeignSig is a
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// signature by the SAME key over the SAME message under the SIBLING
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// slot's context ("lux-evm-precompile-pulsar-v1", precompile 0x012204)
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// and must NOT verify here. That third blob is what makes the
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// domain-separation claim testable against a genuine signature instead
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// of a corrupted one: without context binding it would be replayable
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// from 0x012204 to 0x012205 verbatim.
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//
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// Provenance: mldsa.GenerateKey + SignCtx, self-checked in both
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// directions at generation time.
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const (
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katExtMsgHex = "a0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebf"
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kat65PubHex = "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"
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kat65SigHex = "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"
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kat65ForeignSigHex = "b611cde62adbf5d17f2ec030980754e2c50206aa91925594bacfea955cf4b565037110dcf8724379a3e38fcc002b4f4a4d89e9c88123aceddc98368ba04f8d22b092daa1ab8d3b6711a46bc931003148d8b5e492f30aebff0dbfbb059043f738db23854a2ae4e351fda0e629861e610489ecba836588bee72f89dfb506903260363aed827a0f043d1bd17a0fa94d76c9f31d56a8c650752ea8a46f01efc29e9d58b3abb1ba73315295e02c60ff69b5e76228f5543220a23bbd4dca0581760792742e106d41267785018219cb3716db05862862c7fd13819427c5328e0c8b941d8c28426941986edcbcb6d950a8201f88a9469f05bae7f29b63fa8e435919734f617433efe5e07071f4c2ad6bd78c349566794bd87b45c2e9ddf75a8da24ca2c9a56bd36b65444f9967b397863b3a0ed85df7912e43198d218e5c31d92e8057c1cc891d740db3ac3c7afb46990b6992b730672fd3c97f9afe0ba12b630cb3f2c477e52fdce2d7c1b04e8603d51040da36a291d0b2395e1077685af23ce8804b50d8e3aeec1457c16dfb5a9db9baafb621e4cc715fbe405ebb9955d15fb3d5dc245a6e4f0d88270cc2706edb16ccbbcc0b66bb0aa42a7b15f5667773e534cc8bf0ebceab38b3517e1cef08a286a77246e1d1910aa297b0518ed242e76ac6c13282a233773f82c2dd19174c85d9479d87d087dad9518aeb6375ff02dac84c9f0035bdd7c908bf01c4d57145ba9e0de1c96c1d16d7890b11ceb75a3c872dc6f4b2b1e5a2a52be8a0afdffcc2818aa59d416ae52244c25d6b6c088b426c458ae009168479bde30a53ee122994e02678e0e64878e8e7be231135108719519545ac084d31a1c73cbda82a70b35880d1c1383497fed7178b150bbc810507bbc132eceffb560890aac8b2d9c664952fdaeb5cf084082194792cd4e2567c0c8b5d0ca58a344e74190fe742882c7d3c4aadf0c8ccd1eae34d0d9303e5e702f29db52008ae91e30c54f1db439f2643b56d8a8662eb5da6c1dfe973dd9a2dbddca48dd50dfa9d16dbdf00b631ac761490a99cde2f97da43bf31a57b8de37e3ac3a380964e10e22dd2afcdd3bfc8d59774cb998aabdf26e5fd0effae55ad2e88f1cec6531dc0f831c82568d04dd2802a914e255c397add0a29247c92cb4915603ba63e0328033a967a4f54c2806bd4247f331efb90ea481c74b8553cb6c9d5613706b3a0bba17022a9502c08470d5e361b982523c2261ffe52ef78895ed4cae097395df84ed188163350bfd3b426bd4be760f85304578e5b1c4724ba058adca56725209824a49ebc2e379adf32c996801606257a9fe1114bae784f0abb80533d01a8203208e3603996b81e574f82668362349ad5cae56cd04467337e06f7756dda4336d6198c0e2ab8b99474fdcd1cc90cc5d65d566e644ab499f023cc33817842ac0e97e9f86c9d2dc58db833ce6353ef657b51c907aeae8a4c1dc3eb3ee7b0e6af1b7502acde0755b05d1423de493f77f7054f0c90244db64ae4692ac57210dcd03c39ed2d461a5f7906821963d1279da576028ca65d3011c408200285a6c55e3903f22f160300315442ddc01a241087d30f0d77069b379202235ee0c7f8137ad7022648ff04332b934d6b2938727766f4fd415e1b9ef4f3920cb3869444f396cc099211acdfdcee562a24e4930906fdd575720860e26b86c0c1a7a7a85086fd1c3afd3ab52f5d866088d6e87aa191bd7e6b909aa52a404858117b9f6d11d77e4892da8f2b6ef7d578b777a7b4dcb17f475f47c9feb88425527d3707576e716b7894d1b27132dc8ef8a141e50864966980dcd95bd644f1be1e8c3d0ed3f133eb55ab34846532ac74c5f7fc321df63b676268fbd94ce615de4af7318b31d2f41eb72cf04482638672b6ab7ac59a30f0751fee25641999ee748d63d18b3f8fbe8259264080544336f4b85fdd7d0e30ba775803e713b04499a84e0fcd367deec698fba33323ee0c8b95ba3efece95c71dc71d989c98b70b1add5dc98a5710bcec103b5a30f7f756671d7b075bad4e43c90ab460e753c40aa0f7fd01eb6b19b0384e598e6c4d15eed6c9bf18468d5ca46c6aae05cbf29653b382d573d8aab0efa39ebe57136aae175cd6702fbaebe57bb0e5bd851a5ebfa0d34bedb9b6d240262d9d22e94743b0f665bdf71292c545448b684e6393f577e8d64cd9d9d446efdbf4eba04331cf5b15fc977dc72be62c8e3703d72569dee5b3d07f111d3ad4f553ee6b7c41541cdab6b1ea407ab5d0724dfc3c27f471234de501e3d4ebfa3c9dc0d02c40fdaa5984561c6083b5521e98a5aa6d961088aa2ab491a1de9f566d2e12c70bdbef88457f27d1343397927043aafe12c7e0d672a99e7085b7ed3d29330290ca3996e13ce51cecb8c00979537597bc45922ca82b450560dba81dc9690e98917a95293d94b21be4c1c29148b5337773a61a5b4e58c267f2e431d6657409f8a2e7bb9995ae2fb821cea4f206a197a8f3bb7e5c21e10d1d28ec2bd06cd6e65c8b8e20e8e82bd2d86fdb5991c43740bd5e5d52d0d75f241bbbaca2766f2b21c572a681f1fe2e41b7eff87151e75a0dce652e5caf2990415ed1f9d81851374a6e5f0bd2c894b7062a57689770a532ba180ce9b7e005338ddb0799cc9abc74a977a4dfd42bb0265dd5da83cb6ef14b396be0bfb15c8c8ddabf339a6320f272e60b0c47670773ca969aece27dd0685b88064e5e1f79e9b01f1b9f055ab87319e41c8d01585f1147ab4ffddeb56df07bf171e68f998e3f53d023901fc11a46a367b6da091133bb6b93e66816fdd364e153f8dfd8c969f4156462e24556906350b41857f5f588a0bb5c0ef93540bd1101f7e73307049df8b5ca9522051b1899aa0d76a799d0153cb85dc6e99fb6076a6feb8b9fcbbdc70e43d7b7b647aa2dcd0b1ef0b3c326122188c1ed3ae266b8e6b1b0b7753d24f16b360b71a4ed9b9b9daa8d8f395bfb184218342b537b4f008aadd58572018ea4cc7949a9276aaa315b579eb873a1fd1498d6ea8926f9cf5b2a4bc66f1ae8b739fa57f600ede94377533b07e1a6ca832da5da991f8ff6ea77fbb3b5c9612e2bfc916ab0e307e0feb08185abb26a15ce24020679a7df8b78c551261a4c4f87cb4ced601a5b0e20a9e20bf298b230fa64931b593060a3ecb4a38063e061d3564174c21203e53e29aa34b505c6ec9bbcb35432712f6566e8a9aae4da19549166786b8ca084ca343f4ef79ac6a4362ae74b5b9d164f525814c96178f28d729246d7f8de2c0df8f04d625a00f722bc3cfae909e01b966b4159a319ac7d58f05e74fd1f25ee4949c6bf001dc3e192a96843cbdc23c9c32a510b6115e838926908e3b1969d4e1722c434749c6ad66b5f53272b8478c49d5dd20c15e50cf441e82a34cf676d25f7e991a90999e195da0e551b0dca45b24ed15981dfc0acc4a16547e5eddcdfb6c59b0e8524aa9b3f50257129893e2d38dd7840419f127ecf3bf93b1cfde2e4ec8699b1dfdbaa9f1c550fdae473704757b4a76a5578fb9462cfc0c6b24061b158ba75542c25622dc8d02742f245915a8865a2c203b1ac8a6c8687f57912bc183545bf63c2be158cc1c319fa6d1e0a02e9f3b778bb1eb0836b48f2393120ad2dcd9e7b6f41ac91167e7c49aed0b2da9e6381debc3634284b7c045b210d79023898b2004bfee59000847057cb3408ede88c5a15fb6af8ded43a229cb0fac8c7f7f057319313dcc6fb58f1dc8310486ffa16327003c1b88afac533a24c6802097a4e4c5556e806dcffeb0da04fbda8c7fc730ebeb312e570e263646d05d8bf388f06bd56b0ea19f3abe1f5fe9e0d204c9f2b95bf7377ff345529ec8a267a0ec5c91ad9b3d26588f71bb3b7f5ff06ac7a8d8d9f79b1ca9737e788c1a3bc18a50f43f6c8f2b9fa54c101b29b2b3975de06afaa3795d86356b32b2c90031249e0573d956fd53bfcd59be3bf63f4d8bef94c0fd820b886145ee59cf618ef31f21f72c5adb439ef788251304b88e0557edd34daa6048b36f2310fe5dc06cc351392d1a29fb60ee97a88688e62069d4cac034b7f6f3fc3a8f84b93472c2ff92948487e46d43c1297c194cb437130c7caf51ba71ed92e0967618c858801c8928e1af25a160ac9971e2c3ed511c2847f44865c942a05daf62c187879fd37d536605cf1bc142121c950f492d5d8ed6988d9de5bbe2127d765f7fa14a99a4fa00f739903695e3e67df5ec020c1970ffa26e1d7bda5b8e37d95942f9afc35a23805da03a8cf07789d97fae8af05c664baecff373c52549e19755e08b5ac8993c89263d1eea579954a4aaf15aceda9145b395b8e4423bec645a6e984949d16177e888d0d6b496b2be440f7b62a344b36c22f302103a804027b7cfde19c3935945ac78336c57f61fa7af88f5cf67bc4da2f21bc834d7906fe9d4d2d70346e141b46c9b2ef1bed3d22470b3acbeba4e6717e9f046fba0bcac3f7370f2fa81d9d2a0b2c141c376148769454991e2dca07a64a44e4fcae74f2a725816590e56a108b5f3c6d88f29dbe86794cbe561553bcfb41d6d5c7a74c36aab959aac390223770c5af6a14612198e374c91618404647636797cee0092278b5bbc7d8de387fa8c30e1164dcedf6061a606b8287903142555dc1e100000000000000000000000000000a12161c2329"
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kat87PubHex = "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"
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kat87SigHex = "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kat87ForeignSigHex = 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