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NFC: bigint: Expand use of BoringSSL exponentiation test vectors.

Browse Source 
Prepare to merge the rest of the not-yet-merged BoringSSL changes.

The recent refactoring of `PrivateExponent` lets us add a new test-only
constructor that can support a wider range of exponents. Also, there's
no reason to avoid test vectors with a base of zero. We do need to still
reject 0 as an *exponent* and too-small moduli.

Accordingly, merge in all the relevant test vectors from BoringSSL's
`bn_test.txt` into `bigint_elem_exp_consttime_tests.txt` as of
BoringSSL a8b1633d1c6be133b9f684cc5cdd778bfd8d564e, which is the last
commit of BoringSSL that has been merged into *ring* so far.

```
git diff \
  a8b1633d1c:crypto/fipsmodule/bn/bn_tests.txt \
  src/arithmetic/bigint_elem_exp_consttime_tests.txt
```
This commit is contained in:
Brian Smith 2023-09-09 15:19:21 -07:00
parent 3bd30bb1bf
commit 2251fcd371
3 changed files with 292 additions and 32 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
src/arithmetic/bigint.rs
View File

@ -940,7 +940,7 @@ mod tests {
let base = consume_elem(test_case, "A", &m);
let e = {
let bytes = test_case.consume_bytes("E");
PrivateExponent::from_be_bytes_padded(untrusted::Input::from(&bytes), &m)
PrivateExponent::from_be_bytes_for_test_only(untrusted::Input::from(&bytes), &m)
.expect("valid exponent")
};
let base = into_encoded(base, &m);

17
src/arithmetic/bigint/private_exponent.rs
View File

@ -45,6 +45,23 @@ impl PrivateExponent {
})
}
#[cfg(test)]
pub fn from_be_bytes_for_test_only<M>(
input: untrusted::Input,
p: &Modulus<M>,
) -> Result<Self, error::Unspecified> {
// Do exactly what `from_be_bytes_padded` does for any inputs it accepts.
if let r @ Ok(_) = Self::from_be_bytes_padded(input, p) {
return r;
}
let dP = BoxedLimbs::<M>::positive_minimal_width_from_be_bytes(input)?;
Ok(Self {
limbs: dP.into_limbs(),
})
}
#[inline]
pub(super) fn limbs(&self) -> &[Limb] {
&self.limbs

305
src/arithmetic/bigint_elem_exp_consttime_tests.txt
View File

@ -1,26 +1,119 @@
# ModExp tests.
#
#
# These test vectors satisfy A ^ E = ModExp (mod M) and 0 <= ModExp < M.
# Additionally, and unlike BoringSSL, these test vectors satisify:
#
# * A != 0. Test vectors where A == 0 (mod M) were removed.
# * 0 < A < M. Values of A that were negative or larger than M were reduced
# Additionally, and unlike BoringSSL, these test vectors satisfy:
# * E != 0. Test vectors where E == 0 were removed.
# * 0 <= A < M. Values of A that were negative or larger than M were reduced
# (mod M) to be in range.
# * M requires at least 4 (64-bit) words to represent.
# Regression test for carry propagation bug in sqr8x_reduction.
ModExp = 19324b647d967d644b3219
A = 050505050505
E = 02
M = 414141414141414141414127414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ModExp = 00
A = 00
E = 8de689aef79eba6b20d7debb8d146541348df2f259dff6c3bfabf5517c8caf0473866a03ddbd03fc354bb00beda35e67f342d684896bf8dbb79238a6929692b1a87f58a2dcba596fe1a0514e3019baffe1b580fc810bd9774c00ab0f37af78619b30f273e3bfb95daac34e74566f84bb8809be7650dec75a20be61b4f904ed4e
M = c95943186c7567fe8cd1bb4f07e7c659475fd9f38217571af20dfe7e4666d86286bc5b2bb013197f9b1c452c69a95bb7e450cf6e45d46e452282d5d2826978e06c52c7ca204869e8d1b1fac4911e3aef92c7b2d7551ebd8c6fe0365fad49e275cc2949a124385cadc4ace24671c4fe86a849de07c6fafacb312f55e9f3c79dcb
ModExp = 5150fb769d5c5d341aaf56639a7bcc77c415fe46439938a2190283409692f29cd080bfe3433005d98d24718a03a3553c8560c5e9c8ed0f53b8945eb18290e1c1a83d919302510f66dd89b58acc2de79ad54b8a30d3e1019d4d222556beefca0821b094ecf104b5e4cfce69d2d520d2abf54f3e393d25ed3d27e8c2e3ca2e5ff9
A = 217f828be4deb4523de5929628e0cd1d9245827ebbf5552192a460824d59b1c6db283f88d9531c9ca7adb464a7af169af532c64921b3d1c85343991f8680ae87363aa7c3a35ff00acae37b98c6d2fef8694d41a53b6da552953e3bb7263012aa5c5af1ac5eb6ec657821ad9fffe9190d7b62af9df748b55179c4cfe3a2cb6302
E = 8de689aef79eba6b20d7debb8d146541348df2f259dff6c3bfabf5517c8caf0473866a03ddbd03fc354bb00beda35e67f342d684896bf8dbb79238a6929692b1a87f58a2dcba596fe1a0514e3019baffe1b580fc810bd9774c00ab0f37af78619b30f273e3bfb95daac34e74566f84bb8809be7650dec75a20be61b4f904ed4e
M = c95943186c7567fe8cd1bb4f07e7c659475fd9f38217571af20dfe7e4666d86286bc5b2bb013197f9b1c452c69a95bb7e450cf6e45d46e452282d5d2826978e06c52c7ca204869e8d1b1fac4911e3aef92c7b2d7551ebd8c6fe0365fad49e275cc2949a124385cadc4ace24671c4fe86a849de07c6fafacb312f55e9f3c79dcb
ModExp = 00
A = 00
E = bb552be12c02ae8b9e90c8beb5689ffefe3378d2c30f12a6d14496250ecce30317c642857535a741642c3df689a8d71a276d247ed482b07b50135357da6143ac2f5c74f6c739c5ff6ada21e1ab35439f6445a1019d6b607950bffb0357c6009a2bfc88cd7f4f883dc591d4eb45b1d787e85aba5c10ee4fe05ea47bf556aec94d
M = dcc24236a1bb94c71d9ec162a6aa4697b932717e82b667cad08b6bd1bbcbddf7cd167b7458de2b0b780486b39574e749d6405f9ede774a021d6b547271523e9e84a6fdd3a98315607ccf93356f54daa9c75e1e311e1672d0dc163be13f9ed6762f7dd301f5b0a1bb2398b608f40ac357ae34fc8a87d4fef3b961cbdb806d9061
ModExp = bbad67352704a6321809f742826bf3d1c31c0ad057bf81432abeb30dc9913c896c03e69eb1cde6b78ffcb320c4625bd38ef23a08d6c64dc86aec951b72d74b097e209ce63092959894614e3865a6153ec0ff6fda639e44071a33763f6b18edc1c22094c3f844f04a86d414c4cb618e9812991c61289360c7ba60f190f75038d0
A = 855144760f2be2f2038d8ff628f03a902ae2e07736f2695ec980f84a1781665ab65e2b4e53d31856f431a32fd58d8a7727acee54cc54a62161b035c0293714ca294e2161ea4a48660bf084b885f504ad23ea338030460310bd19186be9030ab5136f09fe6a9223962bce385aaaf9c39fe6ed6d005fa96163fe15cdfa08fc914d
E = bb552be12c02ae8b9e90c8beb5689ffefe3378d2c30f12a6d14496250ecce30317c642857535a741642c3df689a8d71a276d247ed482b07b50135357da6143ac2f5c74f6c739c5ff6ada21e1ab35439f6445a1019d6b607950bffb0357c6009a2bfc88cd7f4f883dc591d4eb45b1d787e85aba5c10ee4fe05ea47bf556aec94d
M = dcc24236a1bb94c71d9ec162a6aa4697b932717e82b667cad08b6bd1bbcbddf7cd167b7458de2b0b780486b39574e749d6405f9ede774a021d6b547271523e9e84a6fdd3a98315607ccf93356f54daa9c75e1e311e1672d0dc163be13f9ed6762f7dd301f5b0a1bb2398b608f40ac357ae34fc8a87d4fef3b961cbdb806d9061
ModExp = 00
A = 00
E = 9f43dcb641f3ecf4dbc97450f2bdf3b7ec6a2f3e8e96bb1df2bf34b8d2d78e1a9018d04d960ffd0e932cfc60d3b9b923e3f9f29b3f3d61cae3a9f7245078143475c7fcb896ff200f7d94c4f2708bb42750e37c185a31c876814e4f06a00771707654e1da2fb69c16b6500b16385e3b933e2276ad3569977473f699b1c7926c3b
M = cd607549668469b792f495c141e500871880b0611c8004293a561ec7f9ab6561f8a9b90872742386adafb5cd1890e8204ae12aec529cca0a9e382c96439137f09de9973b12c8492c62847e107deabb7dd946ffbb9d0ac73b462c481092bd65326a17f21d8d6527c47a5dba50aaa20c7048b8788a49eb3ea5f29bd5cfce24eb3b
ModExp = 24eaead5b57883c2f454928f8edd470a344bfe07a953194f7d635d705ef13ddfc64140c8ad6f363d4c828e7c7891a6b6d4df37335de4552c319dafd1c06d1f743240082a3535df4da1475d3eea3fead20e40815fd5a0876c881c162ab65a1eda494280c258901ca953d1d039a998bf0e9aa09273bbef4865f3054663b72d75ff
A = a31618b4532f53729ba22efb2221432fab1dbb70853d6a1159b42fd19fc949965c709b209de106a652aa422d88922ce51dae47f7f6deaf0055202e13db79ee84fc3d3c6f4c003ef96597c49d6895fa53c22ac9e4819f7048146b5272f6279424fdb389819a0b251c823c76f4bebf4f1246de455aafe82a0d34454f5039e90839
E = 9f43dcb641f3ecf4dbc97450f2bdf3b7ec6a2f3e8e96bb1df2bf34b8d2d78e1a9018d04d960ffd0e932cfc60d3b9b923e3f9f29b3f3d61cae3a9f7245078143475c7fcb896ff200f7d94c4f2708bb42750e37c185a31c876814e4f06a00771707654e1da2fb69c16b6500b16385e3b933e2276ad3569977473f699b1c7926c3b
M = cd607549668469b792f495c141e500871880b0611c8004293a561ec7f9ab6561f8a9b90872742386adafb5cd1890e8204ae12aec529cca0a9e382c96439137f09de9973b12c8492c62847e107deabb7dd946ffbb9d0ac73b462c481092bd65326a17f21d8d6527c47a5dba50aaa20c7048b8788a49eb3ea5f29bd5cfce24eb3b
# Craft inputs whose Montgomery representation is 1, i.e., shorter than M, in
ModExp = 00
A = 00
E = a5524b41dfc6b570df1d8f6633ac7777c1131abe3a99c6166b0d29d3b8883c41b00a0c53cdd6f42820bf05c810b6ec53e77a8c1b9344ea0c91d4f410a2f204c369f3db33bf8c88217fc2cf802a9d9bce8119242d8e781875b85431be170076498c0963574ee423551aec9557e2fc672ab1ab5d0cbb1c400535df9481e7934d8f
M = 88f3c87ac5e3272a21b8a858da640d6939fb8113a95412c38663a0f352686d69a5d7927e60b484b9fcb8ef12978fe25ff2ebc9b61c5450e04222ef20ba3cbbdc5ec45581ce0f58e10be7bb9de7fa08752303a7a1db23b2ac9c6692ec63bf09ecd6639e06c5491ba568ea886620d71da32d329615f0e1443a75d09ae35b8a2d7f
ModExp = 292f0b39ca0f1c850b1a00cffd2d54924fcd5fc7e7504c9d593e6c0ff74760b1f4bdd81679fe06c50248336f3108c593fa111072ee87d0fcc89a63243a1dc89044503663eee9bc18f51c3e0193d9108303e12ac90ff78f6ec752a4386af09c42db524a7cbe9a3d4fcccd56c34d283bcc9debc17158b5fe8df0c1888a9841bf8f
A = 2c0a1a15c162d868aa9f7e49a36bd03764947edabec43236c61b726186de686ea83679fbe9982d4f4720d82b3f77e7e7e4aacaa7531704b2f93e6f0b97f2a21fd51c0fa749a527ba9f9f395c6eb922ff4913cfc2ae30e0240a400694c7691e1199b9a2e8b9b6bbe940055964a088d9a6fc27734b5b0f0873a47f7ca3d018017f
E = a5524b41dfc6b570df1d8f6633ac7777c1131abe3a99c6166b0d29d3b8883c41b00a0c53cdd6f42820bf05c810b6ec53e77a8c1b9344ea0c91d4f410a2f204c369f3db33bf8c88217fc2cf802a9d9bce8119242d8e781875b85431be170076498c0963574ee423551aec9557e2fc672ab1ab5d0cbb1c400535df9481e7934d8f
M = 88f3c87ac5e3272a21b8a858da640d6939fb8113a95412c38663a0f352686d69a5d7927e60b484b9fcb8ef12978fe25ff2ebc9b61c5450e04222ef20ba3cbbdc5ec45581ce0f58e10be7bb9de7fa08752303a7a1db23b2ac9c6692ec63bf09ecd6639e06c5491ba568ea886620d71da32d329615f0e1443a75d09ae35b8a2d7f
ModExp = 00
A = 00
E = a55703a72ca3f6074b939ed3d748196a684a3c8e411c2b39a9beb98993b6eb7ea3fa16f41bc5b5c3710b91c0fc74a8072793052f872f61695db3a2df872eaa427a110f1a8d568c85d58bd350d0df8eced7a10be80f7567360c1a8047b9c44aa2967cd0d9dd2caea2c1492358c2db4f0214da343fdf2e34272865dc5c63be2ae4
M = cf0dee80177869a532f0c6c3a0bda3aad79bdb6b70b6c227b32d75c26e394a90c1f2a6c2bb841ba9f6556b15654a79d8b1dd0c90709a093497bf40be0807cdbb378a74de5893c25067224d3ea8d37387ed6c4a981138853cb89caa9ce6cd0f6a1e95de24d558e90960f93844db4d01e372650350d45a9d34a36042b4d4b9e78d
ModExp = c90e4c69df92e26549b016950b59080947f5403430698e128477782480dd70be96bed2b9042dd8c708eb432e02710555b97af11ce6fa9b53395022851c32d1f53f04237fb0763563b440ca6e81a50d909d907d9c26b7d3c420dbf88f7dadd488666848135f8cdc608dcfb0691989289fb54379c2e84c262f9765f68c012ca1b9
A = 882ea1b9b6c79a3b1bdfd284658cb6227ad825e0178cab713c7413c2ec34f03cfaec470c4f5c521f5e9899a2123878ff0f5b36a4196c08ad1b04d03746c4bfb5d126f5eefbfe172627d6732710a8ac8890cedbd4fdef69a19f2b3253a5aa0e5dd5484f72d59b17bdd1dad3db209a3ab839368ed3975069685911d7b35e41a9e6
E = a55703a72ca3f6074b939ed3d748196a684a3c8e411c2b39a9beb98993b6eb7ea3fa16f41bc5b5c3710b91c0fc74a8072793052f872f61695db3a2df872eaa427a110f1a8d568c85d58bd350d0df8eced7a10be80f7567360c1a8047b9c44aa2967cd0d9dd2caea2c1492358c2db4f0214da343fdf2e34272865dc5c63be2ae4
M = cf0dee80177869a532f0c6c3a0bda3aad79bdb6b70b6c227b32d75c26e394a90c1f2a6c2bb841ba9f6556b15654a79d8b1dd0c90709a093497bf40be0807cdbb378a74de5893c25067224d3ea8d37387ed6c4a981138853cb89caa9ce6cd0f6a1e95de24d558e90960f93844db4d01e372650350d45a9d34a36042b4d4b9e78d
ModExp = 00
A = 00
E = 95793fe33696f53e37498b2b65aaf27079e27acf1da97dda2c3e0803e8a02139f574e04ee03f7d1ddd029f528e3f3644515ad6f10f0beac2767f23d9cd8a8b9b6c6e376e36b64a0ae2711d7d31a5a75011641935b503110edbefe9f0ff2da27b5c5f6bb8cc151fdc86f67191bb99160c6cacc86ca368d5bdfafd3f3ff5161b1e
M = 8315dacf124bd473c578946347e83d1b20c750a7d9533d6215591be40bc78bcca77821f8c8f95375bbd6372515ada63d22bed2fa49bd6fabb0040c538d08db25b09d2fda02a93ab086cd1c27df93c37ee9c6a0527d089179b8f92b5dc3acf5ef1c75906fb80b03f5c2442a7a4088640f66376575ecfa4c697c1a571397ee5a0d
ModExp = 186c50ae259aa0fd31859cbcfea534e626a254de33956d5d719334bb32e7cf37cf199a21f079a5b90497228994d05efe19ccd8c769cd81f896286e8ae557cacd1630a928c629ecdfece29ab3697794aa707734e007318fa7029b050bb09ebbe6986187c6ca843f55266d275620b3f0fec0ad5f847ce8b314d929d128b33a249e
A = 1a48598881af0956d2ef5ddba5f72afba120e74fc97c5997f218f66d3f03e01bd347f82ab495dba74bfc4368c76d64a3b6bf48e00562eadd934c0ad4bfd6037e336a81df3e2dba708be919735ef3214946ae1129a402514ecc721753a607b1b7c330cac6d26e5553aab590a4a8b49d8e5741aaa243e9a9838c45f3a570a25f07
E = 95793fe33696f53e37498b2b65aaf27079e27acf1da97dda2c3e0803e8a02139f574e04ee03f7d1ddd029f528e3f3644515ad6f10f0beac2767f23d9cd8a8b9b6c6e376e36b64a0ae2711d7d31a5a75011641935b503110edbefe9f0ff2da27b5c5f6bb8cc151fdc86f67191bb99160c6cacc86ca368d5bdfafd3f3ff5161b1e
M = 8315dacf124bd473c578946347e83d1b20c750a7d9533d6215591be40bc78bcca77821f8c8f95375bbd6372515ada63d22bed2fa49bd6fabb0040c538d08db25b09d2fda02a93ab086cd1c27df93c37ee9c6a0527d089179b8f92b5dc3acf5ef1c75906fb80b03f5c2442a7a4088640f66376575ecfa4c697c1a571397ee5a0d
ModExp = 00
A = 00
E = f0460c5ca9b3a5c2d1b93c201d020dc43e1c81d1daba432e2cd310902da23eb81a5172b0b357484eb8fa2c04c270893b8198c8ad35453405dadaf05195b3aeb5ec0ccacecb4b6227ca43b27b97e240a4148a472670ed60f304302f757495fd4a91af0fe09800db0c3043a6ae213bee6703ad80523ca433d99ca0eab1e0b7c929
M = 81dd561d5d5327fc5ed7c9236b5fb21ef713c6d5e36264ba65ccc801b8eb107b714aad65bb503bb1f4721c0a6f97e5ab89300f049f42a4616ae43d29c089c286687484d18629c1be1b5befbdd0b3cfc86b1d28add89df4cc5e68dac3f56f2490a9068ca9c634ec258c030ec5023baa9133fd2af32fd1112895f9da549d410247
ModExp = 60719701a2dc0bcde281a93ce0b8421d1a718adee43c1b5d9fe9e697a48ab3db4f9f33c73cff305ab6b6c300c149b05c6b289dce4580860dc56bc59de81ac074ecebdc65aa3ca040b44e5b3c80ddba1658d78b9abbc4c77e5f171f5582e70ab4438a8e1e2f062d618c4ad09c70c73b5b5fbc9f8f0bbdf1d530a933b705f85af8
A = 5fd6aaafddcc07200c6bb1bc70375b0d89f52addb8794c7b1c4acd5048315c1c5a5c128d0912e5798af05b60344bca4e68458a09d9f6ba2031300626f0187adafb18cb3d466db0acee322b3563fafe5b3d349e6a88864df3f04ed8bc64b5a7feb28977777fb67237de3d71cd80efc12d84a8f64e6ac171d2c60d84ed2ab0fb7a
E = f0460c5ca9b3a5c2d1b93c201d020dc43e1c81d1daba432e2cd310902da23eb81a5172b0b357484eb8fa2c04c270893b8198c8ad35453405dadaf05195b3aeb5ec0ccacecb4b6227ca43b27b97e240a4148a472670ed60f304302f757495fd4a91af0fe09800db0c3043a6ae213bee6703ad80523ca433d99ca0eab1e0b7c929
M = 81dd561d5d5327fc5ed7c9236b5fb21ef713c6d5e36264ba65ccc801b8eb107b714aad65bb503bb1f4721c0a6f97e5ab89300f049f42a4616ae43d29c089c286687484d18629c1be1b5befbdd0b3cfc86b1d28add89df4cc5e68dac3f56f2490a9068ca9c634ec258c030ec5023baa9133fd2af32fd1112895f9da549d410247
ModExp = 00
A = 00
E = 8622c37631e428402343dccf8ed09d47b3f4201e95058910289a62707c3ce0b7113c390056cc4796cc9893e471b12cb3f63f900f3356ffd25c8b2fed6f6a7fba2c684eb241ca706c76cecbf72473d8a58c02338e40714b5610465cc319f0a529a7aa3898d9e638b247abd1380c6e8f7fa210c9f1a1a2164db6db83a6bba79436
M = fda6f9d8588e3614f5a68ce867a5619f6ddbb8d64450ff402e1c4f1a08b518f79dca21e5983c207c5b7324c16895a1e9f1282fc6cf60b0645f6b02b652ed5b129e67c939e854ab492dec30ea878c3edde10a4b7d1d14c57100c6cbcc5fc085a0d7308715ed132fb917251919c727487fedb66500d5610b0014a43419acfbb92f
ModExp = 86fb0b8dc161c41de2adb0f3ddcc8ad49c1efd729a52793a3ac987d4011c9c1dadb18657dca718df75c8ddcc49d60f152c46ab85ae9076ee7bfd405679a7da3a5195a1bbfd7d2b998c7b135ea91f8c445cbafe1276fa502c2a85477716829a2e0d24ba02623405a3654bed8f355bc7ccdb67c3f9a01e249e358b60d7699498a9
A = 816610e6018ca47074d55750dd16a281019dbf95dc752605794cbb8ea8d75775317ce685737859728320b529fb3b4414b40bf3a93d08d8994a21ae54682cc1c357eb529837a7b0129a0843eebd9341c9bee3a8ae30475bdbff517e885a0c9f2b6a680643bd981efb53bf9dd49f3dc3cb757e117895fb34b1b4336d9bf8384558
E = 8622c37631e428402343dccf8ed09d47b3f4201e95058910289a62707c3ce0b7113c390056cc4796cc9893e471b12cb3f63f900f3356ffd25c8b2fed6f6a7fba2c684eb241ca706c76cecbf72473d8a58c02338e40714b5610465cc319f0a529a7aa3898d9e638b247abd1380c6e8f7fa210c9f1a1a2164db6db83a6bba79436
M = fda6f9d8588e3614f5a68ce867a5619f6ddbb8d64450ff402e1c4f1a08b518f79dca21e5983c207c5b7324c16895a1e9f1282fc6cf60b0645f6b02b652ed5b129e67c939e854ab492dec30ea878c3edde10a4b7d1d14c57100c6cbcc5fc085a0d7308715ed132fb917251919c727487fedb66500d5610b0014a43419acfbb92f
ModExp = 00
A = 00
E = a3be10ef04535fca6784e5dbf3733d677dedd50fabbc3a860496628950b4747a328c2ce0d903cbe1e700f0af30f59fb917202257815097a2b516df5d0a82642faeffdfc3b7883766c78fc4be5901ebef891a9ca27f3bcf00960729e659bb3fddd54a19ce628e95ab86e4c7a168588bc9f67b05dd21a583acd8dc36e615945648
M = dcb68f6aa530ae9b31d078e2e82670adcc98228e7cf1aa59f81e66426ef14b1591b833d889463564c75b5fd5551ea295a0da581dd80f62c7008ff0f26a1c9f4f756431d48198af157149be8698336b306b0a8b8635d3fc2c4c2194ecc4d2af31ca1892917cc2e621d702eaaeed0d9a0c3dca575451eb8bc5487e313988cae745
ModExp = 442866609915aa6f1bae9dfb59e721e1b63f42c0f75fbf0a88344120fbbd7aacf15208fb7c9d8bb8477d553cbd826d7e685ad764a8423e81c2131c040ee83a03cab8d5ce50866a941b48c78e9f1330794d908562d4141cfbf26e8c80c69551339eec41e37e2b37b54330f7bd75748f8d26d56ab9eb3b0c127540484c6445a7fa
A = 8ff65e2cbcbcd8697cc3ce9a26855d6422ac7eb4e66500648c08be697e005cc3c854a54cfab91d43489cd60be8b516a9b3c9688e5e009a1689c6b164a133859a5464ef422c86344fef42cc477c9df27768377c126a066d1b62f593b7f6d6e906feaee16addb7cfbfc043d741b7dc81a87c17f167b7b8ef1b1fb3dfd1eb14102d
E = a3be10ef04535fca6784e5dbf3733d677dedd50fabbc3a860496628950b4747a328c2ce0d903cbe1e700f0af30f59fb917202257815097a2b516df5d0a82642faeffdfc3b7883766c78fc4be5901ebef891a9ca27f3bcf00960729e659bb3fddd54a19ce628e95ab86e4c7a168588bc9f67b05dd21a583acd8dc36e615945648
M = dcb68f6aa530ae9b31d078e2e82670adcc98228e7cf1aa59f81e66426ef14b1591b833d889463564c75b5fd5551ea295a0da581dd80f62c7008ff0f26a1c9f4f756431d48198af157149be8698336b306b0a8b8635d3fc2c4c2194ecc4d2af31ca1892917cc2e621d702eaaeed0d9a0c3dca575451eb8bc5487e313988cae745
ModExp = 00
A = 00
E = a0bc148ed50a9b54036bb8fa1f214979052ebd47db8b347af3bb03b806bb457b468ba34781f8a25f289a7a90af4903dc14809a166df2f4c3527de2ea6911cb1afb9071a4afbb522a7d50634d66fd584c73f32d05217dc9f7f16394c68a692a953492ca85f89cc11da95fd8cac6231647923ced48a1b3b0ee68c010286d452836
M = e7a96cf6fa930f73c8bdc2726bbba246001a9d27f39cc2b978c99dc6f15af0e8aaf26b565302f1112e607e2df4066948baba931b89cd9bbdea2072e05b9a4968fdf282c43d997987c3a3a0434e925a679ac81f316b7a7b724b79be3d6888b66f4512759bf66cfaaa88b9513dd27a44aaea75437268a014c4eb50ba2e50093511
ModExp = 91fd879d02f95a9f40fcd1037726f73892caf84e9b43b4aa4126d9062a0d22c464e7af2fbd91aa849612d99d9519b724a7fb1cb018fffdcff321d883ab2519953c9f174f09dd8f13ac87339887385966eb4a94842276637b2c36c0a5036b1d3bbea438bc6efd4b4851c7ec06879d60694df894717569bcd31c4b13d80df6cbca
A = cdec5edc1cb3ea974342b85aabc0f9385cf877ca328747d40dd4d297623ad69ab6582653faeed5aef225208305135cfbee32e066cb43e18afacea3a32acc8aabbc49617ac33e741651924ae56dd6aa044a12a1ea50fef573b5befb2f4b21b9cf83ab2aaa6fd153580a0761666ade8fb94f202a3c3dc4f33297eabb4564374168
E = a0bc148ed50a9b54036bb8fa1f214979052ebd47db8b347af3bb03b806bb457b468ba34781f8a25f289a7a90af4903dc14809a166df2f4c3527de2ea6911cb1afb9071a4afbb522a7d50634d66fd584c73f32d05217dc9f7f16394c68a692a953492ca85f89cc11da95fd8cac6231647923ced48a1b3b0ee68c010286d452836
M = e7a96cf6fa930f73c8bdc2726bbba246001a9d27f39cc2b978c99dc6f15af0e8aaf26b565302f1112e607e2df4066948baba931b89cd9bbdea2072e05b9a4968fdf282c43d997987c3a3a0434e925a679ac81f316b7a7b724b79be3d6888b66f4512759bf66cfaaa88b9513dd27a44aaea75437268a014c4eb50ba2e50093511
# Craft inputs whose Montgomery representation is 1, i.e., shorter than M, in
# order to test the const time precomputation scattering/gathering.
ModExp = 9442d2eca2905ad796383947b14ddfcc341f5be8fec079135c36f6f0d9b8b2212f43e08bf29c46167ff0fe16b247cd365df4417d96cc31c94db1cf44b73b0ee3ebcc4920d9b0d003b68e49c1df91e61bc7758a8a1d2d6192ff4e1590b1a792f8be3a1b83db3ad9667d14398d873faf5d885ec3a2bef955026fae6dbf64daea2b
@ -28,96 +121,246 @@ A = 3a4b4c57e62c5e9d1a9065191f8268fed9d5f6f424d071acef66f0662b8210f4c029ed991512
E = a2c56ea1362511cac0301918e15a9afe7d37edd438a5c3538d258ea01f0a6df758de07111e868b3ad8fc89b629b4955d78a1b3af902be1806410ddde25ccc6a196ba5949395c1ad5d8725b18815dc1cd5ac1c7dd17773f571e3f2e628255af14476e0494be23a4a4dfd18e23142f33d7a59c236fec61660e360d9676a747c69f
M = ede35a3a7afac817d413373a2032abbc067b1493f709ae6e1282ee5469743391d891b904938857168802b7872d3cd7ac18ab249a9e540a86f970b1d0f310a4cc29df1cc9d4063d98c554f1a32f4ca5eba3523cdfb142e0fc609907c7a92bb0187009d97ec471db3545f42dd5fd29c07b7816085d09477ba31fcf90084660116d
ModExp = a7f5844fa9e7202d4b70ee252c9846e63d3d091b0387768ded872cec53458e19df0d9b4960226e269b8ca5dd4c4eda423a67b6dbb48235c08c12c6c7c78db47287756d3ed9cecb9232f7d18d5d80b9676cb68ba4a290c97e220beb1a069976b5e6022a4c1e5ddbeec86b62dda24ffea1deda37695c9f61a8817218e6370c0679
A = 7d6d0cc947ceb949cdc4e9e1044f5deca5bb05a491041e0d85bc4b92a0944a57c72845fad91e59010c61ad1712bd2f612d53a846a044632262a9f2e3373b062fde2484e0c165ff947f2469f743ab6e2e5e13c640fc4029b1c9213eb8473c674e7f9e95a4a5c5636d4656c1e696962340d77b322daba47d6fc894f2a2cd9e0afc
E = b78012afe806e2344d004c739c97324256850980ac97d88c4ed9a838517639ca112e235978d21a176c33f5a68703aba0f2a05501bbe3fc8d49a000fbf530cdb431581dfaf8683cb15a2aee5e239cbc542827100da3b47babf4a16ca7c588aff9912e674abb449e0b767a15e415f4e7f2bbd6380d7131da3df8d49b13bfd35ce3
M = b72d5c55bd2998472f1965e75a51be6155c1ba04656da8f66bcb34db36a7b1db66a89d1d05b1bde10206acf85be7b474ab689220faf1bb52ab39d8dc00512dd4e26df1179c11b973e1274db85a88c7cc2a17113abdffe58cb930ddc5f3ccc4d68b4e65c913730509f7ce5656e8bbaba9b1be177ab9f766678f018fea05da9cdf
ModExp = 465ff295786a88496828fdc763e9292d557957544e9322b7996807b87fdbfa7a11614bffeec557ca831c4824c8e4ca3b1a1c7f3f4f95ec3fd6a86b73bb13d78b73af2b3c7e76954d0cc03bcb0cd606867ebb3765a8b3d0108cbe4f343a14016be9c33f6d200f0dc547e7d6b02bfab1e79dcdf9c9835a814cc6c855a12ebeb66d
A = 89ad02bea3e9ab839a6e23f20122409daba52c68e1e893034b30d321c0305434a6af940015e3fa5ca9c35230da34beeb1ed4fbce6c1da3a8bfe3f3ae172276c1d1723b47ee61e6f8fcfdafad102d6f7ee2a79f510c7edb93096205a40a6c9e665b88b18f39a979e2e61286d939952a6f02fe8148b7515bb25f4252337cb6e60d
E = cbd6ac628cc7afa3c61bee9c22a06a395087ec1811fe9681b55216700c435996c815e7cec8aaa90016dd2382d0306a5414630124e14f3d396a4ba02ee17851bf720f1607ff813e4bbddf01338983db12f59bd6371a738eee3eeb716f21051d6174d2d6c77602942b9edaac18d4b3a723096c0d00dd23a8a605c585022f311560
M = fa7a3e40364c8a8d0f14f0213a3f3e035222ca0ea19d46d10ba41580e5dd2805c8a133f3856d7d5d97f922ea540e5eb0d10ad04dfdbb74f518f58da0099a6fc2b3f3def92985176e07fc78aff2faebccca10a429794e5f15ff92f75fe90f527c60ddea8093a9078c703c372ca09f7aeb27ade02f3595308c61dd9c44e62fd101
ModExp = cf08bf00261402102e9fe03f3074471dcf0e9b3c96d4d1503f099f24ec85e1901b023e9e048c1ad042244f5f70b38b25a99f4c0a7b57d5844bb0d0137367f45f4ce2cc7746105b77414768cb97648dc5721149aed2d4c682408cc0d50d26dd0bd77e848911f8625c727cac5f32e63bcb548f41a57d718d772f23983a42f603bd
A = a419646a6631c2c69b18f7aa65011825eb31692eecaee9d74f92d92203811b68e9764bda31a1585bdf69b6273fc6f9f508c395ac081336506525dad88473512f08a205621ac8b16e9864c7a7c5a4f17435de00d0b32badec6ce4897e3e1076c562b6d9523f63d0b2079eaa416cb090471657763f24931d955d1fa2720c80a9c9
E = d5a6f4a1842aaee39805356dc8d0d678ee03b2c81277345beccb2742f899132feb43271f95968a01ae68aa8277201851992dc0aa7a71c90aae71b124d873ee264ea400fb131be0fc6c4ce8c04c45f6bdaca89ac743635caf6158983d257e21cef6800d7f990e912ba21bbfb8fb779afa4abd19e07e7e07eee9908493d1ca502c
M = e739689b6cc6def1d45fb1a2ab551643beeb303f4aaa4da47ee5e4948510f8445b4c40e99ae8354dede60b2ba6694e93bc4d573b7e8adf871b7a9a9636eb7d70f2e49328e2d7978143b177cee8374ef01bd1ee2d95862765883f5e7971668b53ef0ff41b6539faf63c397522b0bdce916388e72e26c8d3d2e58dadeb9eb5d479
ModExp = 827e6312ec3b14600203bb83f5b277ded197b2967363630ef673240df05edd3ba8ab2b11c86251a612206569c6c33952b31e264f129909bfe723bd0ee1624b36cfcfaa893a6ec8b5a1f7de79f83e79b459a3350f89f412ad1cfd6bc4c2a7a29272c783d6ecceeb1398fa17041835643f4debef9b5e87b098d104bb8912dddf7c
A = b8e49c637829021d32db3a39a0c1e58cdd4c6e4eda7e8e9293be379e9c2e2d184f929d278598a81ae231cfedcf69cce4a6e31cda3c8ac14d753a7311f2436e29795f0dfb60259a0f61a997918ff984aa2284b43a9d64c974059e9682adfffd018305835f74eda8c75fe4877d811c1620f654ec9f7f32d1af5ce59115e2f41785
E = 80e0febf369d234bf1aaad4f82df2e2ff02882c3184781f6ccdf4f7cd93b6887af86830077c84dfb02109ada05b40970b1c65228b0c19030bd6361c3537fee22a8155c03b4e7007ca006c6daa3659518d05bb81ea0079456d0ef6116df248dffdb0c935f321f5a1034deefd5a9414a0652aa6548de33325b474b9e5a8507a082
M = d5eb1d14af842a9973274f7463d90cf0ccff19c47d710edbae184478d4f29b02693ed7958bd487054327b9e6d8879e24c9af7730b92f323eeac05558da6c1b952e5dbf13de236050a77628bb5325fe0d14cc5773bf73338759d5ab43c212b414581280f1cee250007e53791b800b61c90de0328acd7bc43fbdda48158939392d
ModExp = 4a1efd29c7e78549f5cd4deed1454b37462c7810ee6a8a2493b764dfa479be13b314cf9ff98259517d61865567ef499a511630c0038c97914625df181c6fe07892f329f98b344a78d751e9471483eebaa7977371bf97bb25187ae7e93a9227d6c124ccb4644423c961a11ae59c4354f89d5a95164c23d9aa256e289e9cc0858e
A = bd86c9211fa6a47a06e5016c46cb8a99e34a043a29e22f8c3196fa7197c26b38927b8d9bc0ddc11a5fa4bcc44deb69dbf37cbe7ebc9a2fad6c74e09ab5a9dd929fa04ab4319b6caad1035739be78ba631fb0748d9e53944836d37ccda6e6a62823c696d8f31139ccd7f2f86b22fa026ecf433cfb1271a3539ac4f1c83aaac059
E = c40b9972006d28a84c2769a86e526a2b274f73afc7c5c6a2742166757f61b5f5fdbb228afa157af62af989ffe966f232bba9e6beef5403d1690ade31a6410f7f349a35bc4267a129afd647993df7d45cc0e1a1ba4678d7f1b6e8a344d8ff7037679e1f4db25a454e4246f6b55c416567fcfa188e8a3865115851d9edf0aa8902
M = cf424d7af75ce7eef90cad75ae55ca8810cc7b4703fdb5bce701e7bac07e0c371cae06df2aa8facb55a0faa6793e4d2bd9d7969703743b9be170be82792aeea55e2bc0f7ab7617b276486bf474dee2f4556aab595ff3ef115139cfe5e21ccd4ee05c0e1cf901bd85df86cc17195a783b0be836d00bee82ce064077f9191188f9
ModExp = 3137a3049fd4ad2e26d870f5c998cf11bfe82101884a82e85e43facd0928cd7434a2e346ca124619769fa141bbe92ad6f36b99231032ddaec3b349a410f82b5ca36f45e56e5fb85dc63d32053dc90805d3f1854ab385281a71a57726bf97158494e7476057214ca7379ab8b70f5bdc15f70bdad3adf33c3a1f9cd1b6bbbad556
A = 039a1dc6a4c3f14d9c350ee968d5ce139ef725952c967a2d1bedf48ace22091283525be03807e2e263d2640be77f0525247bcd07149bba50568cec5a082c87d72962cf9e43bcb5cdb1e7e9a650fb53e0ec2fad37f09a9f036c0d7dfa528fef846769f80a9a60854910ca1b4ee05dba82ed2ee018348d6b3e52a764b8ffae61e0
E = deaee3a3f80c9f684ed7110c0653847ccc7be5ff6d982fd4b49f59b5dd35f7210b1077babbcedbc127df35cd469dc6e569a0f84e58149b5605c94b09fd7f0b098d02b4a04631328b3fae39e6c2fce25334225cab71829abdb9507cb903701559660f2c08c3b743336119d1260a0db27054cad3f28bc1b04b2289baa58fb33965
M = 938388927d06ed3bb1286c0f06d3054cb0ee16dc7a0bbbf13a45293c09a5f40f1d611b2e1a1b0ec2ef109b508e27af4274954905cae52034f8740a744153b4d22059f0dd262ea51785522098ecacced6da07709ee6b5acc8c4e99331379a7c3de7f4e2d1431e43b19570140955b7bcba118dfbaa552cbfa2be531e8f781166ed
ModExp = c15ae334455d9f4d1030cd33e734726a27c63624c2afc576238cce5e0498298a4a0c93090a0d19568b41290303c4b558f3d9dd74f9cde8798710f68569ea0d6fd971ce67ec5b54495031de3d8842b8b49288725bee5c9f72b99054d64986ccd4e18d70d5f33943f08cd694eff538f84438ea993ebaba0910c95b3a694f213510
A = def633b955a917569df3ba8517455eef0655e7a35985edda27097a063e0d82c7c3a76dc36c5d8a71ba9d540790ddd0ea514aaed98925f9a1808eb288d387aaf9605a9ef8a333ebee7ad7057bca012efd619d5867f02266f65976ef4b16da17468426ac4f99b3e8921707e01b4de20f6f9a068e6a19d872079a27f3a44449db83
E = a465c47b0d15d48e01bb8b1d8e3b3253e11515f6874dbed6c25818adf1a8fd927124d5593beb367f685c11e46f18415be73ccdf16fa2e93a600b728163d21d232849e5278c3749d903edad3f1c4535a2f55a2ab65e7ebc64888bd2a0527e876ecf38cec3ab1980d08138709fad8eb88ae65d960adc3f0f8e92f784fe96fcb693
M = e43cb9ac1446154356cdc31ec771c79b0e461e22d95185bbe1a279c0945e3af07903a0cb54d553380716fcdcafb4b7cf5dc6da481dc74a8c583d75ff6c1f8e429182d200246ebc473bb56e173787987c1b7fb2dd23f5b2e438a97bc4a1df628bc044fdd1e80c0cf37030adb7b04784dab827d0dcd64f0dbf37c980612570ce11
ModExp = 75c3f79ab7c991b98e65505342a8a563cfb08b5d3ccf8664c7db1de50256b1d17ebf7096dc98c7bb5d7f027a894ae5cbb14dee04d5d445e775ad7e239acc82673b0ac2d819a69c83864f34e73d9a636f05de8279619a067b4c90ad038db5910447e03841d2034635018f08cbcd21efa00994247763a249082594128112f95232
A = 34def7d76f6f158a359fd12759fb889cdf6af0a24830dc3e84283a1ab4e9b2647a6a36b86482f829b2cdf3e3d6028f9a884b1f64f7262315446bea8b0231828e2f3d990fb103c17f820b39e4b8427c85643ceeca8f5dc8f191d1255768300e859bd7d88c770319ef38269660d221cb3bc061389b6fc0783485ef042b1c7d6fef
E = c6c46453dd5aac6b37277a446b1d0c69cbe476eeff55b3ac35edb89ba97116b0e7783660f2c7b31b2a2d6c4709d0ab45d01a838100694b0777c9c9c14c959b07c437c73a5eabb7402f1001e802d797a2e7707285834fb6440a1c2f727f7bb84ddb2a49312d32fa0ce620c43872655cb5c394749c9e75d7fa25be00efe50d47d6
M = fbbab6698a9142095c46b38a732592e4366c1838b84bf40f8c8fc7b630f73380a0d09765562365798f8c8030ed1b6728329d8bb06e882c35a1d59bfe84146a9db2afe42a414014e247390281c782fce806d62adb54778d2bcb49555459429d6ed446af5359657667f6aa19e8e3e0e24ab2bc312b2d90b5cb1ce6f2f15af15d9d
ModExp = ba16d7f3f6e162ce248490d164a13c00e7720d8a667e2d3ebeb13f1663e15ef5408d5b56cbc7bc793a8ca787cc50f8e15e0e9d4ee764531d04a9114eea556bb3e206ed7d85267151a056b6e68fbf35e03f2cf829708ffe1de13e95ecfe365aff1eea36340ffcd3892dee659fb1ecbe50f5080e54737c10f9c1ba638b14ef537e
A = 9025e6183706105e948b1b0edf922f9011b9e11887d70adb00b26f272b9e76a38f3099084d9cccf12d04b1a99c0f654f8b9ed90c6dff9478c60bf05d58d734ab60eaefa14a22230ec60c90dc1f0704b61eef0bef345785ae0e6a9af7db069cf6bd2b4e0fe58a0ade83c7e46a04b9fe1d24cb9b65c6f80de713e61d70eae5b286
E = d7e6df5d755284929b986cd9b61c9c2c8843f24c711fbdbae1a468edcae159400943725570726cdc92b3ea94f9f206729516fdda83e31d815b0c7720e7598a91d992273e3bd8ac413b441d8f1dfe5aa7c3bf3ef573adc38292676217467731e6cf440a59611b8110af88d3e62f60209b513b01fbb69a097458ad02096b5e38f0
M = e4e784aa1fa88625a43ba0185a153a929663920be7fe674a4d33c943d3b898cff051482e7050a070cede53be5e89f31515772c7aea637576f99f82708f89d9e244f6ad3a24a02cbe5c0ff7bcf2dad5491f53db7c3f2698a7c41b44f086652f17bb05fe4c5c0a92433c34086b49d7e1825b28bab6c5a9bd0bc95b53d659afa0d7
# See https://github.com/openssl/openssl/commit/e9e726506cd2a3fd9c0f12daf8cc1fe934c7dddb.
# OpenSSL's test vectors do not include the expected value, so ModExp was
# computed with Python 3.
ModExp = 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
A = 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
E = 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
M = 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
# RSAZ 512-bit.
#
# These are regression tests for code which historically reached the RSAZ-512
# code. That has since been removed, but the test vectors remain. Note that the
# lengths of the inputs, especially the *bit* length of |M|, matter a lot.
# Control: No relationship between A and M except that A < M and they're the
# same number of limbs.
# Control: No relationship between A and M except that A < M and they're the same number of limbs.
ModExp = 7f34c1cd63377bc3abf2bb5b2d1bf5f06454e1e8040fe19a72245ce9731cbee1bf9e84532300776c8021ed4f3a8de508d85b4cf320bd82065a013754857b50c4
A = 8e4e67da6ff890643d0599387955996ef6f0c2045eb9944576ddb965ca64cdb6247727ce128ef178d4a84e5a56d2e67eb0fe389ecbf691f9244ae80f4c11b364
E = 0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1
M = f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491
# Same as above except A was negative.
ModExp = 71fa6a4c8ae75368eda8cc6282c26afa69e2af12a97fb9444f16b7dd6c99e0a5d6034cab4248cae4357346b211039f4a2bc4c5a20a297372094162417af703cd
A = 62e0c43f7e263ec85c95ee853688c77bd746cef64ed606994a5d5b611551d1d1712aa93052ba50d7e0ece5a6f4be9dd45321d9f65ef0637f3ef7b186b460a12d
E = 0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1
M = f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491
# A == M - 1 == -1 (mod M) and the exponent is odd so A ^ E (mod M) == A.
ModExp = f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725490
A = f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725490
E = 0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1
M = f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491
# Same inputs as above except A was negative. Note that A mod M with a "correct
# top" isn't the right length for RSAZ.
# Same inputs as above except A was negative. Note that A mod M with a "correct top" isn't the right length for RSAZ.
ModExp = 01
A = 01
E = 0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1
M = f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491
# A was negative, and A (mod M) is the right length for RSAZ.
# A == 0 (mod M) so A ^ E (mod M) == 0. Note that A mod M with a "correct top" isn't the right length for RSAZ.
ModExp = 00
A = 00
E = 0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1
M = f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491
# A is negative, and A (mod M) is the right length for RSAZ.
ModExp = 8d76eb0f8c7bc3160cc8bb0e0c3590fbed26c5932f5f525b48045c0bd46dda287ba5483f97c851fb7c12c2e858ee7a4a4d1af745cbfb3eb311fa54bea12cde25
A = 712f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491
E = 0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1
M = f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491
# RSAZ 1024-bit.
# Note that the lengths of the inputs, especially the *bit* length of |M|, matter a lot.
# Note that the lengths of the inputs, especially the *bit* length of |M|,
# matter a lot.
# Control: No relationship between A and M except that A < M and they're the
# same number of limbs.
# Control: No relationship between A and M except that A < M and they're the same number of limbs.
ModExp = 8984f8c16044f9c0ad7bd72347af90f58e6e003acda92b76e3c7c4a56ea8e918409d8e9b34884d4c89d0b17cb40fe898f2627c084a0f1698e46beccbf6f48eecc281e11ea9e5135adba460ddae157f2c655b5f589ce29b254d43a960a71cede8a08dbb86be4dac22458da232fb1ec2470856827302ed772c9ddafa408c931aa7
A = 21158da5fe20356825e72b3f5384ec57720d22f727b27ce2f945c8ee311db781add73bf8fae96b775c909bd22fca75c44c2b0584284a5bb1c07f8eefcd6b0a44047a02b185df34f897f11d4fb9a86c9eb841b4cb8d0383441fdc5af3ef385b5e8380f605d73ed41bb42eb2c2a5704d6034b3ad058dafffce83dbbfb6295daaf8
E = ecdebd112b3b5788669449dcddbd479a203ee9ab72a9bb9c406b97623513bf0ab9a22f1f23634d269e16bfd6d3b64202b71fc355057411967b6ac70f8d9cef0a4e06819a9a18cc06bbe438243fa9759303d98be8a65dc1cb13595ee9b99f138554425d50f6fbc025d8ffa3eaea828d6f3b82a3584146bafde34da257995f0575
M = ff3a3e023db3bba929ca4ededbace13d0d1264387b5ef62734e177eaf47a78af56b58aacc8ac5d46f5b066bafb95d93d4442bb948653613eec76837b4ffb7991cb080b6c8b403fb09bc817d026e283ee47ab2fc9af274b12f626eda2fe02004a8e27b9ed7d3b614e8955c7e7c2c0700edd079455237c4475fbd41857e206e4b7
# Same as above except A was negative.
ModExp = 75b54540dd6ec1e87c4e77bb93fd50477ea463fdadb5cab05119b34585d18f971617fc1194240ffa6bdfb53e4785f0a451e03f8c3c444aa6080a96af5906eaa508862a4de15b2c55c023b6f278cd04c1e24fd0711244afeda8e3444256e51261ed99fe66beedb52c43c825b4c7a1adc7d4b111e2208ecd495df91e175573ca10
A = de24b05c3f93864103e3239f8827f4e59b05414153ac79443b9baefcc35cc12da8de4eb3cdc2f1cf991fcae8cbcb6378f817b6105e09058d2bf6f48b82906f4dc68e08bb05610ab803d6fa806d3a174f8f697afe2223c7ced64a92af0ec9a4ec0aa6c3e7a5fc8d32d52715251d5022aea853e74f95cc44a777f858a1b8a939bf
E = ecdebd112b3b5788669449dcddbd479a203ee9ab72a9bb9c406b97623513bf0ab9a22f1f23634d269e16bfd6d3b64202b71fc355057411967b6ac70f8d9cef0a4e06819a9a18cc06bbe438243fa9759303d98be8a65dc1cb13595ee9b99f138554425d50f6fbc025d8ffa3eaea828d6f3b82a3584146bafde34da257995f0575
M = ff3a3e023db3bba929ca4ededbace13d0d1264387b5ef62734e177eaf47a78af56b58aacc8ac5d46f5b066bafb95d93d4442bb948653613eec76837b4ffb7991cb080b6c8b403fb09bc817d026e283ee47ab2fc9af274b12f626eda2fe02004a8e27b9ed7d3b614e8955c7e7c2c0700edd079455237c4475fbd41857e206e4b7
# A == M - 1 == -1 (mod M) and the exponent is odd so A ^ E (mod M) == A.
ModExp = b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d964
A = b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d964
E = 61803d4973ae68cfb2ba6770dbed70d36760fa42c01a16d1482eacf0d01adf7a917bc86ece58a73b920295c1291b90f49167ef856ecad149330e1fd49ec71392fb62d47270b53e6d4f3c8f044b80a5736753364896932abc6d872c4c5e135d1edb200597a93ceb262ff6c99079177cd10808b9ed20c8cd7352d80ac7f6963103
M = b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d965
# Same inputs as above except A was negative. Note that A mod M with a "correct
# top" isn't the right length for RSAZ.
# Same inputs as above except A was negative. Note that A mod M with a "correct top" isn't the right length for RSAZ.
ModExp = 01
A = 01
E = 61803d4973ae68cfb2ba6770dbed70d36760fa42c01a16d1482eacf0d01adf7a917bc86ece58a73b920295c1291b90f49167ef856ecad149330e1fd49ec71392fb62d47270b53e6d4f3c8f044b80a5736753364896932abc6d872c4c5e135d1edb200597a93ceb262ff6c99079177cd10808b9ed20c8cd7352d80ac7f6963103
M = b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d965
# A was negative, and A (mod M) is the right length for RSAZ.
# A == 0 (mod M) so A ^ E (mod M) == 0. Note that A mod M with a "correct top" isn't the right length for RSAZ.
ModExp = 00
A = 00
E = 61803d4973ae68cfb2ba6770dbed70d36760fa42c01a16d1482eacf0d01adf7a917bc86ece58a73b920295c1291b90f49167ef856ecad149330e1fd49ec71392fb62d47270b53e6d4f3c8f044b80a5736753364896932abc6d872c4c5e135d1edb200597a93ceb262ff6c99079177cd10808b9ed20c8cd7352d80ac7f6963103
M = b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d965
# A was negative, and A (mod M) is the right length for RSAZ.
ModExp = 9cf810b9e89d5cbc4b79ae64e123ea06d92965e2bab077df97a1b906dc2e1ddcf96a9c4ed14e2cd96309b829ea9cc2a74a7d4b43c5f34d792a7c583201427754b8f78b783608070a84b61f18913e3ced7f7f530972de7764667c54e29d756eea38a93cd1703c676a4587231b0ebfeadddf908e2877a7a84b5bfc370ecf0d158d
A = 35d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d965
E = 61803d4973ae68cfb2ba6770dbed70d36760fa42c01a16d1482eacf0d01adf7a917bc86ece58a73b920295c1291b90f49167ef856ecad149330e1fd49ec71392fb62d47270b53e6d4f3c8f044b80a5736753364896932abc6d872c4c5e135d1edb200597a93ceb262ff6c99079177cd10808b9ed20c8cd7352d80ac7f6963103
M = b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d965
# Regression test for CVE-2017-3738.
ModExp = d360792bd8210786607817c3dda64cc38c8d0f25569597cb1f363c7919a0c3587baff01a2283edaeb04fc288ac0ab3f279b2a89ffcb452d8bdf72422a9f9780f4aa702dc964cf033149d3a339883062cab8564aebdbfac0bf68985e522c6fe545b346044690c525ca85d3f4eb3e3c25cdf541545afc84a309e9b1d7807003461
A = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff2020202020df
E = 2020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020FF2020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020
M = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff2020202020ff
# Test vectors for CVE-2019-1551. (We do not carry the assembly file with the
# bug, but we use the test vectors anyway.)
# Original test vectors by OSS-Fuzz.
ModExp = 9d675d188a07e9bd1b32638cc8cfd5002ef89bd1a9648f806567b87939140a67977dc8da17323b8e4c6bc53875cda8b656df8f54cc32e44fd9c21d122ea3c0d6
A = dea9b3e0b44ae67b2ac9b7c2b18eeb4dab206b014981a46ac409f195eeb6896f132cf8497c87d1188008ee511054ebb426203355b7d515dce9501cb759ac1373
E = 0b01ae745b101e9e45ec05dcff72e7f8fc04c79ffe324301fda0b4f7be81d85c4e875c73fc6c5cb40000000000000000000000000000000000
M = ffffffff01ffffffffffffffffffffffffffe2000000000000000000000000000010fab8d960706cd4c21818115650cad61d4f10da325dffffffff00ffff00ff
ModExp = 651f811b62ee8770e3598c340864dd6b0be9bb6376b6f933ab216fd55538e6ad1000cb2b3c64f54d554e004b6eec8138e6ecff00452d443a42041b72e6cd9ead
A = 3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e
E = 3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e09003e3e3e3e3e3e3e3e3e3e3e3e3e3e010900230a01230a2100ffffff0000adf300a58700000000ffffff00
M = ffffff0b00000000000000000000000000ffffffff0000ffffffff00000a0000000a00000000000000000000ffffffff000000000000ffffffffffff000000ff
# Test vectors for rsaz_512_sqr bug, with rcx/rbx=1
# between first and second iteration
ModExp = 01
A = 624e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d973b6
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between second and third iteration
ModExp = 01
A = 11024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d97360800000000000000f
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between third and fourth iteration
ModExp = 01
A = 4171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d9736080000000000000000000000000000039
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between fourth and fifth iteration
ModExp = 01
A = 06a171024e6a171024e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d97360800000000000000000000000000000000000000000000006
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between fifth and sixth iteration
ModExp = 01
A = 44e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d97360800000000000000000000000000000000000000000000000000000000000003c
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between sixth and seventh iteration
ModExp = 01
A = 1024e6a171024e6a14ce297f2873536f959d8c3390d973608000000000000000000000000000000000000000000000000000000000000000000000000000000e
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between seventh and eighth iteration
ModExp = 01
A = 626eee5e3c8653be47ed15e84b97cc7f800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000187
E = c00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002f8
M = c00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002f9
# Test vectors for rsaz_512_srq bug, with rcx/rbx=2
# between first and second iteration
ModExp = 01
A = 3c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf7c
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between second and third iteration
ModExp = 01
A = 485c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf47800000000000003f
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between third and forth iteration
ModExp = 01
A = 59a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf478000000000000000000000000000004e
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between forth and fifth iteration
ModExp = 01
A = 2939a85c40939a85c40939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf47800000000000000000000000000000000000000000000024
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between fifth and sixth iteration
ModExp = 01
A = 640939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf478000000000000000000000000000000000000000000000000000000000000057
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between sixth and seventh iteration
ModExp = 01
A = 25c40939a85c4093995e8efdb195e8efd8caf477ed8caf4780000000000000000000000000000000000000000000000000000000000000000000000000000021
E = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e
M = 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
# between seventh and eighth iteration
ModExp = 01
A = 7b4919849931b28a14fcace213f2b3884fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff84b6e67b66ce4d9c
E = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000000004c
M = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000000004d