diff --git a/scripts/mbedtls_dev/bignum_common.py b/scripts/mbedtls_dev/bignum_common.py index 7857dd65c..c340cd53a 100644 --- a/scripts/mbedtls_dev/bignum_common.py +++ b/scripts/mbedtls_dev/bignum_common.py @@ -22,6 +22,21 @@ from typing import Iterator, List, Tuple, TypeVar T = TypeVar('T') #pylint: disable=invalid-name +def invmod(a: int, n: int) -> int: + """Return inverse of a to modulo n. + + Equivalent to pow(a, -1, n) in Python 3.8+. Implementation is equivalent + to long_invmod() in CPython. + """ + b, c = 1, 0 + while n: + q, r = divmod(a, n) + a, b, c, n = n, c, b - q*c, r + # at this point a is the gcd of the original inputs + if a == 1: + return b + raise ValueError("Not invertible") + def hex_to_int(val: str) -> int: return int(val, 16) if val else 0 diff --git a/scripts/mbedtls_dev/bignum_core.py b/scripts/mbedtls_dev/bignum_core.py index 47b09fd40..f04db2648 100644 --- a/scripts/mbedtls_dev/bignum_core.py +++ b/scripts/mbedtls_dev/bignum_core.py @@ -15,7 +15,7 @@ # limitations under the License. from abc import ABCMeta -from typing import Iterator, List +from typing import Iterator, List, Tuple from . import test_case from . import test_data_generation @@ -181,3 +181,431 @@ class BignumCoreMLA(BignumCoreOperation): for s_value in cls.input_scalars: cur_op = cls(a_value, b_value, s_value) yield cur_op.create_test_case() + + +class BignumCoreMontmul(BignumCoreTarget): + """Test cases for Montgomery multiplication.""" + count = 0 + test_function = "mpi_core_montmul" + test_name = "mbedtls_mpi_core_montmul" + + start_2_mpi4 = False + start_2_mpi8 = False + + replay_test_cases = [ + (2, 1, 1, 1, "19", "1", "1D"), (2, 1, 1, 1, "7", "1", "9"), + (2, 1, 1, 1, "4", "1", "9"), + ( + 12, 1, 6, 1, ( + "3C246D0E059A93A266288A7718419EC741661B474C58C032C5EDAF92709402" + "B07CC8C7CE0B781C641A1EA8DB2F4343" + ), "1", ( + "66A198186C18C10B2F5ED9B522752A9830B69916E535C8F047518A889A43A5" + "94B6BED27A168D31D4A52F88925AA8F5" + ) + ), ( + 8, 1, 4, 1, + "1E442976B0E63D64FCCE74B999E470CA9888165CB75BFA1F340E918CE03C6211", + "1", "B3A119602EE213CDE28581ECD892E0F592A338655DCE4CA88054B3D124D0E561" + ), ( + 22, 1, 11, 1, ( + "7CF5AC97304E0B63C65413F57249F59994B0FED1D2A8D3D83ED5FA38560FFB" + "82392870D6D08F87D711917FD7537E13B7E125BE407E74157776839B0AC9DB" + "23CBDFC696104353E4D2780B2B4968F8D8542306BCA7A2366E" + ), "1", ( + "284139EA19C139EBE09A8111926AAA39A2C2BE12ED487A809D3CB5BC558547" + "25B4CDCB5734C58F90B2F60D99CC1950CDBC8D651793E93C9C6F0EAD752500" + "A32C56C62082912B66132B2A6AA42ADA923E1AD22CEB7BA0123" + ) + ) + ] # type: List[Tuple[int, int, int, int, str, str, str]] + + random_test_cases = [ + ("2", "2", "3", ""), ("1", "2", "3", ""), ("2", "1", "3", ""), + ("6", "5", "7", ""), ("3", "4", "7", ""), ("1", "6", "7", ""), ("5", "6", "7", ""), + ("3", "4", "B", ""), ("7", "4", "B", ""), ("9", "7", "B", ""), ("2", "a", "B", ""), + ("25", "16", "29", "(0x29 is prime)"), ("8", "28", "29", ""), + ("18", "21", "29", ""), ("15", "f", "29", ""), + ("e2", "ea", "FF", ""), ("43", "72", "FF", ""), + ("d8", "70", "FF", ""), ("3c", "7c", "FF", ""), + ("99", "b9", "101", "(0x101 is prime)"), ("65", "b2", "101", ""), + ("81", "32", "101", ""), ("51", "dd", "101", ""), + ("d5", "143", "38B", "(0x38B is prime)"), ("3d", "387", "38B", ""), + ("160", "2e5", "38B", ""), ("10f", "137", "38B", ""), + ("7dac", "25a", "8003", "(0x8003 is prime)"), ("6f1c", "3286", "8003", ""), + ("59ed", "2f3f", "8003", ""), ("6893", "736d", "8003", ""), + ("d199", "2832", "10001", "(0x10001 is prime)"), ("c3b2", "3e5b", "10001", ""), + ("abe4", "214e", "10001", ""), ("4360", "a05d", "10001", ""), + ("3f5a1", "165b2", "7F7F7", ""), ("3bd29", "37863", "7F7F7", ""), + ("60c47", "64819", "7F7F7", ""), ("16584", "12c49", "7F7F7", ""), + ("1ff03f", "610347", "800009", "(0x800009 is prime)"), ("340fd5", "19812e", "800009", ""), + ("3fe2e8", "4d0dc7", "800009", ""), ("40356", "e6392", "800009", ""), + ("dd8a1d", "266c0e", "100002B", "(0x100002B is prime)"), + ("3fa1cb", "847fd6", "100002B", ""), ("5f439d", "5c3196", "100002B", ""), + ("18d645", "f72dc6", "100002B", ""), + ("20051ad", "37def6e", "37EEE9D", "(0x37EEE9D is prime)"), + ("2ec140b", "3580dbf", "37EEE9D", ""), ("1d91b46", "190d4fc", "37EEE9D", ""), + ("34e488d", "1224d24", "37EEE9D", ""), + ("2a4fe2cb", "263466a9", "8000000B", "(0x8000000B is prime)"), + ("5643fe94", "29a1aefa", "8000000B", ""), ("29633513", "7b007ac4", "8000000B", ""), + ("2439cef5", "5c9d5a47", "8000000B", ""), + ("4de3cfaa", "50dea178", "8CD626B9", "(0x8CD626B9 is prime)"), + ("b8b8563", "10dbbbac", "8CD626B9", ""), ("4e8a6151", "5574ec19", "8CD626B9", ""), + ("69224878", "309cfc23", "8CD626B9", ""), + ("fb6f7fb6", "afb05423", "10000000F", "(0x10000000F is prime)"), + ("8391a243", "26034dcd", "10000000F", ""), ("d26b98c", "14b2d6aa", "10000000F", ""), + ("6b9f1371", "a21daf1d", "10000000F", ""), + ( + "9f49435ad", "c8264ade8", "174876E7E9", + "0x174876E7E9 is prime (dec) 99999999977" + ), + ("c402da434", "1fb427acf", "174876E7E9", ""), + ("f6ebc2bb1", "1096d39f2a", "174876E7E9", ""), + ("153b7f7b6b", "878fda8ff", "174876E7E9", ""), + ("2c1adbb8d6", "4384d2d3c6", "8000000017", "(0x8000000017 is prime)"), + ("2e4f9cf5fb", "794f3443d9", "8000000017", ""), + ("149e495582", "3802b8f7b7", "8000000017", ""), + ("7b9d49df82", "69c68a442a", "8000000017", ""), + ("683a134600", "6dd80ea9f6", "864CB9076D", "(0x864CB9076D is prime)"), + ("13a870ff0d", "59b099694a", "864CB9076D", ""), + ("37d06b0e63", "4d2147e46f", "864CB9076D", ""), + ("661714f8f4", "22e55df507", "864CB9076D", ""), + ("2f0a96363", "52693307b4", "F7F7F7F7F7", ""), + ("3c85078e64", "f2275ecb6d", "F7F7F7F7F7", ""), + ("352dae68d1", "707775b4c6", "F7F7F7F7F7", ""), + ("37ae0f3e0b", "912113040f", "F7F7F7F7F7", ""), + ("6dada15e31", "f58ed9eff7", "1000000000F", "(0x1000000000F is prime)"), + ("69627a7c89", "cfb5ebd13d", "1000000000F", ""), + ("a5e1ad239b", "afc030c731", "1000000000F", ""), + ("f1cc45f4c5", "c64ad607c8", "1000000000F", ""), + ("2ebad87d2e31", "4c72d90bca78", "800000000005", "(0x800000000005 is prime)"), + ("a30b3cc50d", "29ac4fe59490", "800000000005", ""), + ("33674e9647b4", "5ec7ee7e72d3", "800000000005", ""), + ("3d956f474f61", "74070040257d", "800000000005", ""), + ("48348e3717d6", "43fcb4399571", "800795D9BA47", "(0x800795D9BA47 is prime)"), + ("5234c03cc99b", "2f3cccb87803", "800795D9BA47", ""), + ("3ed13db194ab", "44b8f4ba7030", "800795D9BA47", ""), + ("1c11e843bfdb", "95bd1b47b08", "800795D9BA47", ""), + ("a81d11cb81fd", "1e5753a3f33d", "1000000000015", "(0x1000000000015 is prime)"), + ("688c4db99232", "36fc0cf7ed", "1000000000015", ""), + ("f0720cc07e07", "fc76140ed903", "1000000000015", ""), + ("2ec61f8d17d1", "d270c85e36d2", "1000000000015", ""), + ( + "6a24cd3ab63820", "ed4aad55e5e348", "100000000000051", + "(0x100000000000051 is prime)" + ), + ("e680c160d3b248", "31e0d8840ed510", "100000000000051", ""), + ("a80637e9aebc38", "bb81decc4e1738", "100000000000051", ""), + ("9afa5a59e9d630", "be9e65a6d42938", "100000000000051", ""), + ("ab5e104eeb71c000", "2cffbd639e9fea00", "ABCDEF0123456789", ""), + ("197b867547f68a00", "44b796cf94654800", "ABCDEF0123456789", ""), + ("329f9483a04f2c00", "9892f76961d0f000", "ABCDEF0123456789", ""), + ("4a2e12dfb4545000", "1aa3e89a69794500", "ABCDEF0123456789", ""), + ( + "8b9acdf013d140f000", "12e4ceaefabdf2b2f00", "25A55A46E5DA99C71C7", + "0x25A55A46E5DA99C71C7 is the 3rd repunit prime(dec) 11111111111111111111111" + ), + ("1b8d960ea277e3f5500", "14418aa980e37dd000", "25A55A46E5DA99C71C7", ""), + ("7314524977e8075980", "8172fa45618ccd0d80", "25A55A46E5DA99C71C7", ""), + ("ca14f031769be63580", "147a2f3cf2964ca9400", "25A55A46E5DA99C71C7", ""), + ( + "18532ba119d5cd0cf39735c0000", "25f9838e31634844924733000000", + "314DC643FB763F2B8C0E2DE00879", + "0x314DC643FB763F2B8C0E2DE00879 is (dec)99999999977^3" + ), + ( + "a56e2d2517519e3970e70c40000", "ec27428d4bb380458588fa80000", + "314DC643FB763F2B8C0E2DE00879", "" + ), + ( + "1cb5e8257710e8653fff33a00000", "15fdd42fe440fd3a1d121380000", + "314DC643FB763F2B8C0E2DE00879", "" + ), + ( + "e50d07a65fc6f93e538ce040000", "1f4b059ca609f3ce597f61240000", + "314DC643FB763F2B8C0E2DE00879", "" + ), + ( + "1ea3ade786a095d978d387f30df9f20000000", + "127c448575f04af5a367a7be06c7da0000000", + "47BF19662275FA2F6845C74942ED1D852E521", + "0x47BF19662275FA2F6845C74942ED1D852E521 is (dec) 99999999977^4" + ), + ( + "16e15b0ca82764e72e38357b1f10a20000000", + "43e2355d8514bbe22b0838fdc3983a0000000", + "47BF19662275FA2F6845C74942ED1D852E521", "" + ), + ( + "be39332529d93f25c3d116c004c620000000", + "5cccec42370a0a2c89c6772da801a0000000", + "47BF19662275FA2F6845C74942ED1D852E521", "" + ), + ( + "ecaa468d90de0eeda474d39b3e1fc0000000", + "1e714554018de6dc0fe576bfd3b5660000000", + "47BF19662275FA2F6845C74942ED1D852E521", "" + ), + ( + "32298816711c5dce46f9ba06e775c4bedfc770e6700000000000000", + "8ee751fd5fb24f0b4a653cb3a0c8b7d9e724574d168000000000000", + "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", + ( + "0x97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931" + " is (dec) 99999999977^6" + ) + ), + ( + "29213b9df3cfd15f4b428645b67b677c29d1378d810000000000000", + "6cbb732c65e10a28872394dfdd1936d5171c3c3aac0000000000000", + "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", "" + ), + ( + "6f18db06ad4abc52c0c50643dd13098abccd4a232f0000000000000", + "7e6bf41f2a86098ad51f98dfc10490ba3e8081bc830000000000000", + "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", "" + ), + ( + "62d3286cd706ad9d73caff63f1722775d7e8c731208000000000000", + "530f7ba02ae2b04c2fe3e3d27ec095925631a6c2528000000000000", + "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", "" + ), + ( + "a6c6503e3c031fdbf6009a89ed60582b7233c5a85de28b16000000000000000", + "75c8ed18270b583f16d442a467d32bf95c5e491e9b8523798000000000000000", + "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", + ( + "0xDD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499" + "is (dec) 99999999977^7" + ) + ), + ( + "bf84d1f85cf6b51e04d2c8f4ffd03532d852053cf99b387d4000000000000000", + "397ba5a743c349f4f28bc583ecd5f06e0a25f9c6d98f09134000000000000000", + "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", "" + ), + ( + "6db11c3a4152ed1a2aa6fa34b0903ec82ea1b88908dcb482000000000000000", + "ac8ac576a74ad6ca48f201bf89f77350ce86e821358d85920000000000000000", + "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", "" + ), + ( + "3001d96d7fe8b733f33687646fc3017e3ac417eb32e0ec708000000000000000", + "925ddbdac4174e8321a48a32f79640e8cf7ec6f46ea235a80000000000000000", + "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", "" + ), + ( + "1029048755f2e60dd98c8de6d9989226b6bb4f0db8e46bd1939de560000000000000000000", + "51bb7270b2e25cec0301a03e8275213bb6c2f6e6ec93d4d46d36ca0000000000000000000", + "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", + ( + "0x141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146" + "380E41 is 99999999977^8" + ) + ), + ( + "1c5337ff982b3ad6611257dbff5bbd7a9920ba2d4f5838a0cc681ce000000000000000000", + "520c5d049ca4702031ba728591b665c4d4ccd3b2b86864d4c160fd2000000000000000000", + "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", + "" + ), + ( + "57074dfa00e42f6555bae624b7f0209f218adf57f73ed34ab0ff90c000000000000000000", + "41eb14b6c07bfd3d1fe4f4a610c17cc44fcfcda695db040e011065000000000000000000", + "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", + "" + ), + ( + "d8ed7feed2fe855e6997ad6397f776158573d425031bf085a615784000000000000000000", + "6f121dcd18c578ab5e229881006007bb6d319b179f11015fe958b9c000000000000000000", + "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", + "" + ), + ( + ( + "2a462b156180ea5fe550d3758c764e06fae54e626b5f503265a09df76edbdfbf" + "a1e6000000000000000000000000" + ), ( + "1136f41d1879fd4fb9e49e0943a46b6704d77c068ee237c3121f9071cfd3e6a0" + "0315800000000000000000000000" + ), ( + "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC90" + "2713E40F51E3B3C214EDFABC451" + ), ( + "0x2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC" + "902713E40F51E3B3C214EDFABC451 is (dec) 99999999977^10" + ) + ), + ( + ( + "c1ac3800dfb3c6954dea391d206200cf3c47f795bf4a5603b4cb88ae7e574de47" + "40800000000000000000000000" + ), ( + "c0d16eda0549ede42fa0deb4635f7b7ce061fadea02ee4d85cba4c4f709603419" + "3c800000000000000000000000" + ), ( + "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC90" + "2713E40F51E3B3C214EDFABC451" + ), "" + ), + ( + ( + "19e45bb7633094d272588ad2e43bcb3ee341991c6731b6fa9d47c4018d7ce7bba" + "5ee800000000000000000000000" + ), ( + "1e4f83166ae59f6b9cc8fd3e7677ed8bfc01bb99c98bd3eb084246b64c1e18c33" + "65b800000000000000000000000" + ), ( + "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC90" + "2713E40F51E3B3C214EDFABC451" + ), "" + ), + ( + ( + "1aa93395fad5f9b7f20b8f9028a054c0bb7c11bb8520e6a95e5a34f06cb70bcdd" + "01a800000000000000000000000" + ), ( + "54b45afa5d4310192f8d224634242dd7dcfb342318df3d9bd37b4c614788ba13b" + "8b000000000000000000000000" + ), ( + "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC90" + "2713E40F51E3B3C214EDFABC451" + ), "" + ), + ( + ( + "544f2628a28cfb5ce0a1b7180ee66b49716f1d9476c466c57f0c4b23089917843" + "06d48f78686115ee19e25400000000000000000000000000000000" + ), ( + "677eb31ef8d66c120fa872a60cd47f6e10cbfdf94f90501bd7883cba03d185be0" + "a0148d1625745e9c4c827300000000000000000000000000000000" + ), ( + "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA1" + "1DABD6E6144BEF37C6800000000000000000000000000000000051" + ), ( + "0x8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBF" + "A11DABD6E6144BEF37C6800000000000000000000000000000000051 is prime," + " (dec) 10^143 + 3^4" + ) + ), + ( + ( + "76bb3470985174915e9993522aec989666908f9e8cf5cb9f037bf4aee33d8865c" + "b6464174795d07e30015b80000000000000000000000000000000" + ), ( + "6aaaf60d5784dcef612d133613b179a317532ecca0eed40b8ad0c01e6d4a6d8c7" + "9a52af190abd51739009a900000000000000000000000000000000" + ), ( + "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA1" + "1DABD6E6144BEF37C6800000000000000000000000000000000051" + ), "" + ), + ( + ( + "6cfdd6e60912e441d2d1fc88f421b533f0103a5322ccd3f4db84861643ad63fd6" + "3d1d8cfbc1d498162786ba00000000000000000000000000000000" + ), ( + "1177246ec5e93814816465e7f8f248b350d954439d35b2b5d75d917218e7fd5fb" + "4c2f6d0667f9467fdcf33400000000000000000000000000000000" + ), ( + "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA1" + "1DABD6E6144BEF37C6800000000000000000000000000000000051" + ), "" + ), + ( + ( + "7a09a0b0f8bbf8057116fb0277a9bdf3a91b5eaa8830d448081510d8973888be5" + "a9f0ad04facb69aa3715f00000000000000000000000000000000" + ), ( + "764dec6c05a1c0d87b649efa5fd94c91ea28bffb4725d4ab4b33f1a3e8e3b314d" + "799020e244a835a145ec9800000000000000000000000000000000" + ), ( + "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA1" + "1DABD6E6144BEF37C6800000000000000000000000000000000051" + ), "" + ) + ] # type: List[Tuple[str, str, str, str]] + + def __init__( + self, val_a: str, val_b: str, val_n: str, case_description: str = "" + ): + self.case_description = case_description + self.arg_a = val_a + self.int_a = bignum_common.hex_to_int(val_a) + self.arg_b = val_b + self.int_b = bignum_common.hex_to_int(val_b) + self.arg_n = val_n + self.int_n = bignum_common.hex_to_int(val_n) + + limbs_a4 = bignum_common.limbs_mpi4(self.int_a) + limbs_a8 = bignum_common.limbs_mpi8(self.int_a) + self.limbs_b4 = bignum_common.limbs_mpi4(self.int_b) + self.limbs_b8 = bignum_common.limbs_mpi8(self.int_b) + self.limbs_an4 = bignum_common.limbs_mpi4(self.int_n) + self.limbs_an8 = bignum_common.limbs_mpi8(self.int_n) + + if limbs_a4 > self.limbs_an4 or limbs_a8 > self.limbs_an8: + raise Exception("Limbs of input A ({}) exceeds N ({})".format( + self.arg_a, self.arg_n + )) + + def arguments(self) -> List[str]: + return [ + str(self.limbs_an4), str(self.limbs_b4), + str(self.limbs_an8), str(self.limbs_b8), + bignum_common.quote_str(self.arg_a), + bignum_common.quote_str(self.arg_b), + bignum_common.quote_str(self.arg_n), + self.result() + ] + + def description(self) -> str: + if self.case_description != "replay": + if not self.start_2_mpi4 and self.limbs_an4 > 1: + tmp = "(start of 2-MPI 4-byte bignums) " + self.__class__.start_2_mpi4 = True + elif not self.start_2_mpi8 and self.limbs_an8 > 1: + tmp = "(start of 2-MPI 8-byte bignums) " + self.__class__.start_2_mpi8 = True + else: + tmp = "(gen) " + self.case_description = tmp + self.case_description + return super().description() + + def result(self) -> str: + """Get the result of the operation.""" + r4 = bignum_common.bound_mpi4_limbs(self.limbs_an4) + i4 = bignum_common.invmod(r4, self.int_n) + x4 = self.int_a * self.int_b * i4 + x4 = x4 % self.int_n + + r8 = bignum_common.bound_mpi8_limbs(self.limbs_an8) + i8 = bignum_common.invmod(r8, self.int_n) + x8 = self.int_a * self.int_b * i8 + x8 = x8 % self.int_n + return "\"{:x}\":\"{:x}\"".format(x4, x8) + + def set_limbs( + self, limbs_an4: int, limbs_b4: int, limbs_an8: int, limbs_b8: int + ) -> None: + """Set number of limbs for each input. + + Replaces default values set during initialization. + """ + self.limbs_an4 = limbs_an4 + self.limbs_b4 = limbs_b4 + self.limbs_an8 = limbs_an8 + self.limbs_b8 = limbs_b8 + + @classmethod + def generate_function_tests(cls) -> Iterator[test_case.TestCase]: + """Generate replay and randomly generated test cases.""" + # Test cases which replay captured invocations during unit test runs. + for limbs_an4, limbs_b4, limbs_an8, limbs_b8, a, b, n in cls.replay_test_cases: + cur_op = cls(a, b, n, case_description="replay") + cur_op.set_limbs(limbs_an4, limbs_b4, limbs_an8, limbs_b8) + yield cur_op.create_test_case() + # Test cases generated randomly + for a, b, n, description in cls.random_test_cases: + cur_op = cls(a, b, n, case_description=description) + yield cur_op.create_test_case()