aws-crt/crt/aws-lc/third_party/wycheproof_testvectors/primality_test.json

NodeJS/browser bindings to the aws-c-* libraries

{
  "algorithm" : "PrimalityTest",
  "generatorVersion" : "0.8rc17",
  "numberOfTests" : 280,
  "header" : [
    "Test vector of type PrimalityTest are intended for testing primality tests."
  ],
  "notes" : {
    "CarmichaelNumber" : "Carmichael numbers are composite numbers that are pseudoprime to all bases. Carmichael numbers (especially those with a small nubmer of factors) have a high probability of passing a Miller-Rabin test.",
    "NegativeOfPrime" : "Some libraries accept the negative of a prime number  as prime. For crypto libraries this just adds another  potential pitfall.",
    "WorstCaseMillerRabin" : "This is a composite number that passes the Miller-Rabin for about 1/4 of all bases. Such composite number pass primality tests, because the author of the primality test misinterprets the paper  \"Average case error estimates for the strong probable prime test.\" Math. of Comp. v.61 (203), pp. 177-194 by I. Damgard, P. Landrock, and C. Pomerance.  This paper gives bounds for the number of bases necessary to distinguish composites from primes assuming that the tested integer has been chosen at random."
  },
  "schema" : "primality_test_schema.json",
  "testGroups" : [
    {
      "type" : "PrimalityTest",
      "tests" : [
        {
          "tcId" : 1,
          "comment" : "small non prime integer",
          "value" : "ff",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 2,
          "comment" : "small non prime integer",
          "value" : "00",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 3,
          "comment" : "small non prime integer",
          "value" : "01",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 4,
          "comment" : "Non-prime Mersenne number that is pseudoprime to base 2",
          "value" : "07ffffffffffffffff",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 5,
          "comment" : "Non-prime Mersenne number that is pseudoprime to base 2",
          "value" : "7fffffffffffffffff",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 6,
          "comment" : "Non-prime Fermat number",
          "value" : "0100000000000000000000000000000001",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 7,
          "comment" : "Non-prime Fermat number",
          "value" : "010000000000000000000000000000000000000000000000000000000000000001",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 8,
          "comment" : "Non-prime Fermat number",
          "value" : "0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 9,
          "comment" : "pseudoprime square derived from Wiefrich prime",
          "value" : "123a99",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 10,
          "comment" : "pseudoprime square derived from Wiefrich prime",
          "value" : "00bc18d1",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 11,
          "comment" : "square",
          "value" : "04",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 12,
          "comment" : "square",
          "value" : "09",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 13,
          "comment" : "square",
          "value" : "010201",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 14,
          "comment" : "square",
          "value" : "0f2ad9",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 15,
          "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926",
          "value" : "01f51f3fee3b",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 16,
          "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926",
          "value" : "032907381cdf",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 17,
          "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926",
          "value" : "0136a352b2c8c1",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 18,
          "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926",
          "value" : "023c3db80e80e53bd1",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 19,
          "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926",
          "value" : "0504e8e504fd585e79193ca1",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 20,
          "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926",
          "value" : "00b7d84161830e3f6f2231a7a1",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 21,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "4c6092d9a7a5462b34e5",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 22,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "22c9a603ee84bb9c4cad",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 23,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "437ae92817f9fc85b7e5",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 24,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "0190e262098f0d746505",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 25,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "027a5f7ca7b29ee74d5525",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 26,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "008d60a89f3f36cb1fd495",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 27,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "02be6951adc5b22410a5fd",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 28,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "0292a0068ebb0ed3251f55",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 29,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "750b703e68cb957ab415",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 30,
          "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf",
          "value" : "02d0facc78aeeb89f5b299",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 31,
          "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Maple",
          "value" : "09bdc1c98b9b",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 32,
          "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Maple",
          "value" : "0ffb48c934842b",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 33,
          "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Maple",
          "value" : "18444fdb12afb7",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 34,
          "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Mathematica 2.0",
          "value" : "08e4f37e51",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 35,
          "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Mathematica 2.0",
          "value" : "179d55b600e7f1",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 36,
          "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Axioms primality test",
          "value" : "085270bd76a142abc3037d1aab3b",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 37,
          "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Axioms primality test",
          "value" : "02cb78fe3f36c4f5f05dbe92b82798d5fc18f2bfaaa388ef",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 38,
          "comment" : "A composite q that was acceptied by Gnu Crypto. http://www.iacr.org/archive/pkc2005/33860010/33860010.pdf",
          "value" : "4682f52f0b54308d315b2fbec25065506c77be95912b137bc6eecffad8a299b631c55ce068702b1b3e4ce50958994c289b148fb298a8c603a0959cb0ba5ad4bcba278cf4c87e0ff85a62a25c40849662c53d0f81cf9e4431d8c391586629260e558db473997db20108278b1ae374089140d93bc2c5a808ad3aaf212f60bfc93cc0c788149dcd82f7ab",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 39,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "00f67307e54779cfe9120bf862afc5466c5d6d0783d12df5215c0c981c51e4bfc098e9afd574f51b18c820259b692ec0bf7c9d6e56e9bb99fbd3b7ecc4082146a9d7a5b7bc6519d476c4a9975d9c3e3b12bee45b7accb07a6a68ea583ac2523ef32ee6d01bc766b59c43031f9c6980c9b4317da6825be9f7c5db03283d04c13323",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 40,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "00c1d00b32d63e3ea4fb69ab6b9dee40a17fada46c122e52a53fecd3fe613303f51c07871dc0b5d8d8c1705b484de6bdb7f442efecd7d9f59dc36e495f72905c7619bc4d3706283774e704a3adad7d6c1be42ddeffc2ca5b1c0e31b58ed606f16dc14676e60ecff42ae33e503621e232ba449e91e3a9909e80a8318610aea3b7cf",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 41,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "01c2faadef91d43c9ab1320020e08e2ec3c34012bd0db94a1175170dc5aec26897e867d0b7a7273119fbe1115f02875b522566016f69f319ad5485e7458fcf50205d22ba765cc586a6037be987b6832c46227df19cd8ce0641794b60b73fbdd3c104870ae9bdf0194e772c985536e860b90b7fa3eb205af6b224413f5813836abb",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 42,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "0109fddd44575367466c67aaa921047b367515c9aa579eb60728034ad2d56f10eb01cfadb3ba0abde99f348bc3c70559bc24551b85937ca4c886abc0826cc1c310f14393652c1b4994953881bd2d81de0f2a280839829543f429bc41bf3c6db120bb150173e2707f36d1f76318249851f4fedc39e36aaaca48686de03e6d256973",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 43,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "00ffd0847cdda5a4fdfd2345bc731f1bc77843478950d33b2830ef0caf8deffdbe6309fe61fb67dded6659e433f30363339dbcc7c0832593f33c24a8b8f0e28038cb6edeed58ae765e6884ac0b66b5218cc758e6247269d24be9f91865d33c105219ffbce00c6c2d6391448643bcf5138268f510258f638b90a6c8b53bfc121759",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 44,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "0118d077827c6db85bc61d53063edf5676d6ac65b611d836eed07ee7e1d15c02d999a3eb78ce662edaf457f0f7d9c0a0305acc1faec4170400f0610a797de50ebfb08fd0a5da77144a1e0236e2bc6d8d2a6a719e59df071367cd61275f372e23b1c0187d87d15bda5f71f4705b1c3aaaa8ad951d20cee93274b151f3f9a55bd693",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 45,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "01c09377e15f53b1329b6e8a08bf0f94da27dd29c89be74544d705173a0bdd410935e186dd95ac113732674fe08585690ebe9f749a116a8c64e1b4a281ef0cb28bc70b1639bc1352ff5777783bd72e3b8495c1494ae11fb32bdaba8c80870a3de71c0c27f07983e97500c0ec0321b86c679c53ae7f8c76ddbf6a9cc3ff63e45023",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 46,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "00f35cac3bb3c7cf5e4e50162f4ca889ac7b875f4aac08c5a2433600e9bc64db6c9895aaccf3ee98783ee2cfd8a5e448b265bbc4cda6cb80d487c7967d5a6724fae1ffd27c70f579e62b49f29819c6221d7659fa9364e8e37795d88611506b552a20533f1f6446a35b41a986d304fdd7a39f484331b4fbf242f95b80788cff39cd",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 47,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "01e9df6f069f5984c080087127f90437f2d38f19385b3592d17a5f23603ec6315c36a88d2012e85eca62a983de7ef27673c605155b5647311840cf8887be8267fbc01cec3f7e0467d5e9a812e5dca577cc8ac93971c84f8cea94637c60c0bfe5d7f4b4f950e60ad077941190afaa905d6d5d570c9b4dab98c32c7abc42346f894d",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 48,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "00c5286502dda772fc22d43b0a2f46823777a91f580f3a1261c47be8e2010a5ad9395e2c036b32813dcdaad33c8f2f4a522593e31ae55ef05c8df8ed58636ac1b9db2b205797d39343e0868ff02bef46d18736bedc6f527730da8594d45d0447e7c7f0e8ca12b285b88aea5e343264874ac22038f5821bd96519d49caf45184f97",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 49,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "01c29fe8b7e63795218563774685b9fe85eada73691a6420c38f0e9f2f802e89c77ae78716924e4efb5e4c639ca98ddb0c9e35cbc6313196b3327672527404b6da8ff7813915702fb7fa254c1cdc167a34170da57606ccff876ca0ce5e920f443e389fc9d0c071b908c6675b6a9f5903d6d22ad490e6476a7e13adcaf988663b3b",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 50,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "01e8648f8abce82efb0afa9861c96c428f690c5fe33b9c9d47f97198542c982e607fd9700f876159ea404983f4eecbaf2a73b262085da4b7b5de8f6e8ca0b712f5e89c0e8f024033879f858f814275a3ea5543fd539e74f5e099769d0d726ebd8bc74bda6e2f8ffabbb7d043f7818cd8d531180a827731fac59f45b2af35d273f9",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 51,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "00cedc5db464312d6f1ecf53a40bde07ae0d5540ef75a4802ff469142270049dbba2b74e4ece7340d8eb99bac1a3d6f0b52ebb41794d3cd4e4a588431879ff81818abc50bca5e686a06d48461b425be62d3c064321429e346960163f897d21b362dc72f306a6865cfb9c8c5682cc7fcd7dc6ac4202e8d070729ef9e3b526236c71",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 52,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "0093ec9e6681f1bc1d6534add99d97e0d907828996bb3d7b481f3ceaefbe8f3fdf15698302ce26feb84c08994079c9f368af8171faf76801fe6dfdaecd587fa0edc751d64ff7e9aa73fb7aa51a8469379bac38e9d7941e0bbdcf658633daea40738e81f5605198b04fe8fd49646da4e98c2282a8041c25bb9894252412472294f9",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 53,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "0129fffd0bf1827f2847f45bd490d5423f67d87eb8254535d57078707e19f2ca5ca10602c5eca552fbdc77e30592b7498254f901cad02e0bf59802f5582cbb3059a1979a5e5311855807b1cbeff86a651dbf3818c3b6cf50092c9b744c4831873d1d0d8c23f23b39517ce435a257e5026cfa0be280672e1bba3074b2cdc6474a37",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 54,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "017232b942eedc8a0df14f5c1ad4e099f192b242b7d3dff09c50cecfe636c72c6c8ba1c65dde4396282e1a1c823b6d5d9c0c9068b39e202dcba26a9d35a00b7bb6bede272820fbbba503bc1866c6ae183d8b50e28555a921121929862ce87ea4ddde8f9d6ff2e17a8ee7cf9d306faa0815a4d46e8dfd4b7ea538b7399cc1c06c1f",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 55,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "00d3768b43c242fa7ac1de856dc7bd413b79d544bb8d38677bc9f44aa116ac5525c3e7fcf2fb2c1d3de61844931f47646b4c5f7de226031c925acbe57f1cd292fec7e7d4fd25afa128704ffd8da910ef18961e081e88d40bc37582b087f1b1f39fe4d23a03ec6b869c76fa3aed7a3606c469069c4fa1d4ff1c6112da16ba9dcf97",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 56,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "011b5119e5c68a710158c36d414597b4e1ccff332d1b437a4d2da2d2269ad2b626fde79e3ba7ed92128e5feaa87556f18ca6937b5a88f4738608d6bb6aacaf4fb719d67561d66dba9690009bcdbea2db4ee48d575722cbafbf1e487bab1c62ba0cde30a34620c7733b3e13d8b27fa035115680fb81016d1ca777b8a2bb7c399a47",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 57,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "008e9ee596ea83d06e1a9a4c3b75fc67f3c01de737be4dcdc18f1d10e322df48e455546ac8ac810129dbcb0fbf568987033cadef9d051f6032c8dca2804fc8d8d6e79f5d767963e4b6d72ac29d98d2520c29c8e69ffa59164d6a1e4cb55b7fcc60c7cb274da264203839873ec2f85f4ae377eeb6189e031b17e8603a01ef877b3f",
          "result" : "invalid",
          "flags" : [
            "WorstCaseMillerRabin"
          ]
        },
        {
          "tcId" : 58,
          "comment" : "Worst case for Miller-Rabin test",
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        {
          "tcId" : 83,
          "comment" : "Worst case for Miller-Rabin test",
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        },
        {
          "tcId" : 84,
          "comment" : "Worst case for Miller-Rabin test",
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          "result" : "invalid",
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            "WorstCaseMillerRabin"
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        },
        {
          "tcId" : 85,
          "comment" : "Worst case for Miller-Rabin test",
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        },
        {
          "tcId" : 86,
          "comment" : "Worst case for Miller-Rabin test",
          "value" : "550fda19f97cdfbd13930911ef6e9e1cb2b7b5215a35c215d51ebffeb435642174cbe998f4451bde2d4bd2ce92ab5b9493b657f1d77d9ad4d348550247b903906109c608ecba7f88c239c76f0afc231e7f1ac1cee87b4c34448a16f7979ff4c18e65e05d5a86909615fe56587576962a2cb3ba467d9806445a0f039907601af77ba7d07578eff612364fbcac11d35e243734aa6d9a6cdcf912a2dd0a12ba7e87",
          "result" : "invalid",
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            "WorstCaseMillerRabin"
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        },
        {
          "tcId" : 87,
          "comment" : "A strong pseudoprime for the first 46 primes. F. Arnault, \"Rabin-Miller primality test: composite numbers which pass it\", Math. comp. v.64, n.209, p 355-361.",
          "value" : "00907b5573c3d72ca5afda9df723d24066410e3d2b61f89c5c600f90732d0ad7db06a02e209f6792b609fee2ac6f3d73a5805f2b30642d1e2654f7ffd155153e5fbdcb17c76c27fbcc15010ccbfa7a1737cdf032edd5da7edebc9703e51572ce452c2319f1d91bee276d3e1121f9563b1700448ff37346b5a88098c9a682a59ccab86401aeeb74c8ce45dbf8b5",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 88,
          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
          "value" : "19bc037ff6b1",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 89,
          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
          "value" : "01933ecb87a0c1",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 90,
          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
          "value" : "021229a85a2f91",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 91,
          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
          "value" : "032d4a135c4d51",
          "result" : "invalid",
          "flags" : []
        },
        {
          "tcId" : 92,
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          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
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          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
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          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
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          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
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          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
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          "tcId" : 99,
          "comment" : "Richard G.E. Pinch, \"Absolute quadratic pseudorprimes\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf",
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          "tcId" : 102,
          "comment" : "Safety in Numbers: \"On the Need for Robust Diffie-Hellman Parameter Validation\" Galbraith, Massimo, Paterson, https://eprint.iacr.org/2019/032.pdf",
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          "tcId" : 103,
          "comment" : "Safety in Numbers: \"On the Need for Robust Diffie-Hellman Parameter Validation\" Galbraith, Massimo, Paterson, https://eprint.iacr.org/2019/032.pdf",
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          "tcId" : 104,
          "comment" : "Safety in Numbers: \"On the Need for Robust Diffie-Hellman Parameter Validation\" Galbraith, Massimo, Paterson, https://eprint.iacr.org/2019/032.pdf",
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          "tcId" : 105,
          "comment" : "Safety in Numbers: \"On the Need for Robust Diffie-Hellman Parameter Validation\" Galbraith, Massimo, Paterson, https://eprint.iacr.org/2019/032.pdf",
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