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Diffstat (limited to 'lib/base/devel/FGInt.pas')
| -rw-r--r-- | lib/base/devel/FGInt.pas | 2199 |
1 files changed, 0 insertions, 2199 deletions
diff --git a/lib/base/devel/FGInt.pas b/lib/base/devel/FGInt.pas deleted file mode 100644 index 7cb5a8516..000000000 --- a/lib/base/devel/FGInt.pas +++ /dev/null @@ -1,2199 +0,0 @@ -{License, info, etc - ------------------ - -This implementation is made by me, Walied Othman, to contact me -mail to Walied.Othman@belgacom.net or Triade@ulyssis.org, -always mention wether it 's about the FGInt for Delphi or for -FreePascal, or wether it 's about the 6xs, preferably in the subject line. -If you 're going to use these implementations, at least mention my -name or something and notify me so I may even put a link on my page. -This implementation is freeware and according to the coderpunks' -manifesto it should remain so, so don 't use these implementations -in commercial software. Encryption, as a tool to ensure privacy -should be free and accessible for anyone. If you plan to use these -implementations in a commercial application, contact me before -doing so, that way you can license the software to use it in commercial -Software. If any algorithm is patented in your country, you should -acquire a license before using this software. Modified versions of this -software must contain an acknowledgement of the original author (=me). -This implementation is available at -http://triade.studentenweb.org - -copyright 2000, Walied Othman -This header may not be removed. -} - -Unit FGInt; - -{$H+} - -Interface - -Uses SysUtils, Math; - -Type - TCompare = (Lt, St, Eq, Er); - TSign = (negative, positive); - TFGInt = Record - Sign : TSign; - Number : Array Of LongWord; - End; - -Procedure zeronetochar8(Var g : char; Const x : String); -Procedure zeronetochar6(Var g : integer; Const x : String); -Procedure initialize8(Var trans : Array Of String); -Procedure initialize6(Var trans : Array Of String); -Procedure initialize6PGP(Var trans : Array Of String); -Procedure ConvertBase256to64(Const str256 : String; Var str64 : String); -Procedure ConvertBase64to256(Const str64 : String; Var str256 : String); -Procedure ConvertBase256to2(Const str256 : String; Var str2 : String); -Procedure ConvertBase64to2(Const str64 : String; Var str2 : String); -Procedure ConvertBase2to256(str2 : String; Var str256 : String); -Procedure ConvertBase2to64(str2 : String; Var str64 : String); -Procedure ConvertBase256StringToHexString(Str256 : String; Var HexStr : String); -Procedure ConvertHexStringToBase256String(HexStr : String; Var Str256 : String); -Procedure PGPConvertBase256to64(Var str256, str64 : String); -Procedure PGPConvertBase64to256(str64 : String; Var str256 : String); -Procedure PGPConvertBase64to2(str64 : String; Var str2 : String); -Procedure FGIntToBase2String(Const FGInt : TFGInt; Var S : String); -Procedure Base2StringToFGInt(S : String; Var FGInt : TFGInt); -Procedure FGIntToBase256String(Const FGInt : TFGInt; Var str256 : String); -Procedure Base256StringToFGInt(str256 : String; Var FGInt : TFGInt); -Procedure PGPMPIToFGInt(PGPMPI : String; Var FGInt : TFGInt); -Procedure FGIntToPGPMPI(FGInt : TFGInt; Var PGPMPI : String); -Procedure Base10StringToFGInt(Base10 : String; Var FGInt : TFGInt); -Procedure FGIntToBase10String(Const FGInt : TFGInt; Var Base10 : String); -Procedure FGIntDestroy(Var FGInt : TFGInt); -Function FGIntCompareAbs(Const FGInt1, FGInt2 : TFGInt) : TCompare; -Procedure FGIntAdd(Const FGInt1, FGInt2 : TFGInt; Var Sum : TFGInt); -Procedure FGIntChangeSign(Var FGInt : TFGInt); -Procedure FGIntSub(Var FGInt1, FGInt2, dif : TFGInt); -Procedure FGIntMulByInt(Const FGInt : TFGInt; Var res : TFGInt; by : LongWord); -Procedure FGIntMulByIntbis(Var FGInt : TFGInt; by : LongWord); -Procedure FGIntDivByInt(Const FGInt : TFGInt; Var res : TFGInt; by : LongWord; Var modres : LongWord); -Procedure FGIntDivByIntBis(Var FGInt : TFGInt; by : LongWord; Var modres : LongWord); -Procedure FGIntModByInt(Const FGInt : TFGInt; by : LongWord; Var modres : LongWord); -Procedure FGIntAbs(Var FGInt : TFGInt); -Procedure FGIntCopy(Const FGInt1 : TFGInt; Var FGInt2 : TFGInt); -Procedure FGIntShiftLeft(Var FGInt : TFGInt); -Procedure FGIntShiftRight(Var FGInt : TFGInt); -Procedure FGIntShiftRightBy31(Var FGInt : TFGInt); -Procedure FGIntAddBis(Var FGInt1 : TFGInt; Const FGInt2 : TFGInt); -Procedure FGIntSubBis(Var FGInt1 : TFGInt; Const FGInt2 : TFGInt); -Procedure FGIntMul(Const FGInt1, FGInt2 : TFGInt; Var Prod : TFGInt); -Procedure FGIntSquare(Const FGInt : TFGInt; Var Square : TFGInt); -Procedure FGIntExp(Const FGInt, exp : TFGInt; Var res : TFGInt); -Procedure FGIntFac(Const FGInt : TFGInt; Var res : TFGInt); -Procedure FGIntShiftLeftBy31(Var FGInt : TFGInt); -Procedure FGIntDivMod(Var FGInt1, FGInt2, QFGInt, MFGInt : TFGInt); -Procedure FGIntDiv(Var FGInt1, FGInt2, QFGInt : TFGInt); -Procedure FGIntMod(Var FGInt1, FGInt2, MFGInt : TFGInt); -Procedure FGIntSquareMod(Var FGInt, Modb, FGIntSM : TFGInt); -Procedure FGIntAddMod(Var FGInt1, FGInt2, base, FGIntres : TFGInt); -Procedure FGIntMulMod(Var FGInt1, FGInt2, base, FGIntres : TFGInt); -Procedure FGIntModExp(Var FGInt, exp, modb, res : TFGInt); -Procedure FGIntModBis(Const FGInt : TFGInt; Var FGIntOut : TFGInt; b, head : LongWord); -Procedure FGIntMulModBis(Const FGInt1, FGInt2 : TFGInt; Var Prod : TFGInt; b, head : LongWord); -Procedure FGIntMontgomeryMod(Const GInt, base, baseInv : TFGInt; Var MGInt : TFGInt; b : Longword; head : LongWord); -Procedure FGIntMontgomeryModExp(Var FGInt, exp, modb, res : TFGInt); -Procedure FGIntGCD(Const FGInt1, FGInt2 : TFGInt; Var GCD : TFGInt); -Procedure FGIntLCM(Const FGInt1, FGInt2 : TFGInt; Var LCM : TFGInt); -Procedure FGIntTrialDiv9999(Const FGInt : TFGInt; Var ok : boolean); -Procedure FGIntRandom1(Var Seed, RandomFGInt : TFGInt); -Procedure FGIntRabinMiller(Var FGIntp : TFGInt; nrtest : Longword; Var ok : boolean); -Procedure FGIntBezoutBachet(Var FGInt1, FGInt2, a, b : TFGInt); -Procedure FGIntModInv(Const FGInt1, base : TFGInt; Var Inverse : TFGInt); -Procedure FGIntPrimetest(Var FGIntp : TFGInt; nrRMtests : integer; Var ok : boolean); -Procedure FGIntLegendreSymbol(Var a, p : TFGInt; Var L : integer); -Procedure FGIntSquareRootModP(Square, Prime : TFGInt; Var SquareRoot : TFGInt); - - - -Implementation - -Var - primes : Array[1..1228] Of integer = - (3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, - 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, - 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, - 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, - 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, - 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, - 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, - 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, - 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, - 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, - 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, - 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, - 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, - 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, - 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, - 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, - 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, - 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, - 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, - 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, - 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, - 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, - 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, - 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, - 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, - 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, - 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, - 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, - 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, - 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, - 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, - 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, - 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, - 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, - 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, - 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, - 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, - 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, - 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, - 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, - 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, - 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, - 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, - 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, - 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, - 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, - 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, - 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, - 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, - 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, - 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, - 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, - 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, - 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, - 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, - 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, - 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, - 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, - 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, - 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, - 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, - 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, - 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973); - chr64 : Array[1..64] Of char = ('a', 'A', 'b', 'B', 'c', 'C', 'd', 'D', 'e', 'E', 'f', 'F', - 'g', 'G', 'h', 'H', 'i', 'I', 'j', 'J', 'k', 'K', 'l', 'L', 'm', 'M', 'n', 'N', 'o', 'O', 'p', - 'P', 'q', 'Q', 'r', 'R', 's', 'S', 't', 'T', 'u', 'U', 'v', 'V', 'w', 'W', 'x', 'X', 'y', 'Y', - 'z', 'Z', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '+', '='); - PGPchr64 : Array[1..64] Of char = ('A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', - 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e', 'f', - 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', - 'z', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '+', '/'); - - - -Procedure zeronetochar8(Var g : char; Const x : String); -Var - i : Integer; - b : byte; -Begin - b := 0; - For i := 1 To 8 Do - Begin - If copy(x, i, 1) = '1' Then - b := b Or (1 Shl (8 - I)); - End; - g := chr(b); -End; - - -Procedure zeronetochar6(Var g : integer; Const x : String); -Var - I : Integer; -Begin - G := 0; - For I := 1 To Length(X) Do - Begin - If I > 6 Then - Break; - If X[I] <> '0' Then - G := G Or (1 Shl (6 - I)); - End; - Inc(G); -End; - - -Procedure initialize8(Var trans : Array Of String); -Var - c1, c2, c3, c4, c5, c6, c7, c8 : integer; - x : String; - g : char; -Begin - For c1 := 0 To 1 Do - For c2 := 0 To 1 Do - For c3 := 0 To 1 Do - For c4 := 0 To 1 Do - For c5 := 0 To 1 Do - For c6 := 0 To 1 Do - For c7 := 0 To 1 Do - For c8 := 0 To 1 Do - Begin - x := chr(48+c1) + chr(48+c2) + chr(48+c3) + chr(48+c4) + chr(48+c5) + chr(48+c6) + chr(48+c7) + chr(48+c8); - zeronetochar8(g, x); - trans[ord(g)] := x; - End; -End; - - -Procedure initialize6(Var trans : Array Of String); -Var - c1, c2, c3, c4, c5, c6 : integer; - x : String; - g : integer; -Begin - For c1 := 0 To 1 Do - For c2 := 0 To 1 Do - For c3 := 0 To 1 Do - For c4 := 0 To 1 Do - For c5 := 0 To 1 Do - For c6 := 0 To 1 Do - Begin - x := chr(48+c1) + chr(48+c2) + chr(48+c3) + chr(48+c4) + chr(48+c5) + chr(48+c6); - zeronetochar6(g, x); - trans[ord(chr64[g])] := x; - End; -End; - -Procedure initialize6PGP(Var trans : Array Of String); -Var - c1, c2, c3, c4, c5, c6 : integer; - x : String; - g : integer; -Begin - For c1 := 0 To 1 Do - For c2 := 0 To 1 Do - For c3 := 0 To 1 Do - For c4 := 0 To 1 Do - For c5 := 0 To 1 Do - For c6 := 0 To 1 Do - Begin - x := chr(48+c1) + chr(48+c2) + chr(48+c3) + chr(48+c4) + chr(48+c5) + chr(48+c6); - zeronetochar6(g, x); - trans[ord(PGPchr64[g])] := x; - End; -End; - - -// Convert base 8 strings to base 6 strings and visa versa - -Procedure ConvertBase256to64(Const str256 : String; Var str64 : String); -Var - temp : String; - trans : Array[0..255] Of String; - i, len6 : longint; - g : integer; -Begin - initialize8(trans); - temp := ''; - For i := 1 To length(str256) Do temp := temp + trans[ord(str256[i])]; - While (length(temp) Mod 6) <> 0 Do temp := temp + '0'; - len6 := length(temp) Div 6; - str64 := ''; - For i := 1 To len6 Do - Begin - zeronetochar6(g, copy(temp, 1, 6)); - str64 := str64 + chr64[g]; - delete(temp, 1, 6); - End; -End; - - -Procedure ConvertBase64to256(Const str64 : String; Var str256 : String); -Var - temp : String; - trans : Array[0..255] Of String; - i, len8 : longint; - g : char; -Begin - initialize6(trans); - temp := ''; - For i := 1 To length(str64) Do temp := temp + trans[ord(str64[i])]; - str256 := ''; - len8 := length(temp) Div 8; - For i := 1 To len8 Do - Begin - zeronetochar8(g, copy(temp, 1, 8)); - str256 := str256 + g; - delete(temp, 1, 8); - End; -End; - - -// Convert base 8 & 6 bit strings to base 2 strings and visa versa - -Procedure ConvertBase256to2(Const str256 : String; Var str2 : String); -Var - trans : Array[0..255] Of String; - i : longint; -Begin - str2 := ''; - initialize8(trans); - For i := 1 To length(str256) Do str2 := str2 + trans[ord(str256[i])]; -End; - - -Procedure ConvertBase64to2(Const str64 : String; Var str2 : String); -Var - trans : Array[0..255] Of String; - i : longint; -Begin - str2 := ''; - initialize6(trans); - For i := 1 To length(str64) Do str2 := str2 + trans[ord(str64[i])]; -End; - - -Procedure ConvertBase2to256(str2 : String; Var str256 : String); -Var - i, len8 : longint; - g : char; -Begin - str256 := ''; - While (length(str2) Mod 8) <> 0 Do str2 := '0' + str2; - len8 := length(str2) Div 8; - For i := 1 To len8 Do - Begin - zeronetochar8(g, copy(str2, 1, 8)); - str256 := str256 + g; - delete(str2, 1, 8); - End; -End; - - -Procedure ConvertBase2to64(str2 : String; Var str64 : String); -Var - i, len6 : longint; - g : integer; -Begin - str64 := ''; - While (length(str2) Mod 6) <> 0 Do str2 := '0' + str2; - len6 := length(str2) Div 6; - For i := 1 To len6 Do - Begin - zeronetochar6(g, copy(str2, 1, 6)); - str64 := str64 + chr64[g]; - delete(str2, 1, 6); - End; -End; - - -// Convert base 256 strings to base 16 (HexaDecimal) strings and visa versa - -Procedure ConvertBase256StringToHexString(Str256 : String; Var HexStr : String); -Var - i : longint; - b : byte; -Begin - HexStr := ''; - For i := 1 To length(str256) Do - Begin - b := ord(str256[i]); - If (b Shr 4) < 10 Then HexStr := HexStr + chr(48 + (b Shr 4)) - Else HexStr := HexStr + chr(55 + (b Shr 4)); - If (b And 15) < 10 Then HexStr := HexStr + chr(48 + (b And 15)) - Else HexStr := HexStr + chr(55 + (b And 15)); - End; -End; - - -Procedure ConvertHexStringToBase256String(HexStr : String; Var Str256 : String); -Var - i : longint; - b, h1, h2 : byte; - temp : string; -Begin - Str256 := ''; - If (length(Hexstr) mod 2) = 1 Then temp := '0' + HexStr Else temp := HexStr; - For i := 1 To (length(temp) Div 2) Do - Begin - h2 := ord(temp[2 * i]); - h1 := ord(temp[2 * i - 1]); - If h1 < 58 Then - b := ((h1 - 48) Shl 4) - Else - b := ((h1 - 55) Shl 4); - If h2 < 58 Then - b := (b Or (h2 - 48)) - Else - b := (b Or ((h2 - 55) and 15)); - Str256 := Str256 + chr(b); - End; -End; - - -// Convert base 256 strings to base 64 strings and visa versa, PGP style - -Procedure PGPConvertBase256to64(Var str256, str64 : String); -Var - temp, x, a : String; - i, len6 : longint; - g : integer; - trans : Array[0..255] Of String; -Begin - initialize8(trans); - temp := ''; - For i := 1 To length(str256) Do temp := temp + trans[ord(str256[i])]; - If (length(temp) Mod 6) = 0 Then a := '' Else - If (length(temp) Mod 6) = 4 Then - Begin - temp := temp + '00'; - a := '=' - End - Else - Begin - temp := temp + '0000'; - a := '==' - End; - str64 := ''; - len6 := length(temp) Div 6; - For i := 1 To len6 Do - Begin - x := copy(temp, 1, 6); - zeronetochar6(g, x); - str64 := str64 + PGPchr64[g]; - delete(temp, 1, 6); - End; - str64 := str64 + a; -End; - - -Procedure PGPConvertBase64to256(str64 : String; Var str256 : String); -Var - temp, x : String; - i, j, len8 : longint; - g : char; - trans : Array[0..255] Of String; -Begin - initialize6PGP(trans); - temp := ''; - str256 := ''; - If str64[length(str64) - 1] = '=' Then j := 2 Else - If str64[length(str64)] = '=' Then j := 1 Else j := 0; - For i := 1 To (length(str64) - j) Do temp := temp + trans[ord(str64[i])]; - If j <> 0 Then delete(temp, length(temp) - 2 * j + 1, 2 * j); - len8 := length(temp) Div 8; - For i := 1 To len8 Do - Begin - x := copy(temp, 1, 8); - zeronetochar8(g, x); - str256 := str256 + g; - delete(temp, 1, 8); - End; -End; - -// Convert base 64 strings to base 2 strings, PGP style - - -Procedure PGPConvertBase64to2(str64 : String; Var str2 : String); -Var - i, j : longint; - trans : Array[0..255] Of String; -Begin - str2 := ''; - initialize6(trans); - If str64[length(str64) - 1] = '=' Then j := 2 Else - If str64[length(str64)] = '=' Then j := 1 Else j := 0; - For i := 1 To (length(str64) - j) Do str2 := str2 + trans[ord(str64[i])]; - delete(str2, length(str2) - 2 * j + 1, 2 * j); -End; - - -// Convert a FGInt to a binary string (base 2) & visa versa - -Procedure FGIntToBase2String(Const FGInt : TFGInt; Var S : String); -Var - i : LongWord; - j : integer; -Begin - S := ''; - For i := 1 To FGInt.Number[0] Do - Begin - For j := 0 To 30 Do - If (1 And (FGInt.Number[i] Shr j)) = 1 Then - S := '1' + S - Else - S := '0' + S; - End; - While (length(S) > 1) And (S[1] = '0') Do - delete(S, 1, 1); - If S = '' Then S := '0'; -End; - - -Procedure Base2StringToFGInt(S : String; Var FGInt : TFGInt); -Var - i, j, size : LongWord; -Begin - While (S[1] = '0') And (length(S) > 1) Do - delete(S, 1, 1); - size := length(S) Div 31; - If (length(S) Mod 31) <> 0 Then size := size + 1; - SetLength(FGInt.Number, (size + 1)); - FGInt.Number[0] := size; - j := 1; - FGInt.Number[j] := 0; - i := 0; - While length(S) > 0 Do - Begin - If S[length(S)] = '1' Then - FGInt.Number[j] := FGInt.Number[j] Or (1 Shl i); - i := i + 1; - If i = 31 Then - Begin - i := 0; - j := j + 1; - If j <= size Then FGInt.Number[j] := 0; - End; - delete(S, length(S), 1); - End; - FGInt.Sign := positive; -End; - - -// Convert a FGInt to an base 256 string & visa versa - -Procedure FGIntToBase256String(Const FGInt : TFGInt; Var str256 : String); -Var - temp1 : String; - i, len8 : LongWord; - g : char; -Begin - FGIntToBase2String(FGInt, temp1); - While (length(temp1) Mod 8) <> 0 Do temp1 := '0' + temp1; - len8 := length(temp1) Div 8; - str256 := ''; - For i := 1 To len8 Do - Begin - zeronetochar8(g, copy(temp1, 1, 8)); - str256 := str256 + g; - delete(temp1, 1, 8); - End; -End; - - -Procedure Base256StringToFGInt(str256 : String; Var FGInt : TFGInt); -Var - temp1 : String; - i : longint; - trans : Array[0..255] Of String; -Begin - temp1 := ''; - initialize8(trans); - For i := 1 To length(str256) Do temp1 := temp1 + trans[ord(str256[i])]; - While (temp1[1] = '0') And (temp1 <> '0') Do delete(temp1, 1, 1); - Base2StringToFGInt(temp1, FGInt); -End; - -// Convert an MPI (Multiple Precision Integer, PGP style) to an FGInt & -// visa versa - -Procedure PGPMPIToFGInt(PGPMPI : String; Var FGInt : TFGInt); -Var - temp : String; -Begin - temp := PGPMPI; - delete(temp, 1, 2); - Base256StringToFGInt(temp, FGInt); -End; - - -Procedure FGIntToPGPMPI(FGInt : TFGInt; Var PGPMPI : String); -Var - len, i : word; - c : char; - b : byte; -Begin - FGIntToBase256String(FGInt, PGPMPI); - len := length(PGPMPI) * 8; - c := PGPMPI[1]; - For i := 7 Downto 0 Do If (ord(c) Shr i) = 0 Then len := len - 1 Else break; - b := len Mod 256; - PGPMPI := chr(b) + PGPMPI; - b := len Div 256; - PGPMPI := chr(b) + PGPMPI; -End; - - -// Convert a base 10 string to a FGInt -// NESTED -Procedure GIntDivByIntBis1(Var GInt : TFGInt; by : LongWord; Var modres : word); -Var - i, size, rest, temp : LongWord; -Begin - size := GInt.Number[0]; - temp := 0; - For i := size Downto 1 Do - Begin - temp := temp * 10000; - rest := temp + GInt.Number[i]; - GInt.Number[i] := rest Div by; - temp := rest Mod by; - End; - modres := temp; - While (GInt.Number[size] = 0) And (size > 1) Do - size := size - 1; - If size <> GInt.Number[0] Then - Begin - SetLength(GInt.Number, size + 1); - GInt.Number[0] := size; - End; -End; - -Procedure Base10StringToFGInt(Base10 : String; Var FGInt : TFGInt); -Var - i, size : LongWord; - j : word; - S, x : String; - sign : TSign; - - -Begin - While (Not (Base10[1] In ['-', '0'..'9'])) And (length(Base10) > 1) Do - delete(Base10, 1, 1); - If copy(Base10, 1, 1) = '-' Then - Begin - Sign := negative; - delete(Base10, 1, 1); - End - Else - Sign := positive; - While (length(Base10) > 1) And (copy(Base10, 1, 1) = '0') Do - delete(Base10, 1, 1); - size := length(Base10) Div 4; - If (length(Base10) Mod 4) <> 0 Then size := size + 1; - SetLength(FGInt.Number, size + 1); - FGInt.Number[0] := size; - For i := 1 To (size - 1) Do - Begin - x := copy(Base10, length(Base10) - 3, 4); - FGInt.Number[i] := StrToInt(x); - delete(Base10, length(Base10) - 3, 4); - End; - FGInt.Number[size] := StrToInt(Base10); - - S := ''; - While (FGInt.Number[0] <> 1) Or (FGInt.Number[1] <> 0) Do - Begin - GIntDivByIntBis1(FGInt, 2, j); - S := inttostr(j) + S; - End; - If S = '' Then S := '0'; - FGIntDestroy(FGInt); - Base2StringToFGInt(S, FGInt); - FGInt.Sign := sign; -End; - - -// Convert a FGInt to a base 10 string - -Procedure FGIntToBase10String(Const FGInt : TFGInt; Var Base10 : String); -Var - S : String; - j : LongWord; - temp : TFGInt; -Begin - FGIntCopy(FGInt, temp); - Base10 := ''; - While (temp.Number[0] > 1) Or (temp.Number[1] > 0) Do - Begin - FGIntDivByIntBis(temp, 10000, j); - S := IntToStr(j); - While Length(S) < 4 Do - S := '0' + S; - Base10 := S + Base10; - End; - Base10 := '0' + Base10; - While (length(Base10) > 1) And (Base10[1] = '0') Do - delete(Base10, 1, 1); - If FGInt.Sign = negative Then Base10 := '-' + Base10; -End; - - -// Destroy a FGInt to free memory - -Procedure FGIntDestroy(Var FGInt : TFGInt); -Begin - FGInt.Number := Nil; -End; - - -// Compare 2 FGInts in absolute value, returns -// Lt if FGInt1 > FGInt2, St if FGInt1 < FGInt2, Eq if FGInt1 = FGInt2, -// Er otherwise - -Function FGIntCompareAbs(Const FGInt1, FGInt2 : TFGInt) : TCompare; -Var - size1, size2, i : LongWord; -Begin - FGIntCompareAbs := Er; - size1 := FGInt1.Number[0]; - size2 := FGInt2.Number[0]; - If size1 > size2 Then FGIntCompareAbs := Lt Else - If size1 < size2 Then FGIntCompareAbs := St Else - Begin - i := size2; - While (FGInt1.Number[i] = FGInt2.Number[i]) And (i > 1) Do i := i - 1; - If FGInt1.Number[i] = FGInt2.Number[i] Then FGIntCompareAbs := Eq Else - If FGInt1.Number[i] < FGInt2.Number[i] Then FGIntCompareAbs := St Else - If FGInt1.Number[i] > FGInt2.Number[i] Then FGIntCompareAbs := Lt; - End; -End; - - -// Add 2 FGInts, FGInt1 + FGInt2 = Sum - -Procedure FGIntAdd(Const FGInt1, FGInt2 : TFGInt; Var Sum : TFGInt); -Var - i, size1, size2, size, rest, Trest : LongWord; -Begin - size1 := FGInt1.Number[0]; - size2 := FGInt2.Number[0]; - If size1 < size2 Then - FGIntAdd(FGInt2, FGInt1, Sum) - Else - Begin - If FGInt1.Sign = FGInt2.Sign Then - Begin - Sum.Sign := FGInt1.Sign; - setlength(Sum.Number, (size1 + 2)); - rest := 0; - For i := 1 To size2 Do - Begin - Trest := FGInt1.Number[i]; - Trest := Trest + FGInt2.Number[i]; - Trest := Trest + rest; - Sum.Number[i] := Trest And 2147483647; - rest := Trest Shr 31; - End; - For i := (size2 + 1) To size1 Do - Begin - Trest := FGInt1.Number[i] + rest; - Sum.Number[i] := Trest And 2147483647; - rest := Trest Shr 31; - End; - size := size1 + 1; - Sum.Number[0] := size; - Sum.Number[size] := rest; - While (Sum.Number[size] = 0) And (size > 1) Do - size := size - 1; - If Sum.Number[0] <> size Then SetLength(Sum.Number, size + 1); - Sum.Number[0] := size; - End - Else - Begin - If FGIntCompareAbs(FGInt2, FGInt1) = Lt Then - FGIntAdd(FGInt2, FGInt1, Sum) - Else - Begin - SetLength(Sum.Number, (size1 + 1)); - rest := 0; - For i := 1 To size2 Do - Begin - Trest := $80000000; // 2147483648; - TRest := Trest + FGInt1.Number[i]; - TRest := Trest - FGInt2.Number[i]; - TRest := Trest - rest; - Sum.Number[i] := Trest And 2147483647; - If (Trest > 2147483647) Then - rest := 0 - Else - rest := 1; - End; - For i := (size2 + 1) To size1 Do - Begin - Trest := $80000000; - TRest := Trest + FGInt1.Number[i]; - TRest := Trest - rest; - Sum.Number[i] := Trest And 2147483647; - If (Trest > 2147483647) Then - rest := 0 - Else - rest := 1; - End; - size := size1; - While (Sum.Number[size] = 0) And (size > 1) Do - size := size - 1; - If size <> size1 Then SetLength(Sum.Number, size + 1); - Sum.Number[0] := size; - Sum.Sign := FGInt1.Sign; - End; - End; - End; -End; - - - -Procedure FGIntChangeSign(Var FGInt : TFGInt); -Begin - If FGInt.Sign = negative Then FGInt.Sign := positive Else FGInt.Sign := negative; -End; - - -// Substract 2 FGInts, FGInt1 - FGInt2 = dif - -Procedure FGIntSub(Var FGInt1, FGInt2, dif : TFGInt); -Begin - FGIntChangeSign(FGInt2); - FGIntAdd(FGInt1, FGInt2, dif); - FGIntChangeSign(FGInt2); -End; - - -// multiply a FGInt by an integer, FGInt * by = res, by < 2147483648 - -Procedure FGIntMulByInt(Const FGInt : TFGInt; Var res : TFGInt; by : LongWord); -Var - i, size, rest : LongWord; - Trest : int64; -Begin - size := FGInt.Number[0]; - setlength(res.Number, (size + 2)); - rest := 0; - For i := 1 To size Do - Begin - Trest := FGInt.Number[i]; - TRest := Trest * by; - TRest := Trest + rest; - res.Number[i] := Trest And 2147483647; - rest := Trest Shr 31; - End; - If rest <> 0 Then - Begin - size := size + 1; - Res.Number[size] := rest; - End - Else - SetLength(Res.Number, size + 1); - Res.Number[0] := size; - Res.Sign := FGInt.Sign; -End; - - -// multiply a FGInt by an integer, FGInt * by = res, by < 1000000000 - -Procedure FGIntMulByIntbis(Var FGInt : TFGInt; by : LongWord); -Var - i, size, rest : LongWord; - Trest : int64; -Begin - size := FGInt.Number[0]; - Setlength(FGInt.Number, size + 2); - rest := 0; - For i := 1 To size Do - Begin - Trest := FGInt.Number[i]; - TRest := Trest * by; - TRest := Trest + rest; - FGInt.Number[i] := Trest And 2147483647; - rest := Trest Shr 31; - End; - If rest <> 0 Then - Begin - size := size + 1; - FGInt.Number[size] := rest; - End - Else - SetLength(FGInt.Number, size + 1); - FGInt.Number[0] := size; -End; - - -// divide a FGInt by an integer, FGInt = res * by + modres - -Procedure FGIntDivByInt(Const FGInt : TFGInt; Var res : TFGInt; by : LongWord; Var modres : LongWord); -Var - i, size : LongWord; - rest : int64; -Begin - size := FGInt.Number[0]; - setlength(res.Number, (size + 1)); - modres := 0; - For i := size Downto 1 Do - Begin - rest := modres; - rest := rest Shl 31; - rest := rest Or FGInt.Number[i]; - res.Number[i] := rest Div by; - modres := rest Mod by; - End; - While (res.Number[size] = 0) And (size > 1) Do - size := size - 1; - If size <> FGInt.Number[0] Then SetLength(res.Number, size + 1); - res.Number[0] := size; - Res.Sign := FGInt.Sign; - If FGInt.sign = negative Then modres := by - modres; -End; - - -// divide a FGInt by an integer, FGInt = FGInt * by + modres - -Procedure FGIntDivByIntBis(Var FGInt : TFGInt; by : LongWord; Var modres : LongWord); -Var - i, size : LongWord; - temp, rest : int64; -Begin - size := FGInt.Number[0]; - temp := 0; - For i := size Downto 1 Do - Begin - temp := temp Shl 31; - rest := temp Or FGInt.Number[i]; - FGInt.Number[i] := rest Div by; - temp := rest Mod by; - End; - modres := temp; - While (FGInt.Number[size] = 0) And (size > 1) Do - size := size - 1; - If size <> FGInt.Number[0] Then - Begin - SetLength(FGInt.Number, size + 1); - FGInt.Number[0] := size; - End; -End; - - -// Reduce a FGInt modulo by (=an integer), FGInt mod by = modres - -Procedure FGIntModByInt(Const FGInt : TFGInt; by : LongWord; Var modres : LongWord); -Var - i, size : LongWord; - temp, rest : int64; -Begin - size := FGInt.Number[0]; - temp := 0; - For i := size Downto 1 Do - Begin - temp := temp Shl 31; - rest := temp Or FGInt.Number[i]; - temp := rest Mod by; - End; - modres := temp; - If FGInt.sign = negative Then modres := by - modres; -End; - - -// Returns the FGInt in absolute value - -Procedure FGIntAbs(Var FGInt : TFGInt); -Begin - FGInt.Sign := positive; -End; - - -// Copy a FGInt1 into FGInt2 - -Procedure FGIntCopy(Const FGInt1 : TFGInt; Var FGInt2 : TFGInt); -Begin - FGInt2.Sign := FGInt1.Sign; - FGInt2.Number := Nil; - FGInt2.Number := Copy(FGInt1.Number, 0, FGInt1.Number[0] + 1); -End; - - -// Shift the FGInt to the left in base 2 notation, ie FGInt = FGInt * 2 - -Procedure FGIntShiftLeft(Var FGInt : TFGInt); -Var - l, m, i, size : LongWord; -Begin - size := FGInt.Number[0]; - l := 0; - For i := 1 To Size Do - Begin - m := FGInt.Number[i] Shr 30; - FGInt.Number[i] := ((FGInt.Number[i] Shl 1) Or l) And 2147483647; - l := m; - End; - If l <> 0 Then - Begin - setlength(FGInt.Number, size + 2); - FGInt.Number[size + 1] := l; - FGInt.Number[0] := size + 1; - End; -End; - - -// Shift the FGInt to the right in base 2 notation, ie FGInt = FGInt div 2 - -Procedure FGIntShiftRight(Var FGInt : TFGInt); -Var - l, m, i, size : LongWord; -Begin - size := FGInt.Number[0]; - l := 0; - For i := size Downto 1 Do - Begin - m := FGInt.Number[i] And 1; - FGInt.Number[i] := (FGInt.Number[i] Shr 1) Or l; - l := m Shl 30; - End; - If (FGInt.Number[size] = 0) And (size > 1) Then - Begin - setlength(FGInt.Number, size); - FGInt.Number[0] := size - 1; - End; -End; - - -// FGInt = FGInt / 2147483648 - -Procedure FGIntShiftRightBy31(Var FGInt : TFGInt); -Var - size, i : LongWord; -Begin - size := FGInt.Number[0]; - If size > 1 Then - Begin - For i := 1 To size - 1 Do - Begin - FGInt.Number[i] := FGInt.Number[i + 1]; - End; - SetLength(FGInt.Number, Size); - FGInt.Number[0] := size - 1; - End - Else - FGInt.Number[1] := 0; -End; - - -// FGInt1 = FGInt1 + FGInt2, FGInt1 > FGInt2 - -Procedure FGIntAddBis(Var FGInt1 : TFGInt; Const FGInt2 : TFGInt); -Var - i, size1, size2, Trest, rest : LongWord; -Begin - size1 := FGInt1.Number[0]; - size2 := FGInt2.Number[0]; - rest := 0; - For i := 1 To size2 Do - Begin - Trest := FGInt1.Number[i] + FGInt2.Number[i] + rest; - rest := Trest Shr 31; - FGInt1.Number[i] := Trest And 2147483647; - End; - For i := size2 + 1 To size1 Do - Begin - Trest := FGInt1.Number[i] + rest; - rest := Trest Shr 31; - FGInt1.Number[i] := Trest And 2147483647; - End; - If rest <> 0 Then - Begin - SetLength(FGInt1.Number, size1 + 2); - FGInt1.Number[0] := size1 + 1; - FGInt1.Number[size1 + 1] := rest; - End; -End; - - -// FGInt1 = FGInt1 - FGInt2, use only when 0 < FGInt2 < FGInt1 - -Procedure FGIntSubBis(Var FGInt1 : TFGInt; Const FGInt2 : TFGInt); -Var - i, size1, size2, rest, Trest : LongWord; -Begin - size1 := FGInt1.Number[0]; - size2 := FGInt2.Number[0]; - rest := 0; - For i := 1 To size2 Do - Begin - Trest := ($80000000 Or FGInt1.Number[i]) - FGInt2.Number[i] - rest; - If (Trest > 2147483647) Then - rest := 0 - Else - rest := 1; - FGInt1.Number[i] := Trest And 2147483647; - End; - For i := size2 + 1 To size1 Do - Begin - Trest := ($80000000 Or FGInt1.Number[i]) - rest; - If (Trest > 2147483647) Then - rest := 0 - Else - rest := 1; - FGInt1.Number[i] := Trest And 2147483647; - End; - i := size1; - While (FGInt1.Number[i] = 0) And (i > 1) Do - i := i - 1; - If i <> size1 Then - Begin - SetLength(FGInt1.Number, i + 1); - FGInt1.Number[0] := i; - End; -End; - - -// Multiply 2 FGInts, FGInt1 * FGInt2 = Prod - -Procedure FGIntMul(Const FGInt1, FGInt2 : TFGInt; Var Prod : TFGInt); -Var - i, j, size, size1, size2, rest : LongWord; - Trest : int64; -Begin - size1 := FGInt1.Number[0]; - size2 := FGInt2.Number[0]; - size := size1 + size2; - SetLength(Prod.Number, (size + 1)); - For i := 1 To size Do - Prod.Number[i] := 0; - - For i := 1 To size2 Do - Begin - rest := 0; - For j := 1 To size1 Do - Begin - Trest := FGInt1.Number[j]; - Trest := Trest * FGInt2.Number[i]; - Trest := Trest + Prod.Number[j + i - 1]; - Trest := Trest + rest; - Prod.Number[j + i - 1] := Trest And 2147483647; - rest := Trest Shr 31; - End; - Prod.Number[i + size1] := rest; - End; - - Prod.Number[0] := size; - While (Prod.Number[size] = 0) And (size > 1) Do - size := size - 1; - If size <> Prod.Number[0] Then - Begin - SetLength(Prod.Number, size + 1); - Prod.Number[0] := size; - End; - If FGInt1.Sign = FGInt2.Sign Then - Prod.Sign := Positive - Else - prod.Sign := negative; -End; - - -// Square a FGInt, FGInt² = Square - -Procedure FGIntSquare(Const FGInt : TFGInt; Var Square : TFGInt); -Var - size, size1, i, j, rest : LongWord; - Trest : int64; -Begin - size1 := FGInt.Number[0]; - size := 2 * size1; - SetLength(Square.Number, (size + 1)); - Square.Number[0] := size; - For i := 1 To size Do - Square.Number[i] := 0; - For i := 1 To size1 Do - Begin - Trest := FGInt.Number[i]; - Trest := Trest * FGInt.Number[i]; - Trest := Trest + Square.Number[2 * i - 1]; - Square.Number[2 * i - 1] := Trest And 2147483647; - rest := Trest Shr 31; - For j := i + 1 To size1 Do - Begin - Trest := FGInt.Number[i] Shl 1; - Trest := Trest * FGInt.Number[j]; - Trest := Trest + Square.Number[i + j - 1]; - Trest := Trest + rest; - Square.Number[i + j - 1] := Trest And 2147483647; - rest := Trest Shr 31; - End; - Square.Number[i + size1] := rest; - End; - Square.Sign := positive; - While (Square.Number[size] = 0) And (size > 1) Do - size := size - 1; - If size <> (2 * size1) Then - Begin - SetLength(Square.Number, size + 1); - Square.Number[0] := size; - End; -End; - - -// Exponentiate a FGInt, FGInt^exp = res - -Procedure FGIntExp(Const FGInt, exp : TFGInt; Var res : TFGInt); -Var - temp2, temp3 : TFGInt; - S : String; - i : LongWord; -Begin - FGIntToBase2String(exp, S); - If S[length(S)] = '0' Then Base10StringToFGInt('1', res) Else FGIntCopy(FGInt, res); - FGIntCopy(FGInt, temp2); - If length(S) > 1 Then - For i := (length(S) - 1) Downto 1 Do - Begin - FGIntSquare(temp2, temp3); - FGIntCopy(temp3, temp2); - If S[i] = '1' Then - Begin - FGIntMul(res, temp2, temp3); - FGIntCopy(temp3, res); - End; - End; -End; - - -// Compute FGInt! = FGInt * (FGInt - 1) * (FGInt - 2) * ... * 3 * 2 * 1 - -Procedure FGIntFac(Const FGInt : TFGInt; Var res : TFGInt); -Var - one, temp, temp1 : TFGInt; -Begin - FGIntCopy(FGInt, temp); - Base10StringToFGInt('1', res); - Base10StringToFGInt('1', one); - - While Not (FGIntCompareAbs(temp, one) = Eq) Do - Begin - FGIntMul(temp, res, temp1); - FGIntCopy(temp1, res); - FGIntSubBis(temp, one); - End; - - FGIntDestroy(one); - FGIntDestroy(temp); -End; - - -// FGInt = FGInt * 2147483648 - -Procedure FGIntShiftLeftBy31(Var FGInt : TFGInt); -Var - f1, f2 : LongWord; - i, size : longint; -Begin - size := FGInt.Number[0]; - SetLength(FGInt.Number, size + 2); - f1 := 0; - For i := 1 To (size + 1) Do - Begin - f2 := FGInt.Number[i]; - FGInt.Number[i] := f1; - f1 := f2; - End; - FGInt.Number[0] := size + 1; -End; - - -// Divide 2 FGInts, FGInt1 = FGInt2 * QFGInt + MFGInt, MFGInt is always positive - -Procedure FGIntDivMod(Var FGInt1, FGInt2, QFGInt, MFGInt : TFGInt); -Var - one, zero, temp1, temp2 : TFGInt; - s1, s2 : TSign; - j, s, t : LongWord; - i : int64; -Begin - s1 := FGInt1.Sign; - s2 := FGInt2.Sign; - FGIntAbs(FGInt1); - FGIntAbs(FGInt2); - FGIntCopy(FGInt1, MFGInt); - FGIntCopy(FGInt2, temp1); - - If FGIntCompareAbs(FGInt1, FGInt2) <> St Then - Begin - s := FGInt1.Number[0] - FGInt2.Number[0]; - SetLength(QFGInt.Number, (s + 2)); - QFGInt.Number[0] := s + 1; - For t := 1 To s Do - Begin - FGIntShiftLeftBy31(temp1); - QFGInt.Number[t] := 0; - End; - j := s + 1; - QFGInt.Number[j] := 0; - While FGIntCompareAbs(MFGInt, FGInt2) <> St Do - Begin - While FGIntCompareAbs(MFGInt, temp1) <> St Do - Begin - If MFGInt.Number[0] > temp1.Number[0] Then - Begin - i := MFGInt.Number[MFGInt.Number[0]]; - i := i Shl 31; - i := i + MFGInt.Number[MFGInt.Number[0] - 1]; - i := i Div (temp1.Number[temp1.Number[0]] + 1); - End - Else - i := MFGInt.Number[MFGInt.Number[0]] Div (temp1.Number[temp1.Number[0]] + 1); - If (i <> 0) Then - Begin - FGIntCopy(temp1, temp2); - FGIntMulByIntBis(temp2, i); - FGIntSubBis(MFGInt, temp2); - QFGInt.Number[j] := QFGInt.Number[j] + i; - If FGIntCompareAbs(MFGInt, temp2) <> St Then - Begin - QFGInt.Number[j] := QFGInt.Number[j] + i; - FGIntSubBis(MFGInt, temp2); - End; - FGIntDestroy(temp2); - End - Else - Begin - QFGInt.Number[j] := QFGInt.Number[j] + 1; - FGIntSubBis(MFGInt, temp1); - End; - End; - If MFGInt.Number[0] <= temp1.Number[0] Then - If FGIntCompareAbs(temp1, FGInt2) <> Eq Then - Begin - FGIntShiftRightBy31(temp1); - j := j - 1; - End; - End; - End - Else - Base10StringToFGInt('0', QFGInt); - s := QFGInt.Number[0]; - While (s > 1) And (QFGInt.Number[s] = 0) Do - s := s - 1; - If s < QFGInt.Number[0] Then - Begin - setlength(QFGInt.Number, s + 1); - QFGInt.Number[0] := s; - End; - QFGInt.Sign := positive; - - FGIntDestroy(temp1); - Base10StringToFGInt('0', zero); - Base10StringToFGInt('1', one); - If s1 = negative Then - Begin - If FGIntCompareAbs(MFGInt, zero) <> Eq Then - Begin - FGIntadd(QFGInt, one, temp1); - FGIntDestroy(QFGInt); - FGIntCopy(temp1, QFGInt); - FGIntDestroy(temp1); - FGIntsub(FGInt2, MFGInt, temp1); - FGIntDestroy(MFGInt); - FGIntCopy(temp1, MFGInt); - FGIntDestroy(temp1); - End; - If s2 = positive Then QFGInt.Sign := negative; - End - Else - QFGInt.Sign := s2; - FGIntDestroy(one); - FGIntDestroy(zero); - - FGInt1.Sign := s1; - FGInt2.Sign := s2; -End; - - -// Same as above but doesn 't compute MFGInt - -Procedure FGIntDiv(Var FGInt1, FGInt2, QFGInt : TFGInt); -Var - one, zero, temp1, temp2, MFGInt : TFGInt; - s1, s2 : TSign; - j, s, t : LongWord; - i : int64; -Begin - s1 := FGInt1.Sign; - s2 := FGInt2.Sign; - FGIntAbs(FGInt1); - FGIntAbs(FGInt2); - FGIntCopy(FGInt1, MFGInt); - FGIntCopy(FGInt2, temp1); - - If FGIntCompareAbs(FGInt1, FGInt2) <> St Then - Begin - s := FGInt1.Number[0] - FGInt2.Number[0]; - SetLength(QFGInt.Number, (s + 2)); - QFGInt.Number[0] := s + 1; - For t := 1 To s Do - Begin - FGIntShiftLeftBy31(temp1); - QFGInt.Number[t] := 0; - End; - j := s + 1; - QFGInt.Number[j] := 0; - While FGIntCompareAbs(MFGInt, FGInt2) <> St Do - Begin - While FGIntCompareAbs(MFGInt, temp1) <> St Do - Begin - If MFGInt.Number[0] > temp1.Number[0] Then - Begin - i := MFGInt.Number[MFGInt.Number[0]]; - i := i Shl 31; - i := i + MFGInt.Number[MFGInt.Number[0] - 1]; - i := i Div (temp1.Number[temp1.Number[0]] + 1); - End - Else - i := MFGInt.Number[MFGInt.Number[0]] Div (temp1.Number[temp1.Number[0]] + 1); - If (i <> 0) Then - Begin - FGIntCopy(temp1, temp2); - FGIntMulByIntBis(temp2, i); - FGIntSubBis(MFGInt, temp2); - QFGInt.Number[j] := QFGInt.Number[j] + i; - If FGIntCompareAbs(MFGInt, temp2) <> St Then - Begin - QFGInt.Number[j] := QFGInt.Number[j] + i; - FGIntSubBis(MFGInt, temp2); - End; - FGIntDestroy(temp2); - End - Else - Begin - QFGInt.Number[j] := QFGInt.Number[j] + 1; - FGIntSubBis(MFGInt, temp1); - End; - End; - If MFGInt.Number[0] <= temp1.Number[0] Then - If FGIntCompareAbs(temp1, FGInt2) <> Eq Then - Begin - FGIntShiftRightBy31(temp1); - j := j - 1; - End; - End; - End - Else - Base10StringToFGInt('0', QFGInt); - s := QFGInt.Number[0]; - While (s > 1) And (QFGInt.Number[s] = 0) Do - s := s - 1; - If s < QFGInt.Number[0] Then - Begin - setlength(QFGInt.Number, s + 1); - QFGInt.Number[0] := s; - End; - QFGInt.Sign := positive; - - FGIntDestroy(temp1); - Base10StringToFGInt('0', zero); - Base10StringToFGInt('1', one); - If s1 = negative Then - Begin - If FGIntCompareAbs(MFGInt, zero) <> Eq Then - Begin - FGIntadd(QFGInt, one, temp1); - FGIntDestroy(QFGInt); - FGIntCopy(temp1, QFGInt); - FGIntDestroy(temp1); - FGIntsub(FGInt2, MFGInt, temp1); - FGIntDestroy(MFGInt); - FGIntCopy(temp1, MFGInt); - FGIntDestroy(temp1); - End; - If s2 = positive Then QFGInt.Sign := negative; - End - Else - QFGInt.Sign := s2; - FGIntDestroy(one); - FGIntDestroy(zero); - FGIntDestroy(MFGInt); - - FGInt1.Sign := s1; - FGInt2.Sign := s2; -End; - - - -// Same as above but this computes MFGInt in stead of QFGInt -// MFGInt = FGInt1 mod FGInt2 - -Procedure FGIntMod(Var FGInt1, FGInt2, MFGInt : TFGInt); -Var - one, zero, temp1, temp2 : TFGInt; - s1, s2 : TSign; - s, t : LongWord; - i : int64; -Begin - s1 := FGInt1.Sign; - s2 := FGInt2.Sign; - FGIntAbs(FGInt1); - FGIntAbs(FGInt2); - FGIntCopy(FGInt1, MFGInt); - FGIntCopy(FGInt2, temp1); - - If FGIntCompareAbs(FGInt1, FGInt2) <> St Then - Begin - s := FGInt1.Number[0] - FGInt2.Number[0]; - For t := 1 To s Do - FGIntShiftLeftBy31(temp1); - While FGIntCompareAbs(MFGInt, FGInt2) <> St Do - Begin - While FGIntCompareAbs(MFGInt, temp1) <> St Do - Begin - If MFGInt.Number[0] > temp1.Number[0] Then - Begin - i := MFGInt.Number[MFGInt.Number[0]]; - i := i Shl 31; - i := i + MFGInt.Number[MFGInt.Number[0] - 1]; - i := i Div (temp1.Number[temp1.Number[0]] + 1); - End - Else - i := MFGInt.Number[MFGInt.Number[0]] Div (temp1.Number[temp1.Number[0]] + 1); - If (i <> 0) Then - Begin - FGIntCopy(temp1, temp2); - FGIntMulByIntBis(temp2, i); - FGIntSubBis(MFGInt, temp2); - If FGIntCompareAbs(MFGInt, temp2) <> St Then FGIntSubBis(MFGInt, temp2); - FGIntDestroy(temp2); - End - Else - FGIntSubBis(MFGInt, temp1); -// If FGIntCompareAbs(MFGInt, temp1) <> St Then FGIntSubBis(MFGInt,temp1); - End; - If MFGInt.Number[0] <= temp1.Number[0] Then - If FGIntCompareAbs(temp1, FGInt2) <> Eq Then FGIntShiftRightBy31(temp1); - End; - End; - - FGIntDestroy(temp1); - Base10StringToFGInt('0', zero); - Base10StringToFGInt('1', one); - If s1 = negative Then - Begin - If FGIntCompareAbs(MFGInt, zero) <> Eq Then - Begin - FGIntSub(FGInt2, MFGInt, temp1); - FGIntDestroy(MFGInt); - FGIntCopy(temp1, MFGInt); - FGIntDestroy(temp1); - End; - End; - FGIntDestroy(one); - FGIntDestroy(zero); - - FGInt1.Sign := s1; - FGInt2.Sign := s2; -End; - - -// Square a FGInt modulo Modb, FGInt^2 mod Modb = FGIntSM - -Procedure FGIntSquareMod(Var FGInt, Modb, FGIntSM : TFGInt); -Var - temp : TFGInt; -Begin - FGIntSquare(FGInt, temp); - FGIntMod(temp, Modb, FGIntSM); - FGIntDestroy(temp); -End; - - -// Add 2 FGInts modulo base, (FGInt1 + FGInt2) mod base = FGIntres - -Procedure FGIntAddMod(Var FGInt1, FGInt2, base, FGIntres : TFGInt); -Var - temp : TFGInt; -Begin - FGIntadd(FGInt1, FGInt2, temp); - FGIntMod(temp, base, FGIntres); - FGIntDestroy(temp); -End; - - -// Multiply 2 FGInts modulo base, (FGInt1 * FGInt2) mod base = FGIntres - -Procedure FGIntMulMod(Var FGInt1, FGInt2, base, FGIntres : TFGInt); -Var - temp : TFGInt; -Begin - FGIntMul(FGInt1, FGInt2, temp); - FGIntMod(temp, base, FGIntres); - FGIntDestroy(temp); -End; - - -// Exponentiate 2 FGInts modulo base, (FGInt1 ^ FGInt2) mod modb = res - -Procedure FGIntModExp(Var FGInt, exp, modb, res : TFGInt); -Var - temp2, temp3 : TFGInt; - i : LongWord; - S : String; -Begin - If (Modb.Number[1] Mod 2) = 1 Then - Begin - FGIntMontgomeryModExp(FGInt, exp, modb, res); - exit; - End; - FGIntToBase2String(exp, S); - Base10StringToFGInt('1', res); - FGIntcopy(FGInt, temp2); - - For i := length(S) Downto 1 Do - Begin - If S[i] = '1' Then - Begin - FGIntmulMod(res, temp2, modb, temp3); - FGIntCopy(temp3, res); - End; - FGIntSquareMod(temp2, Modb, temp3); - FGIntCopy(temp3, temp2); - End; - FGIntDestroy(temp2); -End; - - -// Procedures for Montgomery Exponentiation - -Procedure FGIntModBis(Const FGInt : TFGInt; Var FGIntOut : TFGInt; b, head : LongWord); -Var - i : LongWord; -Begin - If b <= FGInt.Number[0] Then - Begin - SetLength(FGIntOut.Number, (b + 1)); - For i := 0 To b Do - FGIntOut.Number[i] := FGInt.Number[i]; - FGIntOut.Number[b] := FGIntOut.Number[b] And head; - i := b; - While (FGIntOut.Number[i] = 0) And (i > 1) Do - i := i - 1; - If i < b Then SetLength(FGIntOut.Number, i + 1); - FGIntOut.Number[0] := i; - FGIntOut.Sign := positive; - End - Else - FGIntCopy(FGInt, FGIntOut); -End; - - -Procedure FGIntMulModBis(Const FGInt1, FGInt2 : TFGInt; Var Prod : TFGInt; b, head : LongWord); -Var - i, j, size, size1, size2, t, rest : LongWord; - Trest : int64; -Begin - size1 := FGInt1.Number[0]; - size2 := FGInt2.Number[0]; - size := min(b, size1 + size2); - SetLength(Prod.Number, (size + 1)); - For i := 1 To size Do - Prod.Number[i] := 0; - - For i := 1 To size2 Do - Begin - rest := 0; - t := min(size1, b - i + 1); - For j := 1 To t Do - Begin - Trest := FGInt1.Number[j]; - Trest := Trest * FGInt2.Number[i]; - Trest := Trest + Prod.Number[j + i - 1]; - Trest := Trest + rest; - Prod.Number[j + i - 1] := Trest And 2147483647; - rest := Trest Shr 31; - End; - If (i + size1) <= b Then Prod.Number[i + size1] := rest; - End; - - Prod.Number[0] := size; - If size = b Then Prod.Number[b] := Prod.Number[b] And head; - While (Prod.Number[size] = 0) And (size > 1) Do - size := size - 1; - If size < Prod.Number[0] Then - Begin - SetLength(Prod.Number, size + 1); - Prod.Number[0] := size; - End; - If FGInt1.Sign = FGInt2.Sign Then - Prod.Sign := Positive - Else - prod.Sign := negative; -End; - - -Procedure FGIntMontgomeryMod(Const GInt, base, baseInv : TFGInt; Var MGInt : TFGInt; b : Longword; head : LongWord); -Var - m, temp, temp1 : TFGInt; - r : LongWord; -Begin - FGIntModBis(GInt, temp, b, head); - FGIntMulModBis(temp, baseInv, m, b, head); - FGIntMul(m, base, temp1); - FGIntDestroy(temp); - FGIntAdd(temp1, GInt, temp); - FGIntDestroy(temp1); - MGInt.Number := copy(temp.Number, b - 1, temp.Number[0] - b + 2); - MGInt.Sign := positive; - MGInt.Number[0] := temp.Number[0] - b + 1; - FGIntDestroy(temp); - If (head Shr 30) = 0 Then FGIntDivByIntBis(MGInt, head + 1, r) - Else FGIntShiftRightBy31(MGInt); - If FGIntCompareAbs(MGInt, base) <> St Then FGIntSubBis(MGInt, base); - FGIntDestroy(temp); - FGIntDestroy(m); -End; - - -Procedure FGIntMontgomeryModExp(Var FGInt, exp, modb, res : TFGInt); -Var - temp2, temp3, baseInv, r, zero : TFGInt; - i, j, t, b, head : LongWord; - S : String; -Begin - Base2StringToFGInt('0', zero); - FGIntMod(FGInt, modb, res); - If FGIntCompareAbs(res, zero)=Eq then - Begin - FGIntDestroy(zero); - Exit; - End else FGIntDestroy(res); - FGIntDestroy(zero); - - FGIntToBase2String(exp, S); - t := modb.Number[0]; - b := t; - - If (modb.Number[t] Shr 30) = 1 Then t := t + 1; - SetLength(r.Number, (t + 1)); - r.Number[0] := t; - r.Sign := positive; - For i := 1 To t Do - r.Number[i] := 0; - If t = modb.Number[0] Then - Begin - head := 2147483647; - For j := 29 Downto 0 Do - Begin - head := head Shr 1; - If (modb.Number[t] Shr j) = 1 Then - Begin - r.Number[t] := 1 Shl (j + 1); - break; - End; - End; - End - Else - Begin - r.Number[t] := 1; - head := 2147483647; - End; - - FGIntModInv(modb, r, temp2); - If temp2.Sign = negative Then - FGIntCopy(temp2, BaseInv) - Else - Begin - FGIntCopy(r, BaseInv); - FGIntSubBis(BaseInv, temp2); - End; -// FGIntBezoutBachet(r, modb, temp2, BaseInv); - FGIntAbs(BaseInv); - FGIntDestroy(temp2); - FGIntMod(r, modb, res); - FGIntMulMod(FGInt, res, modb, temp2); - FGIntDestroy(r); - - For i := length(S) Downto 1 Do - Begin - If S[i] = '1' Then - Begin - FGIntmul(res, temp2, temp3); - FGIntDestroy(res); - FGIntMontgomeryMod(temp3, modb, baseinv, res, b, head); - FGIntDestroy(temp3); - End; - FGIntSquare(temp2, temp3); - FGIntDestroy(temp2); - FGIntMontgomeryMod(temp3, modb, baseinv, temp2, b, head); - FGIntDestroy(temp3); - End; - FGIntDestroy(temp2); - FGIntMontgomeryMod(res, modb, baseinv, temp3, b, head); - FGIntCopy(temp3, res); - FGIntDestroy(temp3); - FGIntDestroy(baseinv); -End; - - -// Compute the Greatest Common Divisor of 2 FGInts - -Procedure FGIntGCD(Const FGInt1, FGInt2 : TFGInt; Var GCD : TFGInt); -Var - k : TCompare; - zero, temp1, temp2, temp3 : TFGInt; -Begin - k := FGIntCompareAbs(FGInt1, FGInt2); - If (k = Eq) Then FGIntCopy(FGInt1, GCD) Else - If (k = St) Then FGIntGCD(FGInt2, FGInt1, GCD) Else - Begin - Base10StringToFGInt('0', zero); - FGIntCopy(FGInt1, temp1); - FGIntCopy(FGInt2, temp2); - While (temp2.Number[0] <> 1) Or (temp2.Number[1] <> 0) Do - Begin - FGIntMod(temp1, temp2, temp3); - FGIntCopy(temp2, temp1); - FGIntCopy(temp3, temp2); - FGIntDestroy(temp3); - End; - FGIntCopy(temp1, GCD); - FGIntDestroy(temp2); - FGIntDestroy(zero); - End; -End; - - -// Compute the Least Common Multiple of 2 FGInts - -Procedure FGIntLCM(Const FGInt1, FGInt2 : TFGInt; Var LCM : TFGInt); -Var - temp1, temp2 : TFGInt; -Begin - FGIntGCD(FGInt1, FGInt2, temp1); - FGIntmul(FGInt1, FGInt2, temp2); - FGIntdiv(temp2, temp1, LCM); - FGIntDestroy(temp1); - FGIntDestroy(temp2); -End; - - -// Trialdivision of a FGInt upto 9999 and stopping when a divisor is found, returning ok=false - -Procedure FGIntTrialDiv9999(Const FGInt : TFGInt; Var ok : boolean); -Var - j : LongWord; - i : integer; -Begin - If ((FGInt.Number[1] Mod 2) = 0) Then ok := false - Else - Begin - i := 0; - ok := true; - While ok And (i < 1228) Do - Begin - i := i + 1; - FGIntmodbyint(FGInt, primes[i], j); - If j = 0 Then ok := false; - End; - End; -End; - - -// A prng - -Procedure FGIntRandom1(Var Seed, RandomFGInt : TFGInt); -Var - temp, base : TFGInt; -Begin - Base10StringToFGInt('281474976710656', base); - Base10StringToFGInt('44485709377909', temp); - FGIntMulMod(seed, temp, base, RandomFGInt); - FGIntDestroy(temp); - FGIntDestroy(base); -End; - - -// Perform a Rabin Miller Primality Test nrtest times on FGIntp, returns ok=true when FGIntp passes the test - -Procedure FGIntRabinMiller(Var FGIntp : TFGInt; nrtest : Longword; Var ok : boolean); -Var - j, b, i : LongWord; - m, z, temp1, temp2, temp3, zero, one, two, pmin1 : TFGInt; - ok1, ok2 : boolean; -Begin - randomize; - j := 0; - Base10StringToFGInt('0', zero); - Base10StringToFGInt('1', one); - Base10StringToFGInt('2', two); - FGIntsub(FGIntp, one, temp1); - FGIntsub(FGIntp, one, pmin1); - - b := 0; - While (temp1.Number[1] Mod 2) = 0 Do - Begin - b := b + 1; - FGIntShiftRight(temp1); - End; - m := temp1; - - i := 0; - ok := true; - Randomize; - While (i < nrtest) And ok Do - Begin - i := i + 1; - Base10StringToFGInt(inttostr(Primes[Random(1227) + 1]), temp2); - FGIntMontGomeryModExp(temp2, m, FGIntp, z); - FGIntDestroy(temp2); - ok1 := (FGIntCompareAbs(z, one) = Eq); - ok2 := (FGIntCompareAbs(z, pmin1) = Eq); - If Not (ok1 Or ok2) Then - Begin - - While (ok And (j < b)) Do - Begin - If (j > 0) And ok1 Then ok := false - Else - Begin - j := j + 1; - If (j < b) And (Not ok2) Then - Begin - FGIntSquaremod(z, FGIntp, temp3); - FGIntCopy(temp3, z); - ok1 := (FGIntCompareAbs(z, one) = Eq); - ok2 := (FGIntCompareAbs(z, pmin1) = Eq); - If ok2 Then j := b; - End - Else If (Not ok2) And (j >= b) Then ok := false; - End; - End; - - End - End; - - FGIntDestroy(zero); - FGIntDestroy(one); - FGIntDestroy(two); - FGIntDestroy(m); - FGIntDestroy(z); - FGIntDestroy(pmin1); -End; - - -// Compute the coefficients from the Bezout Bachet theorem, FGInt1 * a + FGInt2 * b = GCD(FGInt1, FGInt2) - -Procedure FGIntBezoutBachet(Var FGInt1, FGInt2, a, b : TFGInt); -Var - zero, r1, r2, r3, ta, gcd, temp, temp1, temp2 : TFGInt; -Begin - If FGIntCompareAbs(FGInt1, FGInt2) <> St Then - Begin - FGIntcopy(FGInt1, r1); - FGIntcopy(FGInt2, r2); - Base10StringToFGInt('0', zero); - Base10StringToFGInt('1', a); - Base10StringToFGInt('0', ta); - - Repeat - FGIntdivmod(r1, r2, temp, r3); - FGIntDestroy(r1); - r1 := r2; - r2 := r3; - - FGIntmul(ta, temp, temp1); - FGIntsub(a, temp1, temp2); - FGIntCopy(ta, a); - FGIntCopy(temp2, ta); - FGIntDestroy(temp1); - - FGIntDestroy(temp); - Until FGIntCompareAbs(r3, zero) = Eq; - - FGIntGCD(FGInt1, FGInt2, gcd); - FGIntmul(a, FGInt1, temp1); - FGIntsub(gcd, temp1, temp2); - FGIntDestroy(temp1); - FGIntdiv(temp2, FGInt2, b); - FGIntDestroy(temp2); - - FGIntDestroy(ta); - FGIntDestroy(r1); - FGIntDestroy(r2); - FGIntDestroy(gcd); - End - Else FGIntBezoutBachet(FGInt2, FGInt1, b, a); -End; - - -// Find the (multiplicative) Modular inverse of a FGInt in a finite ring -// of additive order base - -Procedure FGIntModInv(Const FGInt1, base : TFGInt; Var Inverse : TFGInt); -Var - zero, one, r1, r2, r3, tb, gcd, temp, temp1, temp2 : TFGInt; -Begin - Base10StringToFGInt('1', one); - FGIntGCD(FGInt1, base, gcd); - If FGIntCompareAbs(one, gcd) = Eq Then - Begin - FGIntcopy(base, r1); - FGIntcopy(FGInt1, r2); - Base10StringToFGInt('0', zero); - Base10StringToFGInt('0', inverse); - Base10StringToFGInt('1', tb); - - Repeat - FGIntDestroy(r3); - FGIntdivmod(r1, r2, temp, r3); - FGIntCopy(r2, r1); - FGIntCopy(r3, r2); - - FGIntmul(tb, temp, temp1); - FGIntsub(inverse, temp1, temp2); - FGIntDestroy(inverse); - FGIntDestroy(temp1); - FGIntCopy(tb, inverse); - FGIntCopy(temp2, tb); - - FGIntDestroy(temp); - Until FGIntCompareAbs(r3, zero) = Eq; - - If inverse.Sign = negative Then - Begin - FGIntadd(base, inverse, temp); - FGIntCopy(temp, inverse); - End; - - FGIntDestroy(tb); - FGIntDestroy(r1); - FGIntDestroy(r2); - End; - FGIntDestroy(gcd); - FGIntDestroy(one); -End; - - -// Perform a (combined) primality test on FGIntp consisting of a trialdivision upto 8192, -// if the FGInt passes perform nrRMtests Rabin Miller primality tests, returns ok when a -// FGInt is probably prime - -Procedure FGIntPrimetest(Var FGIntp : TFGInt; nrRMtests : integer; Var ok : boolean); -Begin - FGIntTrialdiv9999(FGIntp, ok); - If ok Then FGIntRabinMiller(FGIntp, nrRMtests, ok); -End; - - -// Computes the Legendre symbol for a any number and -// p a prime, returns 0 if p divides a, 1 if a is a -// quadratic residu mod p, -1 if a is a quadratic -// nonresidu mod p - -Procedure FGIntLegendreSymbol(Var a, p : TFGInt; Var L : integer); -Var - temp1, temp2, temp3, temp4, temp5, zero, one : TFGInt; - i : LongWord; - ok1, ok2 : boolean; -Begin - Base10StringToFGInt('0', zero); - Base10StringToFGInt('1', one); - FGIntMod(a, p, temp1); - If FGIntCompareAbs(zero, temp1) = Eq Then - Begin - FGIntDestroy(temp1); - L := 0; - End - Else - Begin - FGIntDestroy(temp1); - FGIntCopy(p, temp1); - FGIntCopy(a, temp2); - L := 1; - While FGIntCompareAbs(temp2, one) <> Eq Do - Begin - If (temp2.Number[1] Mod 2) = 0 Then - Begin - FGIntSquare(temp1, temp3); - FGIntSub(temp3, one, temp4); - FGIntDestroy(temp3); - FGIntDivByInt(temp4, temp3, 8, i); - If (temp3.Number[1] Mod 2) = 0 Then ok1 := false Else ok1 := true; - FGIntDestroy(temp3); - FGIntDestroy(temp4); - If ok1 = true Then L := L * (-1); - FGIntDivByIntBis(temp2, 2, i); - End - Else - Begin - FGIntSub(temp1, one, temp3); - FGIntSub(temp2, one, temp4); - FGIntMul(temp3, temp4, temp5); - FGIntDestroy(temp3); - FGIntDestroy(temp4); - FGIntDivByInt(temp5, temp3, 4, i); - If (temp3.Number[1] Mod 2) = 0 Then ok2 := false Else ok2 := true; - FGIntDestroy(temp5); - FGIntDestroy(temp3); - If ok2 = true Then L := L * (-1); - FGIntMod(temp1, temp2, temp3); - FGIntCopy(temp2, temp1); - FGIntCopy(temp3, temp2); - End; - End; - FGIntDestroy(temp1); - FGIntDestroy(temp2); - End; - FGIntDestroy(zero); - FGIntDestroy(one); -End; - - -// Compute a square root modulo a prime number -// SquareRoot^2 mod Prime = Square - -Procedure FGIntSquareRootModP(Square, Prime : TFGInt; Var SquareRoot : TFGInt); -Var - one, n, b, s, r, temp, temp1, temp2, temp3 : TFGInt; - a, i, j : longint; - L : Integer; -Begin - Base2StringToFGInt('1', one); - Base2StringToFGInt('10', n); - a := 0; - FGIntLegendreSymbol(n, Prime, L); - While L <> -1 Do - Begin - FGIntAddBis(n, one); - FGIntLegendreSymbol(n, Prime, L); - End; - FGIntCopy(Prime, s); - s.Number[1] := s.Number[1] - 1; - While (s.Number[1] Mod 2) = 0 Do - Begin - FGIntShiftRight(s); - a := a + 1; - End; - FGIntMontgomeryModExp(n, s, Prime, b); - FGIntAdd(s, one, temp); - FGIntShiftRight(temp); - FGIntMontgomeryModExp(Square, temp, Prime, r); - FGIntDestroy(temp); - FGIntModInv(Square, Prime, temp1); - - For i := 0 To (a - 2) Do - Begin - FGIntSquareMod(r, Prime, temp2); - FGIntMulMod(temp1, temp2, Prime, temp); - FGIntDestroy(temp2); - For j := 1 To (a - i - 2) Do - Begin - FGIntSquareMod(temp, Prime, temp2); - FGIntDestroy(temp); - FGIntCopy(temp2, temp); - FGIntDestroy(temp2); - End; - If FGIntCompareAbs(temp, one) <> Eq Then - Begin - FGIntMulMod(r, b, Prime, temp3); - FGIntDestroy(r); - FGIntCopy(temp3, r); - FGIntDestroy(temp3); - End; - FGIntDestroy(temp); - FGIntDestroy(temp2); - If i = (a - 2) Then break; - FGIntSquareMod(b, Prime, temp3); - FGIntDestroy(b); - FGIntCopy(temp3, b); - FGIntDestroy(temp3); - End; - - FGIntCopy(r, SquareRoot); - FGIntDestroy(r); - FGIntDestroy(s); - FGIntDestroy(b); - FGIntDestroy(temp1); - FGIntDestroy(one); - FGIntDestroy(n); -End; - - -End. |