# # # Nimrod's Runtime Library # (c) Copyright 2008 Andreas Rumpf # # See the file "copying.txt", included in this # distribution, for details about the copyright. # ## This module implements big integers for Nimrod. ## This module is an adaptation of the FGInt module for Pascal by Walied ## Othman: http://triade.studentenweb.org # 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. # type TBigInt* {.final.} = object ## type that represent an arbitrary long ## signed integer s: int # sign: -1 or 1 n: seq[int] # the number part proc len(x: TBigInt): int {.inline.} = return x.n.len proc CompareAbs(a, b: TBigInt): int = result = a.len - b.len if result == 0: var i = b.len-1 while (i > 0) and a.n[i] == b.n[i]: dec(i) result = a.n[i] - b.n[i] const bitMask = high(int) bitshift = sizeof(int)*8 - 1 proc cutZeros(a: var TBigInt) = var L = a.len while a.len > 0 and a[L-1] == 0: dec(L) setLen(a.n, L) proc addAux(a, b: TBigInt, bSign: int): TBigInt if a.len < b.len: result = addAux(b, a, bSign) elif a.s == bSign: result.s = a.s result.n = [] setlen(result.n, a.len+1) var rest = 0 for i in 0..b.len-1: var trest = a.n[i] trest = trest +% b.n[i] +% rest result.n[i] = trest and bitMask rest = trest shr bitshift for i in b.len .. a.len-1: var trest = a.n[i] +% rest result.n[i] = trest and bitMask rest = trest shr bitshift result.n[a.len] = rest cutZeros(result) elif compareAbs(a, b) > 0: result = addAux(b, a, bSign) else: setlen(result.n, a.len+1) result.s = a.s var rest = 0 for i in 0..b.len-1: var Trest = low(int) TRest = Trest +% a.n[i] -% b.n[i] -% rest result.n[i] = Trest and bitmask if Trest >% bitMask: rest = 0 else: rest = 1 for i in b.len .. a.len-1: var Trest = low(int) TRest = Trest +% a.n[i] -% rest result.n[i] = Trest and bitmask if (Trest >% bitmask): rest = 0 else: rest = 1 cutZeros(result) proc `+` *(a, b: TBigInt): TBigInt = ## the `+` operator for bigints result = addAux(a, b, +1) proc `-` *(a, b: TBigInt): TBigInt = ## the `-` operator for bigints result = addAux(a, b, -1) proc mulInPlace(a: var TBigInt, b: int) = var size, rest: int32 Trest: int64 size = FGInt.Number[0] setlen(FGInt.Number, size + 2) rest = 0 for i in countup(1, size): Trest = FGInt.Number[i] TRest = Trest * by TRest = Trest + rest FGInt.Number[i] = Trest And 2147483647 rest = Trest Shr 31 if rest != 0: size = size + 1 FGInt.Number[size] = rest else: setlen(FGInt.Number, size + 1) FGInt.Number[0] = size import SysUtils, Math type TCompare* = enum Lt, St, Eq, Er TSign = enum negative, positive TBigInt* {.final.} = object Sign: TSign Number: seq[int32] proc zeronetochar8*(g: var char, x: String) proc zeronetochar6*(g: var int, x: String) proc initialize8*(trans: var openarray[String]) proc initialize6*(trans: var openarray[String]) proc initialize6PGP*(trans: var openarray[String]) proc ConvertBase256to64*(str256: String, str64: var String) proc ConvertBase64to256*(str64: String, str256: var String) proc ConvertBase256to2*(str256: String, str2: var String) proc ConvertBase64to2*(str64: String, str2: var String) proc ConvertBase2to256*(str2: String, str256: var String) proc ConvertBase2to64*(str2: String, str64: var String) proc ConvertBase256StringToHexString*(Str256: String, HexStr: var String) proc ConvertHexStringToBase256String*(HexStr: String, Str256: var String) proc PGPConvertBase256to64*(str256, str64: var String) proc PGPConvertBase64to256*(str64: String, str256: var String) proc PGPConvertBase64to2*(str64: String, str2: var String) proc FGIntToBase2String*(FGInt: TBigInt, S: var String) proc Base2StringToFGInt*(S: String, FGInt: var TBigInt) proc FGIntToBase256String*(FGInt: TBigInt, str256: var String) proc Base256StringToFGInt*(str256: String, FGInt: var TBigInt) proc PGPMPIToFGInt*(PGPMPI: String, FGInt: var TBigInt) proc FGIntToPGPMPI*(FGInt: TBigInt, PGPMPI: var String) proc Base10StringToFGInt*(Base10: String, FGInt: var TBigInt) proc FGIntToBase10String*(FGInt: TBigInt, Base10: var String) proc FGIntDestroy*(FGInt: var TBigInt) proc FGIntCompareAbs*(FGInt1, FGInt2: TBigInt): TCompare proc FGIntAdd*(FGInt1, FGInt2: TBigInt, Sum: var TBigInt) proc FGIntChangeSign*(FGInt: var TBigInt) proc FGIntSub*(FGInt1, FGInt2, dif: var TBigInt) proc FGIntMulByInt*(FGInt: TBigInt, res: var TBigInt, by: int32) proc FGIntMulByIntbis*(FGInt: var TBigInt, by: int32) proc FGIntDivByInt*(FGInt: TBigInt, res: var TBigInt, by: int32, modres: var int32) proc FGIntDivByIntBis*(FGInt: var TBigInt, by: int32, modres: var int32) proc FGIntModByInt*(FGInt: TBigInt, by: int32, modres: var int32) proc FGIntAbs*(FGInt: var TBigInt) proc FGIntCopy*(FGInt1: TBigInt, FGInt2: var TBigInt) proc FGIntShiftLeft*(FGInt: var TBigInt) proc FGIntShiftRight*(FGInt: var TBigInt) proc FGIntShiftRightBy31*(FGInt: var TBigInt) proc FGIntAddBis*(FGInt1: var TBigInt, FGInt2: TBigInt) proc FGIntSubBis*(FGInt1: var TBigInt, FGInt2: TBigInt) proc FGIntMul*(FGInt1, FGInt2: TBigInt, Prod: var TBigInt) proc FGIntSquare*(FGInt: TBigInt, Square: var TBigInt) proc FGIntExp*(FGInt, exp: TBigInt, res: var TBigInt) proc FGIntFac*(FGInt: TBigInt, res: var TBigInt) proc FGIntShiftLeftBy31*(FGInt: var TBigInt) proc FGIntDivMod*(FGInt1, FGInt2, QFGInt, MFGInt: var TBigInt) proc FGIntDiv*(FGInt1, FGInt2, QFGInt: var TBigInt) proc FGIntMod*(FGInt1, FGInt2, MFGInt: var TBigInt) proc FGIntSquareMod*(FGInt, Modb, FGIntSM: var TBigInt) proc FGIntAddMod*(FGInt1, FGInt2, base, FGIntres: var TBigInt) proc FGIntMulMod*(FGInt1, FGInt2, base, FGIntres: var TBigInt) proc FGIntModExp*(FGInt, exp, modb, res: var TBigInt) proc FGIntModBis*(FGInt: TBigInt, FGIntOut: var TBigInt, b, head: int32) proc FGIntMulModBis*(FGInt1, FGInt2: TBigInt, Prod: var TBigInt, b, head: int32) proc FGIntMontgomeryMod*(GInt, base, baseInv: TBigInt, MGInt: var TBigInt, b: int32, head: int32) proc FGIntMontgomeryModExp*(FGInt, exp, modb, res: var TBigInt) proc FGIntGCD*(FGInt1, FGInt2: TBigInt, GCD: var TBigInt) proc FGIntLCM*(FGInt1, FGInt2: TBigInt, LCM: var TBigInt) proc FGIntTrialDiv9999*(FGInt: TBigInt, ok: var bool) proc FGIntRandom1*(Seed, RandomFGInt: var TBigInt) proc FGIntRabinMiller*(FGIntp: var TBigInt, nrtest: int32, ok: var bool) proc FGIntBezoutBachet*(FGInt1, FGInt2, a, b: var TBigInt) proc FGIntModInv*(FGInt1, base: TBigInt, Inverse: var TBigInt) proc FGIntPrimetest*(FGIntp: var TBigInt, nrRMtests: int, ok: var bool) proc FGIntLegendreSymbol*(a, p: var TBigInt, L: var int) proc FGIntSquareRootModP*(Square, Prime: TBigInt, SquareRoot: var TBigInt) # implementation var primes: array[1..1228, int] = [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, 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, 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', '+', '/'] proc zeronetochar8(g: var char, x: String) = var b: int8 b = 0 for i in countup(1, 8): if copy(x, i, 1) == '1': b = b Or (1 Shl (8 - I)) g = chr(b) proc zeronetochar6(g: var int, x: String) = G = 0 for I in countup(1, len(X)): if I > 6: break if X[I] != '0': G = G Or (1 Shl (6 - I)) Inc(G) proc initialize8(trans: var openarray[String]) = var x: String g: char for c1 in countup(0, 1): for c2 in countup(0, 1): for c3 in countup(0, 1): for c4 in countup(0, 1): for c5 in countup(0, 1): for c6 in countup(0, 1): for c7 in countup(0, 1): for c8 in countup(0, 1): 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 proc initialize6(trans: var openarray[String]) = var x: String g: int for c1 in countup(0, 1): for c2 in countup(0, 1): for c3 in countup(0, 1): for c4 in countup(0, 1): for c5 in countup(0, 1): for c6 in countup(0, 1): 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 proc initialize6PGP(trans: var openarray[String]) = var x: String g: int for c1 in countup(0, 1): for c2 in countup(0, 1): for c3 in countup(0, 1): for c4 in countup(0, 1): for c5 in countup(0, 1): for c6 in countup(0, 1): 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 proc ConvertBase256to64(str256: String, str64: var String) = var temp: String trans: array[0..255, String] len6: int32 g: int initialize8(trans) temp = "" for i in countup(1, len(str256)): temp = temp + trans[ord(str256[i])] while (len(temp) Mod 6) != 0: temp = temp & '0' len6 = len(temp) Div 6 str64 = "" for i in countup(1, len6): zeronetochar6(g, copy(temp, 1, 6)) str64 = str64 + chr64[g] delete(temp, 1, 6) proc ConvertBase64to256(str64: String, str256: var String) = var temp: String trans: array[0..255, String] len8: int32 g: char initialize6(trans) temp = "" for i in countup(1, len(str64)): temp = temp + trans[ord(str64[i])] str256 = "" len8 = len(temp) Div 8 for i in countup(1, len8): zeronetochar8(g, copy(temp, 1, 8)) str256 = str256 + g delete(temp, 1, 8) proc ConvertBase256to2(str256: String, str2: var String) = var trans: array[0..255, String] str2 = "" initialize8(trans) for i in countup(1, len(str256)): str2 = str2 + trans[ord(str256[i])] proc ConvertBase64to2(str64: String, str2: var String) = var trans: array[0..255, String] str2 = "" initialize6(trans) for i in countup(1, len(str64)): str2 = str2 + trans[ord(str64[i])] proc ConvertBase2to256(str2: String, str256: var String) = var len8: int32 g: char str256 = "" while (len(str2) Mod 8) != 0: str2 = '0' & str2 len8 = len(str2) Div 8 for i in countup(1, len8): zeronetochar8(g, copy(str2, 1, 8)) str256 = str256 + g delete(str2, 1, 8) proc ConvertBase2to64(str2: String, str64: var String) = var len6: int32 g: int str64 = "" while (len(str2) Mod 6) != 0: str2 = '0' & str2 len6 = len(str2) Div 6 for i in countup(1, len6): zeronetochar6(g, copy(str2, 1, 6)) str64 = str64 + chr64[g] delete(str2, 1, 6) proc ConvertBase256StringToHexString(Str256: String, HexStr: var String) = var b: int8 HexStr = "" for i in countup(1, len(str256)): b = ord(str256[i]) if (b Shr 4) < 10: HexStr = HexStr + chr(48 + (b Shr 4)) else: HexStr = HexStr + chr(55 + (b Shr 4)) if (b And 15) < 10: HexStr = HexStr + chr(48 + (b And 15)) else: HexStr = HexStr + chr(55 + (b And 15)) proc ConvertHexStringToBase256String(HexStr: String, Str256: var String) = var b, h1, h2: int8 temp: string Str256 = "" if (len(Hexstr) mod 2) == 1: temp = '0' & HexStr else: temp = HexStr for i in countup(1, (len(temp) Div 2)): h2 = ord(temp[2 * i]) h1 = ord(temp[2 * i - 1]) if h1 < 58: b = ((h1 - 48) Shl 4) else: b = ((h1 - 55) Shl 4) if h2 < 58: b = (b Or (h2 - 48)) else: b = (b Or ((h2 - 55) and 15)) Str256 = Str256 + chr(b) proc PGPConvertBase256to64(str256, str64: var String) = var temp, x, a: String len6: int32 g: int trans: array[0..255, String] initialize8(trans) temp = "" for i in countup(1, len(str256)): temp = temp + trans[ord(str256[i])] if (len(temp) Mod 6) == 0: a = "" elif (len(temp) Mod 6) == 4: temp = temp & "00" a = '=' else: temp = temp & "0000" a = "==" str64 = "" len6 = len(temp) Div 6 for i in countup(1, len6): x = copy(temp, 1, 6) zeronetochar6(g, x) str64 = str64 + PGPchr64[g] delete(temp, 1, 6) str64 = str64 + a proc PGPConvertBase64to256(str64: String, str256: var String) = var temp, x: String j, len8: int32 g: char trans: array[0..255, String] initialize6PGP(trans) temp = "" str256 = "" if str64[len(str64) - 1] == '=': j = 2 elif str64[len(str64)] == '=': j = 1 else: j = 0 for i in countup(1, (len(str64) - j)): temp = temp + trans[ord(str64[i])] if j != 0: delete(temp, len(temp) - 2 * j + 1, 2 * j) len8 = len(temp) Div 8 for i in countup(1, len8): x = copy(temp, 1, 8) zeronetochar8(g, x) str256 = str256 + g delete(temp, 1, 8) proc PGPConvertBase64to2(str64: String, str2: var String) = var j: int32 trans: array[0..255, String] str2 = "" initialize6(trans) if str64[len(str64) - 1] == '=': j = 2 elif str64[len(str64)] == '=': j = 1 else: j = 0 for i in countup(1, (len(str64) - j)): str2 = str2 + trans[ord(str64[i])] delete(str2, len(str2) - 2 * j + 1, 2 * j) proc FGIntToBase2String(FGInt: TBigInt, S: var String) = S = "" for i in countup(1, FGInt.Number[0]): for j in countup(0, 30): if (1 And (FGInt.Number[i] Shr j)) == 1: S = '1' & S else: S = '0' & S while (len(S) > 1) And (S[1] == '0'): delete(S, 1, 1) if S == "": S = '0' proc Base2StringToFGInt(S: String, FGInt: var TBigInt) = var i, j, size: int32 while (S[1] == '0') And (len(S) > 1): delete(S, 1, 1) size = len(S) Div 31 if (len(S) Mod 31) != 0: size = size + 1 setlen(FGInt.Number, (size + 1)) FGInt.Number[0] = size j = 1 FGInt.Number[j] = 0 i = 0 while len(S) > 0: if S[len(S)] == '1': FGInt.Number[j] = FGInt.Number[j] Or (1 Shl i) i = i + 1 if i == 31: i = 0 j = j + 1 if j <= size: FGInt.Number[j] = 0 delete(S, len(S), 1) FGInt.Sign = positive proc FGIntToBase256String(FGInt: TBigInt, str256: var String) = var temp1: String len8: int32 g: char FGIntToBase2String(FGInt, temp1) while (len(temp1) Mod 8) != 0: temp1 = '0' & temp1 len8 = len(temp1) Div 8 str256 = "" for i in countup(1, len8): zeronetochar8(g, copy(temp1, 1, 8)) str256 = str256 + g delete(temp1, 1, 8) proc Base256StringToFGInt(str256: String, FGInt: var TBigInt) = var temp1: String trans: array[0..255, String] temp1 = "" initialize8(trans) for i in countup(1, len(str256)): temp1 = temp1 + trans[ord(str256[i])] while (temp1[1] == '0') And (temp1 != '0'): delete(temp1, 1, 1) Base2StringToFGInt(temp1, FGInt) proc PGPMPIToFGInt(PGPMPI: String, FGInt: var TBigInt) = var temp: String temp = PGPMPI delete(temp, 1, 2) Base256StringToFGInt(temp, FGInt) proc FGIntToPGPMPI(FGInt: TBigInt, PGPMPI: var String) = var length: int16 c: char b: int8 FGIntToBase256String(FGInt, PGPMPI) length = len(PGPMPI) * 8 c = PGPMPI[1] for i in countdown(7, 0): if (ord(c) Shr i) == 0: length = length - 1 else: break b = length Mod 256 PGPMPI = chr(b) + PGPMPI b = length Div 256 PGPMPI = chr(b) + PGPMPI proc GIntDivByIntBis1(GInt: var TBigInt, by: int32, modres: var int16) = var size, rest, temp: int32 size = GInt.Number[0] temp = 0 for i in countdown(size, 1): temp = temp * 10000 rest = temp + GInt.Number[i] GInt.Number[i] = rest Div by temp = rest Mod by modres = temp while (GInt.Number[size] == 0) And (size > 1): size = size - 1 if size != GInt.Number[0]: setlen(GInt.Number, size + 1) GInt.Number[0] = size proc Base10StringToFGInt(Base10: String, FGInt: var TBigInt) = var size: int32 j: int16 S, x: String sign: TSign while (Not (Base10[1] In {'-', '0'..'9'})) And (len(Base10) > 1): delete(Base10, 1, 1) if copy(Base10, 1, 1) == '-': Sign = negative delete(Base10, 1, 1) else: Sign = positive while (len(Base10) > 1) And (copy(Base10, 1, 1) == '0'): delete(Base10, 1, 1) size = len(Base10) Div 4 if (len(Base10) Mod 4) != 0: size = size + 1 setlen(FGInt.Number, size + 1) FGInt.Number[0] = size for i in countup(1, (size - 1)): x = copy(Base10, len(Base10) - 3, 4) FGInt.Number[i] = StrToInt(x) delete(Base10, len(Base10) - 3, 4) FGInt.Number[size] = StrToInt(Base10) S = "" while (FGInt.Number[0] != 1) Or (FGInt.Number[1] != 0): GIntDivByIntBis1(FGInt, 2, j) S = inttostr(j) + S if S == "": S = '0' FGIntDestroy(FGInt) Base2StringToFGInt(S, FGInt) FGInt.Sign = sign proc FGIntToBase10String(FGInt: TBigInt, Base10: var String) = var S: String j: int32 temp: TBigInt FGIntCopy(FGInt, temp) Base10 = "" while (temp.Number[0] > 1) Or (temp.Number[1] > 0): FGIntDivByIntBis(temp, 10000, j) S = IntToStr(j) while len(S) < 4: S = '0' & S Base10 = S + Base10 Base10 = '0' & Base10 while (len(Base10) > 1) And (Base10[1] == '0'): delete(Base10, 1, 1) if FGInt.Sign == negative: Base10 = '-' & Base10 proc FGIntDestroy(FGInt: var TBigInt) = FGInt.Number = nil proc FGIntCompareAbs(FGInt1, FGInt2: TBigInt): TCompare = var size1, size2, i: int32 FGIntCompareAbs = Er size1 = FGInt1.Number[0] size2 = FGInt2.Number[0] if size1 > size2: FGIntCompareAbs = Lt elif size1 < size2: FGIntCompareAbs = St else: i = size2 while (FGInt1.Number[i] == FGInt2.Number[i]) And (i > 1): i = i - 1 if FGInt1.Number[i] == FGInt2.Number[i]: FGIntCompareAbs = Eq elif FGInt1.Number[i] < FGInt2.Number[i]: FGIntCompareAbs = St elif FGInt1.Number[i] > FGInt2.Number[i]: FGIntCompareAbs = Lt proc FGIntAdd(FGInt1, FGInt2: TBigInt, Sum: var TBigInt) = var size1, size2, size, rest, Trest: int32 size1 = FGInt1.Number[0] size2 = FGInt2.Number[0] if size1 < size2: FGIntAdd(FGInt2, FGInt1, Sum) else: if FGInt1.Sign == FGInt2.Sign: Sum.Sign = FGInt1.Sign setlen(Sum.Number, (size1 + 2)) rest = 0 for i in countup(1, size2): Trest = FGInt1.Number[i] Trest = Trest + FGInt2.Number[i] Trest = Trest + rest Sum.Number[i] = Trest And 2147483647 rest = Trest Shr 31 for i in countup((size2 + 1), size1): Trest = FGInt1.Number[i] + rest Sum.Number[i] = Trest And 2147483647 rest = Trest Shr 31 size = size1 + 1 Sum.Number[0] = size Sum.Number[size] = rest while (Sum.Number[size] == 0) And (size > 1): size = size - 1 if Sum.Number[0] != size: setlen(Sum.Number, size + 1) Sum.Number[0] = size else: if FGIntCompareAbs(FGInt2, FGInt1) == Lt: FGIntAdd(FGInt2, FGInt1, Sum) else: setlen(Sum.Number, (size1 + 1)) rest = 0 for i in countup(1, size2): Trest = 0x80000000 # 2147483648; TRest = Trest + FGInt1.Number[i] TRest = Trest - FGInt2.Number[i] TRest = Trest - rest Sum.Number[i] = Trest And 2147483647 if (Trest > 2147483647): rest = 0 else: rest = 1 for i in countup((size2 + 1), size1): Trest = 0x80000000 TRest = Trest + FGInt1.Number[i] TRest = Trest - rest Sum.Number[i] = Trest And 2147483647 if (Trest > 2147483647): rest = 0 else: rest = 1 size = size1 while (Sum.Number[size] == 0) And (size > 1): size = size - 1 if size != size1: setlen(Sum.Number, size + 1) Sum.Number[0] = size Sum.Sign = FGInt1.Sign proc FGIntChangeSign(FGInt: var TBigInt) = if FGInt.Sign == negative: FGInt.Sign = positive else: FGInt.Sign = negative proc FGIntSub(FGInt1, FGInt2, dif: var TBigInt) = FGIntChangeSign(FGInt2) FGIntAdd(FGInt1, FGInt2, dif) FGIntChangeSign(FGInt2) proc FGIntMulByInt(FGInt: TBigInt, res: var TBigInt, by: int32) = var size, rest: int32 Trest: int64 size = FGInt.Number[0] setlen(res.Number, (size + 2)) rest = 0 for i in countup(1, size): Trest = FGInt.Number[i] TRest = Trest * by TRest = Trest + rest res.Number[i] = Trest And 2147483647 rest = Trest Shr 31 if rest != 0: size = size + 1 Res.Number[size] = rest else: setlen(Res.Number, size + 1) Res.Number[0] = size Res.Sign = FGInt.Sign proc FGIntMulByIntbis(FGInt: var TBigInt, by: int32) = var size, rest: int32 Trest: int64 size = FGInt.Number[0] setlen(FGInt.Number, size + 2) rest = 0 for i in countup(1, size): Trest = FGInt.Number[i] TRest = Trest * by TRest = Trest + rest FGInt.Number[i] = Trest And 2147483647 rest = Trest Shr 31 if rest != 0: size = size + 1 FGInt.Number[size] = rest else: setlen(FGInt.Number, size + 1) FGInt.Number[0] = size proc FGIntDivByInt(FGInt: TBigInt, res: var TBigInt, by: int32, modres: var int32) = var size: int32 rest: int64 size = FGInt.Number[0] setlen(res.Number, (size + 1)) modres = 0 for i in countdown(size, 1): rest = modres rest = rest Shl 31 rest = rest Or FGInt.Number[i] res.Number[i] = rest Div by modres = rest Mod by while (res.Number[size] == 0) And (size > 1): size = size - 1 if size != FGInt.Number[0]: setlen(res.Number, size + 1) res.Number[0] = size Res.Sign = FGInt.Sign if FGInt.sign == negative: modres = by - modres proc FGIntDivByIntBis(FGInt: var TBigInt, by: int32, modres: var int32) = var size: int32 temp, rest: int64 size = FGInt.Number[0] temp = 0 for i in countdown(size, 1): temp = temp Shl 31 rest = temp Or FGInt.Number[i] FGInt.Number[i] = rest Div by temp = rest Mod by modres = temp while (FGInt.Number[size] == 0) And (size > 1): size = size - 1 if size != FGInt.Number[0]: setlen(FGInt.Number, size + 1) FGInt.Number[0] = size proc FGIntModByInt(FGInt: TBigInt, by: int32, modres: var int32) = var size: int32 temp, rest: int64 size = FGInt.Number[0] temp = 0 for i in countdown(size, 1): temp = temp Shl 31 rest = temp Or FGInt.Number[i] temp = rest Mod by modres = temp if FGInt.sign == negative: modres = by - modres proc FGIntAbs(FGInt: var TBigInt) = FGInt.Sign = positive proc FGIntCopy(FGInt1: TBigInt, FGInt2: var TBigInt) = FGInt2.Sign = FGInt1.Sign FGInt2.Number = nil FGInt2.Number = Copy(FGInt1.Number, 0, FGInt1.Number[0] + 1) proc FGIntShiftLeft(FGInt: var TBigInt) = var l, m, size: int32 size = FGInt.Number[0] l = 0 for i in countup(1, Size): m = FGInt.Number[i] Shr 30 FGInt.Number[i] = ((FGInt.Number[i] Shl 1) Or l) And 2147483647 l = m if l != 0: setlen(FGInt.Number, size + 2) FGInt.Number[size + 1] = l FGInt.Number[0] = size + 1 proc FGIntShiftRight(FGInt: var TBigInt) = var l, m, size: int32 size = FGInt.Number[0] l = 0 for i in countdown(size, 1): m = FGInt.Number[i] And 1 FGInt.Number[i] = (FGInt.Number[i] Shr 1) Or l l = m Shl 30 if (FGInt.Number[size] == 0) And (size > 1): setlen(FGInt.Number, size) FGInt.Number[0] = size - 1 proc FGIntShiftRightBy31(FGInt: var TBigInt) = var size: int32 size = FGInt.Number[0] if size > 1: for i in countup(1, size - 1): FGInt.Number[i] = FGInt.Number[i + 1] setlen(FGInt.Number, Size) FGInt.Number[0] = size - 1 else: FGInt.Number[1] = 0 proc FGIntAddBis(FGInt1: var TBigInt, FGInt2: TBigInt) = var size1, size2, Trest, rest: int32 size1 = FGInt1.Number[0] size2 = FGInt2.Number[0] rest = 0 for i in countup(1, size2): Trest = FGInt1.Number[i] + FGInt2.Number[i] + rest rest = Trest Shr 31 FGInt1.Number[i] = Trest And 2147483647 for i in countup(size2 + 1, size1): Trest = FGInt1.Number[i] + rest rest = Trest Shr 31 FGInt1.Number[i] = Trest And 2147483647 if rest != 0: setlen(FGInt1.Number, size1 + 2) FGInt1.Number[0] = size1 + 1 FGInt1.Number[size1 + 1] = rest proc FGIntSubBis(FGInt1: var TBigInt, FGInt2: TBigInt) = var size1, size2, rest, Trest: int32 size1 = FGInt1.Number[0] size2 = FGInt2.Number[0] rest = 0 for i in countup(1, size2): Trest = (0x80000000 Or FGInt1.Number[i]) - FGInt2.Number[i] - rest if (Trest > 2147483647): rest = 0 else: rest = 1 FGInt1.Number[i] = Trest And 2147483647 for i in countup(size2 + 1, size1): Trest = (0x80000000 Or FGInt1.Number[i]) - rest if (Trest > 2147483647): rest = 0 else: rest = 1 FGInt1.Number[i] = Trest And 2147483647 i = size1 while (FGInt1.Number[i] == 0) And (i > 1): i = i - 1 if i != size1: setlen(FGInt1.Number, i + 1) FGInt1.Number[0] = i proc FGIntMul(FGInt1, FGInt2: TBigInt, Prod: var TBigInt) = var size, size1, size2, rest: int32 Trest: int64 size1 = FGInt1.Number[0] size2 = FGInt2.Number[0] size = size1 + size2 setlen(Prod.Number, (size + 1)) for i in countup(1, size): Prod.Number[i] = 0 for i in countup(1, size2): rest = 0 for j in countup(1, size1): 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 Prod.Number[i + size1] = rest Prod.Number[0] = size while (Prod.Number[size] == 0) And (size > 1): size = size - 1 if size != Prod.Number[0]: setlen(Prod.Number, size + 1) Prod.Number[0] = size if FGInt1.Sign == FGInt2.Sign: Prod.Sign = Positive else: prod.Sign = negative proc FGIntSquare(FGInt: TBigInt, Square: var TBigInt) = var size, size1, rest: int32 Trest: int64 size1 = FGInt.Number[0] size = 2 * size1 setlen(Square.Number, (size + 1)) Square.Number[0] = size for i in countup(1, size): Square.Number[i] = 0 for i in countup(1, size1): 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 in countup(i + 1, size1): 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 Square.Number[i + size1] = rest Square.Sign = positive while (Square.Number[size] == 0) And (size > 1): size = size - 1 if size != (2 * size1): setlen(Square.Number, size + 1) Square.Number[0] = size proc FGIntExp(FGInt, exp: TBigInt, res: var TBigInt) = var temp2, temp3: TBigInt S: String FGIntToBase2String(exp, S) if S[len(S)] == '0': Base10StringToFGInt('1', res) else: FGIntCopy(FGInt, res) FGIntCopy(FGInt, temp2) if len(S) > 1: for i in countdown((len(S) - 1), 1): FGIntSquare(temp2, temp3) FGIntCopy(temp3, temp2) if S[i] == '1': FGIntMul(res, temp2, temp3) FGIntCopy(temp3, res) proc FGIntFac(FGInt: TBigInt, res: var TBigInt) = var one, temp, temp1: TBigInt FGIntCopy(FGInt, temp) Base10StringToFGInt('1', res) Base10StringToFGInt('1', one) while Not (FGIntCompareAbs(temp, one) == Eq): FGIntMul(temp, res, temp1) FGIntCopy(temp1, res) FGIntSubBis(temp, one) FGIntDestroy(one) FGIntDestroy(temp) proc FGIntShiftLeftBy31(FGInt: var TBigInt) = var f1, f2: int32 size: int32 size = FGInt.Number[0] setlen(FGInt.Number, size + 2) f1 = 0 for i in countup(1, (size + 1)): f2 = FGInt.Number[i] FGInt.Number[i] = f1 f1 = f2 FGInt.Number[0] = size + 1 proc FGIntDivMod(FGInt1, FGInt2, QFGInt, MFGInt: var TBigInt) = var one, zero, temp1, temp2: TBigInt s1, s2: TSign j, s: int32 i: int64 s1 = FGInt1.Sign s2 = FGInt2.Sign FGIntAbs(FGInt1) FGIntAbs(FGInt2) FGIntCopy(FGInt1, MFGInt) FGIntCopy(FGInt2, temp1) if FGIntCompareAbs(FGInt1, FGInt2) != St: s = FGInt1.Number[0] - FGInt2.Number[0] setlen(QFGInt.Number, (s + 2)) QFGInt.Number[0] = s + 1 for t in countup(1, s): FGIntShiftLeftBy31(temp1) QFGInt.Number[t] = 0 j = s + 1 QFGInt.Number[j] = 0 while FGIntCompareAbs(MFGInt, FGInt2) != St: while FGIntCompareAbs(MFGInt, temp1) != St: if MFGInt.Number[0] > temp1.Number[0]: 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) else: i = MFGInt.Number[MFGInt.Number[0]] Div (temp1.Number[temp1.Number[0]] + 1) if (i != 0): FGIntCopy(temp1, temp2) FGIntMulByIntBis(temp2, i) FGIntSubBis(MFGInt, temp2) QFGInt.Number[j] = QFGInt.Number[j] + i if FGIntCompareAbs(MFGInt, temp2) != St: QFGInt.Number[j] = QFGInt.Number[j] + i FGIntSubBis(MFGInt, temp2) FGIntDestroy(temp2) else: QFGInt.Number[j] = QFGInt.Number[j] + 1 FGIntSubBis(MFGInt, temp1) if MFGInt.Number[0] <= temp1.Number[0]: if FGIntCompareAbs(temp1, FGInt2) != Eq: FGIntShiftRightBy31(temp1) j = j - 1 else: Base10StringToFGInt('0', QFGInt) s = QFGInt.Number[0] while (s > 1) And (QFGInt.Number[s] == 0): s = s - 1 if s < QFGInt.Number[0]: setlen(QFGInt.Number, s + 1) QFGInt.Number[0] = s QFGInt.Sign = positive FGIntDestroy(temp1) Base10StringToFGInt('0', zero) Base10StringToFGInt('1', one) if s1 == negative: if FGIntCompareAbs(MFGInt, zero) != Eq: FGIntadd(QFGInt, one, temp1) FGIntDestroy(QFGInt) FGIntCopy(temp1, QFGInt) FGIntDestroy(temp1) FGIntsub(FGInt2, MFGInt, temp1) FGIntDestroy(MFGInt) FGIntCopy(temp1, MFGInt) FGIntDestroy(temp1) if s2 == positive: QFGInt.Sign = negative else: QFGInt.Sign = s2 FGIntDestroy(one) FGIntDestroy(zero) FGInt1.Sign = s1 FGInt2.Sign = s2 proc FGIntDiv(FGInt1, FGInt2, QFGInt: var TBigInt) = var one, zero, temp1, temp2, MFGInt: TBigInt s1, s2: TSign j, s: int32 i: int64 s1 = FGInt1.Sign s2 = FGInt2.Sign FGIntAbs(FGInt1) FGIntAbs(FGInt2) FGIntCopy(FGInt1, MFGInt) FGIntCopy(FGInt2, temp1) if FGIntCompareAbs(FGInt1, FGInt2) != St: s = FGInt1.Number[0] - FGInt2.Number[0] setlen(QFGInt.Number, (s + 2)) QFGInt.Number[0] = s + 1 for t in countup(1, s): FGIntShiftLeftBy31(temp1) QFGInt.Number[t] = 0 j = s + 1 QFGInt.Number[j] = 0 while FGIntCompareAbs(MFGInt, FGInt2) != St: while FGIntCompareAbs(MFGInt, temp1) != St: if MFGInt.Number[0] > temp1.Number[0]: 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) else: i = MFGInt.Number[MFGInt.Number[0]] Div (temp1.Number[temp1.Number[0]] + 1) if (i != 0): FGIntCopy(temp1, temp2) FGIntMulByIntBis(temp2, i) FGIntSubBis(MFGInt, temp2) QFGInt.Number[j] = QFGInt.Number[j] + i if FGIntCompareAbs(MFGInt, temp2) != St: QFGInt.Number[j] = QFGInt.Number[j] + i FGIntSubBis(MFGInt, temp2) FGIntDestroy(temp2) else: QFGInt.Number[j] = QFGInt.Number[j] + 1 FGIntSubBis(MFGInt, temp1) if MFGInt.Number[0] <= temp1.Number[0]: if FGIntCompareAbs(temp1, FGInt2) != Eq: FGIntShiftRightBy31(temp1) j = j - 1 else: Base10StringToFGInt('0', QFGInt) s = QFGInt.Number[0] while (s > 1) And (QFGInt.Number[s] == 0): s = s - 1 if s < QFGInt.Number[0]: setlen(QFGInt.Number, s + 1) QFGInt.Number[0] = s QFGInt.Sign = positive FGIntDestroy(temp1) Base10StringToFGInt('0', zero) Base10StringToFGInt('1', one) if s1 == negative: if FGIntCompareAbs(MFGInt, zero) != Eq: FGIntadd(QFGInt, one, temp1) FGIntDestroy(QFGInt) FGIntCopy(temp1, QFGInt) FGIntDestroy(temp1) FGIntsub(FGInt2, MFGInt, temp1) FGIntDestroy(MFGInt) FGIntCopy(temp1, MFGInt) FGIntDestroy(temp1) if s2 == positive: QFGInt.Sign = negative else: QFGInt.Sign = s2 FGIntDestroy(one) FGIntDestroy(zero) FGIntDestroy(MFGInt) FGInt1.Sign = s1 FGInt2.Sign = s2 proc FGIntMod(FGInt1, FGInt2, MFGInt: var TBigInt) = var one, zero, temp1, temp2: TBigInt s1, s2: TSign s: int32 i: int64 s1 = FGInt1.Sign s2 = FGInt2.Sign FGIntAbs(FGInt1) FGIntAbs(FGInt2) FGIntCopy(FGInt1, MFGInt) FGIntCopy(FGInt2, temp1) if FGIntCompareAbs(FGInt1, FGInt2) != St: s = FGInt1.Number[0] - FGInt2.Number[0] for t in countup(1, s): FGIntShiftLeftBy31(temp1) while FGIntCompareAbs(MFGInt, FGInt2) != St: while FGIntCompareAbs(MFGInt, temp1) != St: if MFGInt.Number[0] > temp1.Number[0]: 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) else: i = MFGInt.Number[MFGInt.Number[0]] Div (temp1.Number[temp1.Number[0]] + 1) if (i != 0): FGIntCopy(temp1, temp2) FGIntMulByIntBis(temp2, i) FGIntSubBis(MFGInt, temp2) if FGIntCompareAbs(MFGInt, temp2) != St: FGIntSubBis(MFGInt, temp2) FGIntDestroy(temp2) else: FGIntSubBis(MFGInt, temp1) # If FGIntCompareAbs(MFGInt, temp1) <> St Then FGIntSubBis(MFGInt,temp1); if MFGInt.Number[0] <= temp1.Number[0]: if FGIntCompareAbs(temp1, FGInt2) != Eq: FGIntShiftRightBy31(temp1) FGIntDestroy(temp1) Base10StringToFGInt('0', zero) Base10StringToFGInt('1', one) if s1 == negative: if FGIntCompareAbs(MFGInt, zero) != Eq: FGIntSub(FGInt2, MFGInt, temp1) FGIntDestroy(MFGInt) FGIntCopy(temp1, MFGInt) FGIntDestroy(temp1) FGIntDestroy(one) FGIntDestroy(zero) FGInt1.Sign = s1 FGInt2.Sign = s2 proc FGIntSquareMod(FGInt, Modb, FGIntSM: var TBigInt) = var temp: TBigInt FGIntSquare(FGInt, temp) FGIntMod(temp, Modb, FGIntSM) FGIntDestroy(temp) proc FGIntAddMod(FGInt1, FGInt2, base, FGIntres: var TBigInt) = var temp: TBigInt FGIntadd(FGInt1, FGInt2, temp) FGIntMod(temp, base, FGIntres) FGIntDestroy(temp) proc FGIntMulMod(FGInt1, FGInt2, base, FGIntres: var TBigInt) = var temp: TBigInt FGIntMul(FGInt1, FGInt2, temp) FGIntMod(temp, base, FGIntres) FGIntDestroy(temp) proc FGIntModExp(FGInt, exp, modb, res: var TBigInt) = var temp2, temp3: TBigInt S: String if (Modb.Number[1] Mod 2) == 1: FGIntMontgomeryModExp(FGInt, exp, modb, res) return FGIntToBase2String(exp, S) Base10StringToFGInt('1', res) FGIntcopy(FGInt, temp2) for i in countdown(len(S), 1): if S[i] == '1': FGIntmulMod(res, temp2, modb, temp3) FGIntCopy(temp3, res) FGIntSquareMod(temp2, Modb, temp3) FGIntCopy(temp3, temp2) FGIntDestroy(temp2) proc FGIntModBis(FGInt: TBigInt, FGIntOut: var TBigInt, b, head: int32) = if b <= FGInt.Number[0]: setlen(FGIntOut.Number, (b + 1)) for i in countup(0, b): FGIntOut.Number[i] = FGInt.Number[i] FGIntOut.Number[b] = FGIntOut.Number[b] And head i = b while (FGIntOut.Number[i] == 0) And (i > 1): i = i - 1 if i < b: setlen(FGIntOut.Number, i + 1) FGIntOut.Number[0] = i FGIntOut.Sign = positive else: FGIntCopy(FGInt, FGIntOut) proc FGIntMulModBis(FGInt1, FGInt2: TBigInt, Prod: var TBigInt, b, head: int32) = var size, size1, size2, t, rest: int32 Trest: int64 size1 = FGInt1.Number[0] size2 = FGInt2.Number[0] size = min(b, size1 + size2) setlen(Prod.Number, (size + 1)) for i in countup(1, size): Prod.Number[i] = 0 for i in countup(1, size2): rest = 0 t = min(size1, b - i + 1) for j in countup(1, t): 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 if (i + size1) <= b: Prod.Number[i + size1] = rest Prod.Number[0] = size if size == b: Prod.Number[b] = Prod.Number[b] And head while (Prod.Number[size] == 0) And (size > 1): size = size - 1 if size < Prod.Number[0]: setlen(Prod.Number, size + 1) Prod.Number[0] = size if FGInt1.Sign == FGInt2.Sign: Prod.Sign = Positive else: prod.Sign = negative proc FGIntMontgomeryMod(GInt, base, baseInv: TBigInt, MGInt: var TBigInt, b: int32, head: int32) = var m, temp, temp1: TBigInt r: int32 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: FGIntDivByIntBis(MGInt, head + 1, r) else: FGIntShiftRightBy31(MGInt) if FGIntCompareAbs(MGInt, base) != St: FGIntSubBis(MGInt, base) FGIntDestroy(temp) FGIntDestroy(m) proc FGIntMontgomeryModExp(FGInt, exp, modb, res: var TBigInt) = var temp2, temp3, baseInv, r, zero: TBigInt t, b, head: int32 S: String Base2StringToFGInt('0', zero) FGIntMod(FGInt, modb, res) if FGIntCompareAbs(res, zero) == Eq: FGIntDestroy(zero) return else: FGIntDestroy(res) FGIntDestroy(zero) FGIntToBase2String(exp, S) t = modb.Number[0] b = t if (modb.Number[t] Shr 30) == 1: t = t + 1 setlen(r.Number, (t + 1)) r.Number[0] = t r.Sign = positive for i in countup(1, t): r.Number[i] = 0 if t == modb.Number[0]: head = 2147483647 for j in countdown(29, 0): head = head Shr 1 if (modb.Number[t] Shr j) == 1: r.Number[t] = 1 Shl (j + 1) break else: r.Number[t] = 1 head = 2147483647 FGIntModInv(modb, r, temp2) if temp2.Sign == negative: FGIntCopy(temp2, BaseInv) else: FGIntCopy(r, BaseInv) FGIntSubBis(BaseInv, temp2) FGIntAbs(BaseInv) FGIntDestroy(temp2) FGIntMod(r, modb, res) FGIntMulMod(FGInt, res, modb, temp2) FGIntDestroy(r) for i in countdown(len(S), 1): if S[i] == '1': FGIntmul(res, temp2, temp3) FGIntDestroy(res) FGIntMontgomeryMod(temp3, modb, baseinv, res, b, head) FGIntDestroy(temp3) FGIntSquare(temp2, temp3) FGIntDestroy(temp2) FGIntMontgomeryMod(temp3, modb, baseinv, temp2, b, head) FGIntDestroy(temp3) FGIntDestroy(temp2) FGIntMontgomeryMod(res, modb, baseinv, temp3, b, head) FGIntCopy(temp3, res) FGIntDestroy(temp3) FGIntDestroy(baseinv) proc FGIntGCD(FGInt1, FGInt2: TBigInt, GCD: var TBigInt) = var k: TCompare zero, temp1, temp2, temp3: TBigInt k = FGIntCompareAbs(FGInt1, FGInt2) if (k == Eq): FGIntCopy(FGInt1, GCD) elif (k == St): FGIntGCD(FGInt2, FGInt1, GCD) else: Base10StringToFGInt('0', zero) FGIntCopy(FGInt1, temp1) FGIntCopy(FGInt2, temp2) while (temp2.Number[0] != 1) Or (temp2.Number[1] != 0): FGIntMod(temp1, temp2, temp3) FGIntCopy(temp2, temp1) FGIntCopy(temp3, temp2) FGIntDestroy(temp3) FGIntCopy(temp1, GCD) FGIntDestroy(temp2) FGIntDestroy(zero) proc FGIntLCM(FGInt1, FGInt2: TBigInt, LCM: var TBigInt) = var temp1, temp2: TBigInt FGIntGCD(FGInt1, FGInt2, temp1) FGIntmul(FGInt1, FGInt2, temp2) FGIntdiv(temp2, temp1, LCM) FGIntDestroy(temp1) FGIntDestroy(temp2) proc FGIntTrialDiv9999(FGInt: TBigInt, ok: var bool) = var j: int32 i: int if ((FGInt.Number[1] Mod 2) == 0): ok = false else: i = 0 ok = true while ok And (i < 1228): i = i + 1 FGIntmodbyint(FGInt, primes[i], j) if j == 0: ok = false proc FGIntRandom1(Seed, RandomFGInt: var TBigInt) = var temp, base: TBigInt Base10StringToFGInt("281474976710656", base) Base10StringToFGInt("44485709377909", temp) FGIntMulMod(seed, temp, base, RandomFGInt) FGIntDestroy(temp) FGIntDestroy(base) proc FGIntRabinMiller(FGIntp: var TBigInt, nrtest: int32, ok: var bool) = var j, b, i: int32 m, z, temp1, temp2, temp3, zero, one, two, pmin1: TBigInt ok1, ok2: bool 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: b = b + 1 FGIntShiftRight(temp1) m = temp1 i = 0 ok = true Randomize while (i < nrtest) And ok: 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): while (ok And (j < b)): if (j > 0) And ok1: ok = false else: j = j + 1 if (j < b) And (Not ok2): FGIntSquaremod(z, FGIntp, temp3) FGIntCopy(temp3, z) ok1 = (FGIntCompareAbs(z, one) == Eq) ok2 = (FGIntCompareAbs(z, pmin1) == Eq) if ok2: j = b elif (Not ok2) And (j >= b): ok = false FGIntDestroy(zero) FGIntDestroy(one) FGIntDestroy(two) FGIntDestroy(m) FGIntDestroy(z) FGIntDestroy(pmin1) proc FGIntBezoutBachet(FGInt1, FGInt2, a, b: var TBigInt) = var zero, r1, r2, r3, ta, gcd, temp, temp1, temp2: TBigInt if FGIntCompareAbs(FGInt1, FGInt2) != St: FGIntcopy(FGInt1, r1) FGIntcopy(FGInt2, r2) Base10StringToFGInt('0', zero) Base10StringToFGInt('1', a) Base10StringToFGInt('0', ta) while true: 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) if FGIntCompareAbs(r3, zero) == Eq: break 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) else: FGIntBezoutBachet(FGInt2, FGInt1, b, a) proc FGIntModInv(FGInt1, base: TBigInt, Inverse: var TBigInt) = var zero, one, r1, r2, r3, tb, gcd, temp, temp1, temp2: TBigInt Base10StringToFGInt('1', one) FGIntGCD(FGInt1, base, gcd) if FGIntCompareAbs(one, gcd) == Eq: FGIntcopy(base, r1) FGIntcopy(FGInt1, r2) Base10StringToFGInt('0', zero) Base10StringToFGInt('0', inverse) Base10StringToFGInt('1', tb) while true: 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) if FGIntCompareAbs(r3, zero) == Eq: break if inverse.Sign == negative: FGIntadd(base, inverse, temp) FGIntCopy(temp, inverse) FGIntDestroy(tb) FGIntDestroy(r1) FGIntDestroy(r2) FGIntDestroy(gcd) FGIntDestroy(one) proc FGIntPrimetest(FGIntp: var TBigInt, nrRMtests: int, ok: var bool) = FGIntTrialdiv9999(FGIntp, ok) if ok: FGIntRabinMiller(FGIntp, nrRMtests, ok) proc FGIntLegendreSymbol(a, p: var TBigInt, L: var int) = var temp1, temp2, temp3, temp4, temp5, zero, one: TBigInt i: int32 ok1, ok2: bool Base10StringToFGInt('0', zero) Base10StringToFGInt('1', one) FGIntMod(a, p, temp1) if FGIntCompareAbs(zero, temp1) == Eq: FGIntDestroy(temp1) L = 0 else: FGIntDestroy(temp1) FGIntCopy(p, temp1) FGIntCopy(a, temp2) L = 1 while FGIntCompareAbs(temp2, one) != Eq: if (temp2.Number[1] Mod 2) == 0: FGIntSquare(temp1, temp3) FGIntSub(temp3, one, temp4) FGIntDestroy(temp3) FGIntDivByInt(temp4, temp3, 8, i) if (temp3.Number[1] Mod 2) == 0: ok1 = false else: ok1 = true FGIntDestroy(temp3) FGIntDestroy(temp4) if ok1 == true: L = L * (- 1) FGIntDivByIntBis(temp2, 2, i) else: 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: ok2 = false else: ok2 = true FGIntDestroy(temp5) FGIntDestroy(temp3) if ok2 == true: L = L * (- 1) FGIntMod(temp1, temp2, temp3) FGIntCopy(temp2, temp1) FGIntCopy(temp3, temp2) FGIntDestroy(temp1) FGIntDestroy(temp2) FGIntDestroy(zero) FGIntDestroy(one) proc FGIntSquareRootModP(Square, Prime: TBigInt, SquareRoot: var TBigInt) = var one, n, b, s, r, temp, temp1, temp2, temp3: TBigInt a: int32 L: int Base2StringToFGInt('1', one) Base2StringToFGInt("10", n) a = 0 FGIntLegendreSymbol(n, Prime, L) while L != - 1: FGIntAddBis(n, one) FGIntLegendreSymbol(n, Prime, L) FGIntCopy(Prime, s) s.Number[1] = s.Number[1] - 1 while (s.Number[1] Mod 2) == 0: FGIntShiftRight(s) a = a + 1 FGIntMontgomeryModExp(n, s, Prime, b) FGIntAdd(s, one, temp) FGIntShiftRight(temp) FGIntMontgomeryModExp(Square, temp, Prime, r) FGIntDestroy(temp) FGIntModInv(Square, Prime, temp1) for i in countup(0, (a - 2)): FGIntSquareMod(r, Prime, temp2) FGIntMulMod(temp1, temp2, Prime, temp) FGIntDestroy(temp2) for j in countup(1, (a - i - 2)): FGIntSquareMod(temp, Prime, temp2) FGIntDestroy(temp) FGIntCopy(temp2, temp) FGIntDestroy(temp2) if FGIntCompareAbs(temp, one) != Eq: FGIntMulMod(r, b, Prime, temp3) FGIntDestroy(r) FGIntCopy(temp3, r) FGIntDestroy(temp3) FGIntDestroy(temp) FGIntDestroy(temp2) if i == (a - 2): break FGIntSquareMod(b, Prime, temp3) FGIntDestroy(b) FGIntCopy(temp3, b) FGIntDestroy(temp3) FGIntCopy(r, SquareRoot) FGIntDestroy(r) FGIntDestroy(s) FGIntDestroy(b) FGIntDestroy(temp1) FGIntDestroy(one) FGIntDestroy(n)