version 0.7.0

1 files changed, 2199 insertions, 0 deletions

diff --git a/lib/base/devel/FGInt.pas b/lib/base/devel/FGInt.pas
new file mode 100644
index 000000000..7cb5a8516
--- /dev/null
+++ b/lib/base/devel/FGInt.pas
@@ -0,0 +1,2199 @@
+{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.