📄 biginteger.cs
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//************************************************************************************
// BigInteger Class Version 1.03
//
// Copyright (c) 2002 Chew Keong TAN
// All rights reserved.
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the
// "Software"), to deal in the Software without restriction, including
// without limitation the rights to use, copy, modify, merge, publish,
// distribute, and/or sell copies of the Software, and to permit persons
// to whom the Software is furnished to do so, provided that the above
// copyright notice(s) and this permission notice appear in all copies of
// the Software and that both the above copyright notice(s) and this
// permission notice appear in supporting documentation.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
// OF THIRD PARTY RIGHTS. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
// HOLDERS INCLUDED IN THIS NOTICE BE LIABLE FOR ANY CLAIM, OR ANY SPECIAL
// INDIRECT OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING
// FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
// NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION
// WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
//
//
// Disclaimer
// ----------
// Although reasonable care has been taken to ensure the correctness of this
// implementation, this code should never be used in any application without
// proper verification and testing. I disclaim all liability and responsibility
// to any person or entity with respect to any loss or damage caused, or alleged
// to be caused, directly or indirectly, by the use of this BigInteger class.
//
// Comments, bugs and suggestions to
// (http://www.codeproject.com/csharp/biginteger.asp)
//
//
// Overloaded Operators +, -, *, /, %, >>, <<, ==, !=, >, <, >=, <=, &, |, ^, ++, --, ~
//
// Features
// --------
// 1) Arithmetic operations involving large signed integers (2's complement).
// 2) Primality test using Fermat little theorm, Rabin Miller's method,
// Solovay Strassen's method and Lucas strong pseudoprime.
// 3) Modulo exponential with Barrett's reduction.
// 4) Inverse modulo.
// 5) Pseudo prime generation.
// 6) Co-prime generation.
//
//
// Known Problem
// -------------
// This pseudoprime passes my implementation of
// primality test but failed in JDK's isProbablePrime test.
//
// byte[] pseudoPrime1 = { (byte)0x00,
// (byte)0x85, (byte)0x84, (byte)0x64, (byte)0xFD, (byte)0x70, (byte)0x6A,
// (byte)0x9F, (byte)0xF0, (byte)0x94, (byte)0x0C, (byte)0x3E, (byte)0x2C,
// (byte)0x74, (byte)0x34, (byte)0x05, (byte)0xC9, (byte)0x55, (byte)0xB3,
// (byte)0x85, (byte)0x32, (byte)0x98, (byte)0x71, (byte)0xF9, (byte)0x41,
// (byte)0x21, (byte)0x5F, (byte)0x02, (byte)0x9E, (byte)0xEA, (byte)0x56,
// (byte)0x8D, (byte)0x8C, (byte)0x44, (byte)0xCC, (byte)0xEE, (byte)0xEE,
// (byte)0x3D, (byte)0x2C, (byte)0x9D, (byte)0x2C, (byte)0x12, (byte)0x41,
// (byte)0x1E, (byte)0xF1, (byte)0xC5, (byte)0x32, (byte)0xC3, (byte)0xAA,
// (byte)0x31, (byte)0x4A, (byte)0x52, (byte)0xD8, (byte)0xE8, (byte)0xAF,
// (byte)0x42, (byte)0xF4, (byte)0x72, (byte)0xA1, (byte)0x2A, (byte)0x0D,
// (byte)0x97, (byte)0xB1, (byte)0x31, (byte)0xB3,
// };
//
//
// Change Log
// ----------
// 1) September 23, 2002 (Version 1.03)
// - Fixed operator- to give correct data length.
// - Added Lucas sequence generation.
// - Added Strong Lucas Primality test.
// - Added integer square root method.
// - Added setBit/unsetBit methods.
// - New isProbablePrime() method which do not require the
// confident parameter.
//
// 2) August 29, 2002 (Version 1.02)
// - Fixed bug in the exponentiation of negative numbers.
// - Faster modular exponentiation using Barrett reduction.
// - Added getBytes() method.
// - Fixed bug in ToHexString method.
// - Added overloading of ^ operator.
// - Faster computation of Jacobi symbol.
//
// 3) August 19, 2002 (Version 1.01)
// - Big integer is stored and manipulated as unsigned integers (4 bytes) instead of
// individual bytes this gives significant performance improvement.
// - Updated Fermat's Little Theorem test to use a^(p-1) mod p = 1
// - Added isProbablePrime method.
// - Updated documentation.
//
// 4) August 9, 2002 (Version 1.0)
// - Initial Release.
//
//
// References
// [1] D. E. Knuth, "Seminumerical Algorithms", The Art of Computer Programming Vol. 2,
// 3rd Edition, Addison-Wesley, 1998.
//
// [2] K. H. Rosen, "Elementary Number Theory and Its Applications", 3rd Ed,
// Addison-Wesley, 1993.
//
// [3] B. Schneier, "Applied Cryptography", 2nd Ed, John Wiley & Sons, 1996.
//
// [4] A. Menezes, P. van Oorschot, and S. Vanstone, "Handbook of Applied Cryptography",
// CRC Press, 1996, www.cacr.math.uwaterloo.ca/hac
//
// [5] A. Bosselaers, R. Govaerts, and J. Vandewalle, "Comparison of Three Modular
// Reduction Functions," Proc. CRYPTO'93, pp.175-186.
//
// [6] R. Baillie and S. S. Wagstaff Jr, "Lucas Pseudoprimes", Mathematics of Computation,
// Vol. 35, No. 152, Oct 1980, pp. 1391-1417.
//
// [7] H. C. Williams, "蒬ouard Lucas and Primality Testing", Canadian Mathematical
// Society Series of Monographs and Advance Texts, vol. 22, John Wiley & Sons, New York,
// NY, 1998.
//
// [8] P. Ribenboim, "The new book of prime number records", 3rd edition, Springer-Verlag,
// New York, NY, 1995.
//
// [9] M. Joye and J.-J. Quisquater, "Efficient computation of full Lucas sequences",
// Electronics Letters, 32(6), 1996, pp 537-538.
//
//************************************************************************************
using System;
using System.Runtime.InteropServices;
namespace DJD.Security
{
[System.Serializable(), Guid("61109339-CE4D-488f-A6BE-686D85CC2336"), ClassInterface(ClassInterfaceType.AutoDual)]
public class BigInteger
{
// maximum length of the BigInteger in uint (4 bytes)
// change this to suit the required level of precision.
private const int maxLength = 70;
// primes smaller than 2000 to test the generated prime number
public static readonly int[] primesBelow2000 = {
2, 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 };
private uint[] data = null; // stores bytes from the Big Integer
public int dataLength; // number of actual chars used
//***********************************************************************
// Constructor (Default value for BigInteger is 0
//***********************************************************************
public BigInteger()
{
data = new uint[maxLength];
dataLength = 1;
}
//***********************************************************************
// Constructor (Default value provided by long)
//***********************************************************************
public BigInteger(long value)
{
data = new uint[maxLength];
long tempVal = value;
// copy bytes from long to BigInteger without any assumption of
// the length of the long datatype
dataLength = 0;
while(value != 0 && dataLength < maxLength)
{
data[dataLength] = (uint)(value & 0xFFFFFFFF);
value >>= 32;
dataLength++;
}
if(tempVal > 0) // overflow check for +ve value
{
if(value != 0 || (data[maxLength-1] & 0x80000000) != 0)
throw(new ArithmeticException("Positive overflow in constructor."));
}
else if(tempVal < 0) // underflow check for -ve value
{
if(value != -1 || (data[dataLength-1] & 0x80000000) == 0)
throw(new ArithmeticException("Negative underflow in constructor."));
}
if(dataLength == 0)
dataLength = 1;
}
//***********************************************************************
// Constructor (Default value provided by ulong)
//***********************************************************************
public BigInteger(ulong value)
{
data = new uint[maxLength];
// copy bytes from ulong to BigInteger without any assumption of
// the length of the ulong datatype
dataLength = 0;
while(value != 0 && dataLength < maxLength)
{
data[dataLength] = (uint)(value & 0xFFFFFFFF);
value >>= 32;
dataLength++;
}
if(value != 0 || (data[maxLength-1] & 0x80000000) != 0)
throw(new ArithmeticException("Positive overflow in constructor."));
if(dataLength == 0)
dataLength = 1;
}
//***********************************************************************
// Constructor (Default value provided by BigInteger)
//***********************************************************************
public BigInteger(BigInteger bi)
{
data = new uint[maxLength];
dataLength = bi.dataLength;
for(int i = 0; i < dataLength; i++)
data[i] = bi.data[i];
}
//***********************************************************************
// Constructor (Default value provided by a string of digits of the
// specified base)
//
// Example (base 10)
// -----------------
// To initialize "a" with the default value of 1234 in base 10
// BigInteger a = new BigInteger("1234", 10)
//
// To initialize "a" with the default value of -1234
// BigInteger a = new BigInteger("-1234", 10)
//
// Example (base 16)
// -----------------
// To initialize "a" with the default value of 0x1D4F in base 16
// BigInteger a = new BigInteger("1D4F", 16)
//
// To initialize "a" with the default value of -0x1D4F
// BigInteger a = new BigInteger("-1D4F", 16)
//
// Note that string values are specified in the <sign><magnitude>
// format.
//
//***********************************************************************
public BigInteger(string value, int radix)
{
BigInteger multiplier = new BigInteger(1);
BigInteger result = new BigInteger();
value = (value.ToUpper()).Trim();
int limit = 0;
if(value[0] == '-')
limit = 1;
for(int i = value.Length - 1; i >= limit ; i--)
{
int posVal = (int)value[i];
if(posVal >= '0' && posVal <= '9')
posVal -= '0';
else if(posVal >= 'A' && posVal <= 'Z')
posVal = (posVal - 'A') + 10;
else
posVal = 9999999; // arbitrary large
if(posVal >= radix)
throw(new ArithmeticException("Invalid string in constructor."));
else
{
if(value[0] == '-')
posVal = -posVal;
result = result + (multiplier * posVal);
if((i - 1) >= limit)
multiplier = multiplier * radix;
}
}
if(value[0] == '-') // negative values
{
if((result.data[maxLength-1] & 0x80000000) == 0)
throw(new ArithmeticException("Negative underflow in constructor."));
}
else // positive values
{
if((result.data[maxLength-1] & 0x80000000) != 0)
throw(new ArithmeticException("Positive overflow in constructor."));
}
data = new uint[maxLength];
for(int i = 0; i < result.dataLength; i++)
data[i] = result.data[i];
dataLength = result.dataLength;
}
public BigInteger ToBigInteger(string value, int radix)
{
BigInteger multiplier = new BigInteger(1);
BigInteger result = new BigInteger();
value = (value.ToUpper()).Trim();
int limit = 0;
if(value[0] == '-')
limit = 1;
for(int i = value.Length - 1; i >= limit ; i--)
{
int posVal = (int)value[i];
if(posVal >= '0' && posVal <= '9')
posVal -= '0';
else if(posVal >= 'A' && posVal <= 'Z')
posVal = (posVal - 'A') + 10;
else
posVal = 9999999; // arbitrary large
if(posVal >= radix)
throw(new ArithmeticException("Invalid string in constructor."));
else
{
if(value[0] == '-')
posVal = -posVal;
result = result + (multiplier * posVal);
if((i - 1) >= limit)
multiplier = multiplier * radix;
}
}
if(value[0] == '-') // negative values
{
if((result.data[maxLength-1] & 0x80000000) == 0)
throw(new ArithmeticException("Negative underflow in constructor."));
}
else // positive values
{
if((result.data[maxLength-1] & 0x80000000) != 0)
throw(new ArithmeticException("Positive overflow in constructor."));
}
data = new uint[maxLength];
for(int i = 0; i < result.dataLength; i++)
data[i] = result.data[i];
dataLength = result.dataLength;
return this;
}
//***********************************************************************
// Constructor (Default value provided by an array of bytes)
//
// The lowest index of the input byte array (i.e [0]) should contain the
// most significant byte of the number, and the highest index should
// contain the least significant byte.
//
// E.g.
// To initialize "a" with the default value of 0x1D4F in base 16
// byte[] temp = { 0x1D, 0x4F };
// BigInteger a = new BigInteger(temp)
//
// Note that this method of initialization does not allow the
// sign to be specified.
//
//***********************************************************************
public BigInteger(byte[] inData)
{
dataLength = inData.Length >> 2;
int leftOver = inData.Length & 0x3;
if(leftOver != 0) // length not multiples of 4
dataLength++;
if(dataLength > maxLength)
throw(new ArithmeticException("Byte overflow in constructor."));
data = new uint[maxLength];
for(int i = inData.Length - 1, j = 0; i >= 3; i -= 4, j++)
{
data[j] = (uint)((inData[i-3] << 24) + (inData[i-2] << 16) +
(inData[i-1] << 8) + inData[i]);
}
if(leftOver == 1)
data[dataLength-1] = (uint)inData[0];
else if(leftOver == 2)
data[dataLength-1] = (uint)((inData[0] << 8) + inData[1]);
else if(leftOver == 3)
data[dataLength-1] = (uint)((inData[0] << 16) + (inData[1] << 8) + inData[2]);
while(dataLength > 1 && data[dataLength-1] == 0)
dataLength--;
//Console.WriteLine("Len = " + dataLength);
}
//***********************************************************************
// Constructor (Default value provided by an array of bytes of the
// specified length.)
//***********************************************************************
public BigInteger(byte[] inData, int inLen)
{
dataLength = inLen >> 2;
int leftOver = inLen & 0x3;
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