c#rsa 非对称加密
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using System;using System.Collections.Generic;using System.Linq;using System.Text;namespace RSATest{ 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; } //*********************************************************************** // 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; if (leftOver != 0) // length not multiples of 4 dataLength++; if (dataLength > maxLength || inLen > inData.Length) throw (new ArithmeticException("Byte overflow in constructor.")); data = new uint[maxLength]; for (int i = inLen - 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]); if (dataLength == 0) dataLength = 1; while (dataLength > 1 && data[dataLength - 1] == 0) dataLength--; //Console.WriteLine("Len = " + dataLength); } //*********************************************************************** // Constructor (Default value provided by an array of unsigned integers) //********************************************************************* public BigInteger(uint[] inData) { dataLength = inData.Length; if (dataLength > maxLength) throw (new ArithmeticException("Byte overflow in constructor.")); data = new uint[maxLength]; for (int i = dataLength - 1, j = 0; i >= 0; i--, j++) data[j] = inData[i]; while (dataLength > 1 && data[dataLength - 1] == 0) dataLength--; //Console.WriteLine("Len = " + dataLength); } //*********************************************************************** // Overloading of the typecast operator. // For BigInteger bi = 10; //*********************************************************************** public static implicit operator BigInteger(long value) { return (new BigInteger(value)); } public static implicit operator BigInteger(ulong value) { return (new BigInteger(value)); } public static implicit operator BigInteger(int value) { return (new BigInteger((long)value)); } public static implicit operator BigInteger(uint value) { return (new BigInteger((ulong)value)); } //*********************************************************************** // Overloading of addition operator //*********************************************************************** public static BigInteger operator +(BigInteger bi1, BigInteger bi2) { BigInteger result = new BigInteger(); result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; long carry = 0; for (int i = 0; i < result.dataLength; i++) { long sum = (long)bi1.data[i] + (long)bi2.data[i] + carry; carry = sum >> 32; result.data[i] = (uint)(sum & 0xFFFFFFFF); } if (carry != 0 && result.dataLength < maxLength) { result.data[result.dataLength] = (uint)(carry); result.dataLength++; } while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; // overflow check int lastPos = maxLength - 1; if ((bi1.data[lastPos] & 0x80000000) == (bi2.data[lastPos] & 0x80000000) && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000)) { throw (new ArithmeticException()); } return result; } //*********************************************************************** // Overloading of the unary ++ operator //*********************************************************************** public static BigInteger operator ++(BigInteger bi1) { BigInteger result = new BigInteger(bi1); long val, carry = 1; int index = 0; while (carry != 0 && index < maxLength) { val = (long)(result.data[index]); val++; result.data[index] = (uint)(val & 0xFFFFFFFF); carry = val >> 32; index++; } if (index > result.dataLength) result.dataLength = index; else { while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; } // overflow check int lastPos = maxLength - 1; // overflow if initial value was +ve but ++ caused a sign // change to negative. if ((bi1.data[lastPos] & 0x80000000) == 0 && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000)) { throw (new ArithmeticException("Overflow in ++.")); } return result; } //*********************************************************************** // Overloading of subtraction operator //*********************************************************************** public static BigInteger operator -(BigInteger bi1, BigInteger bi2) { BigInteger result = new BigInteger(); result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; long carryIn = 0; for (int i = 0; i < result.dataLength; i++) { long diff; diff = (long)bi1.data[i] - (long)bi2.data[i] - carryIn; result.data[i] = (uint)(diff & 0xFFFFFFFF); if (diff < 0) carryIn = 1; else carryIn = 0; } // roll over to negative if (carryIn != 0) { for (int i = result.dataLength; i < maxLength; i++) result.data[i] = 0xFFFFFFFF; result.dataLength = maxLength; } // fixed in v1.03 to give correct datalength for a - (-b) while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; // overflow check int lastPos = maxLength - 1; if ((bi1.data[lastPos] & 0x80000000) != (bi2.data[lastPos] & 0x80000000) && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000)) { throw (new ArithmeticException()); } return result; } //*********************************************************************** // Overloading of the unary -- operator //*********************************************************************** public static BigInteger operator --(BigInteger bi1) { BigInteger result = new BigInteger(bi1); long val; bool carryIn = true; int index = 0; while (carryIn && index < maxLength) { val = (long)(result.data[index]); val--; result.data[index] = (uint)(val & 0xFFFFFFFF); if (val >= 0) carryIn = false; index++; } if (index > result.dataLength) result.dataLength = index; while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; // overflow check int lastPos = maxLength - 1; // overflow if initial value was -ve but -- caused a sign // change to positive. if ((bi1.data[lastPos] & 0x80000000) != 0 && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000)) { throw (new ArithmeticException("Underflow in --.")); } return result; } //*********************************************************************** // Overloading of multiplication operator //*********************************************************************** public static BigInteger operator *(BigInteger bi1, BigInteger bi2) { int lastPos = maxLength - 1; bool bi1Neg = false, bi2Neg = false; // take the absolute value of the inputs try { if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative { bi1Neg = true; bi1 = -bi1; } if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative { bi2Neg = true; bi2 = -bi2; } } catch (Exception) { } BigInteger result = new BigInteger(); // multiply the absolute values try { for (int i = 0; i < bi1.dataLength; i++) { if (bi1.data[i] == 0) continue; ulong mcarry = 0; for (int j = 0, k = i; j < bi2.dataLength; j++, k++) { // k = i + j ulong val = ((ulong)bi1.data[i] * (ulong)bi2.data[j]) + (ulong)result.data[k] + mcarry; result.data[k] = (uint)(val & 0xFFFFFFFF); mcarry = (val >> 32); } if (mcarry != 0) result.data[i + bi2.dataLength] = (uint)mcarry; } } catch (Exception) { throw (new ArithmeticException("Multiplication overflow.")); } result.dataLength = bi1.dataLength + bi2.dataLength; if (result.dataLength > maxLength) result.dataLength = maxLength; while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; // overflow check (result is -ve) if ((result.data[lastPos] & 0x80000000) != 0) { if (bi1Neg != bi2Neg && result.data[lastPos] == 0x80000000) // different sign { // handle the special case where multiplication produces // a max negative number in 2's complement. if (result.dataLength == 1) return result; else { bool isMaxNeg = true; for (int i = 0; i < result.dataLength - 1 && isMaxNeg; i++) { if (result.data[i] != 0) isMaxNeg = false; } if (isMaxNeg) return result; } } throw (new ArithmeticException("Multiplication overflow.")); } // if input has different signs, then result is -ve if (bi1Neg != bi2Neg) return -result; return result; } //*********************************************************************** // Overloading of unary << operators //*********************************************************************** public static BigInteger operator <<(BigInteger bi1, int shiftVal) { BigInteger result = new BigInteger(bi1); result.dataLength = shiftLeft(result.data, shiftVal); return result; } // least significant bits at lower part of buffer private static int shiftLeft(uint[] buffer, int shiftVal) { int shiftAmount = 32; int bufLen = buffer.Length; while (bufLen > 1 && buffer[bufLen - 1] == 0) bufLen--; for (int count = shiftVal; count > 0; ) { if (count < shiftAmount) shiftAmount = count; //Console.WriteLine("shiftAmount = {0}", shiftAmount); ulong carry = 0; for (int i = 0; i < bufLen; i++) { ulong val = ((ulong)buffer[i]) << shiftAmount; val |= carry; buffer[i] = (uint)(val & 0xFFFFFFFF); carry = val >> 32; } if (carry != 0) { if (bufLen + 1 <= buffer.Length) { buffer[bufLen] = (uint)carry; bufLen++; } } count -= shiftAmount; } return bufLen; } //*********************************************************************** // Overloading of unary >> operators //*********************************************************************** public static BigInteger operator >>(BigInteger bi1, int shiftVal) { BigInteger result = new BigInteger(bi1); result.dataLength = shiftRight(result.data, shiftVal); if ((bi1.data[maxLength - 1] & 0x80000000) != 0) // negative { for (int i = maxLength - 1; i >= result.dataLength; i--) result.data[i] = 0xFFFFFFFF; uint mask = 0x80000000; for (int i = 0; i < 32; i++) { if ((result.data[result.dataLength - 1] & mask) != 0) break; result.data[result.dataLength - 1] |= mask; mask >>= 1; } result.dataLength = maxLength; } return result; } private static int shiftRight(uint[] buffer, int shiftVal) { int shiftAmount = 32; int invShift = 0; int bufLen = buffer.Length; while (bufLen > 1 && buffer[bufLen - 1] == 0) bufLen--; //Console.WriteLine("bufLen = " + bufLen + " buffer.Length = " + buffer.Length); for (int count = shiftVal; count > 0; ) { if (count < shiftAmount) { shiftAmount = count; invShift = 32 - shiftAmount; } //Console.WriteLine("shiftAmount = {0}", shiftAmount); ulong carry = 0; for (int i = bufLen - 1; i >= 0; i--) { ulong val = ((ulong)buffer[i]) >> shiftAmount; val |= carry; carry = ((ulong)buffer[i]) << invShift; buffer[i] = (uint)(val); } count -= shiftAmount; } while (bufLen > 1 && buffer[bufLen - 1] == 0) bufLen--; return bufLen; } //*********************************************************************** // Overloading of the NOT operator (1's complement) //*********************************************************************** public static BigInteger operator ~(BigInteger bi1) { BigInteger result = new BigInteger(bi1); for (int i = 0; i < maxLength; i++) result.data[i] = (uint)(~(bi1.data[i])); result.dataLength = maxLength; while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; return result; } //*********************************************************************** // Overloading of the NEGATE operator (2's complement) //*********************************************************************** public static BigInteger operator -(BigInteger bi1) { // handle neg of zero separately since it'll cause an overflow // if we proceed. if (bi1.dataLength == 1 && bi1.data[0] == 0) return (new BigInteger()); BigInteger result = new BigInteger(bi1); // 1's complement for (int i = 0; i < maxLength; i++) result.data[i] = (uint)(~(bi1.data[i])); // add one to result of 1's complement long val, carry = 1; int index = 0; while (carry != 0 && index < maxLength) { val = (long)(result.data[index]); val++; result.data[index] = (uint)(val & 0xFFFFFFFF); carry = val >> 32; index++; } if ((bi1.data[maxLength - 1] & 0x80000000) == (result.data[maxLength - 1] & 0x80000000)) throw (new ArithmeticException("Overflow in negation.\n")); result.dataLength = maxLength; while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; return result; } //*********************************************************************** // Overloading of equality operator //*********************************************************************** public static bool operator ==(BigInteger bi1, BigInteger bi2) { return bi1.Equals(bi2); } public static bool operator !=(BigInteger bi1, BigInteger bi2) { return !(bi1.Equals(bi2)); } public override bool Equals(object o) { BigInteger bi = (BigInteger)o; if (this.dataLength != bi.dataLength) return false; for (int i = 0; i < this.dataLength; i++) { if (this.data[i] != bi.data[i]) return false; } return true; } public override int GetHashCode() { return this.ToString().GetHashCode(); } //*********************************************************************** // Overloading of inequality operator //*********************************************************************** public static bool operator >(BigInteger bi1, BigInteger bi2) { int pos = maxLength - 1; // bi1 is negative, bi2 is positive if ((bi1.data[pos] & 0x80000000) != 0 && (bi2.data[pos] & 0x80000000) == 0) return false; // bi1 is positive, bi2 is negative else if ((bi1.data[pos] & 0x80000000) == 0 && (bi2.data[pos] & 0x80000000) != 0) return true; // same sign int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; for (pos = len - 1; pos >= 0 && bi1.data[pos] == bi2.data[pos]; pos--) ; if (pos >= 0) { if (bi1.data[pos] > bi2.data[pos]) return true; return false; } return false; } public static bool operator <(BigInteger bi1, BigInteger bi2) { int pos = maxLength - 1; // bi1 is negative, bi2 is positive if ((bi1.data[pos] & 0x80000000) != 0 && (bi2.data[pos] & 0x80000000) == 0) return true; // bi1 is positive, bi2 is negative else if ((bi1.data[pos] & 0x80000000) == 0 && (bi2.data[pos] & 0x80000000) != 0) return false; // same sign int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; for (pos = len - 1; pos >= 0 && bi1.data[pos] == bi2.data[pos]; pos--) ; if (pos >= 0) { if (bi1.data[pos] < bi2.data[pos]) return true; return false; } return false; } public static bool operator >=(BigInteger bi1, BigInteger bi2) { return (bi1 == bi2 || bi1 > bi2); } public static bool operator <=(BigInteger bi1, BigInteger bi2) { return (bi1 == bi2 || bi1 < bi2); } //*********************************************************************** // Private function that supports the division of two numbers with // a divisor that has more than 1 digit. // // Algorithm taken from [1] //*********************************************************************** private static void multiByteDivide(BigInteger bi1, BigInteger bi2, BigInteger outQuotient, BigInteger outRemainder) { uint[] result = new uint[maxLength]; int remainderLen = bi1.dataLength + 1; uint[] remainder = new uint[remainderLen]; uint mask = 0x80000000; uint val = bi2.data[bi2.dataLength - 1]; int shift = 0, resultPos = 0; while (mask != 0 && (val & mask) == 0) { shift++; mask >>= 1; } //Console.WriteLine("shift = {0}", shift); //Console.WriteLine("Before bi1 Len = {0}, bi2 Len = {1}", bi1.dataLength, bi2.dataLength); for (int i = 0; i < bi1.dataLength; i++) remainder[i] = bi1.data[i]; shiftLeft(remainder, shift); bi2 = bi2 << shift; /* Console.WriteLine("bi1 Len = {0}, bi2 Len = {1}", bi1.dataLength, bi2.dataLength); Console.WriteLine("dividend = " + bi1 + "\ndivisor = " + bi2); for(int q = remainderLen - 1; q >= 0; q--) Console.Write("{0:x2}", remainder[q]); Console.WriteLine(); */ int j = remainderLen - bi2.dataLength; int pos = remainderLen - 1; ulong firstDivisorByte = bi2.data[bi2.dataLength - 1]; ulong secondDivisorByte = bi2.data[bi2.dataLength - 2]; int divisorLen = bi2.dataLength + 1; uint[] dividendPart = new uint[divisorLen]; while (j > 0) { ulong dividend = ((ulong)remainder[pos] << 32) + (ulong)remainder[pos - 1]; //Console.WriteLine("dividend = {0}", dividend); ulong q_hat = dividend / firstDivisorByte; ulong r_hat = dividend % firstDivisorByte; //Console.WriteLine("q_hat = {0:X}, r_hat = {1:X}", q_hat, r_hat); bool done = false; while (!done) { done = true; if (q_hat == 0x100000000 || (q_hat * secondDivisorByte) > ((r_hat << 32) + remainder[pos - 2])) { q_hat--; r_hat += firstDivisorByte; if (r_hat < 0x100000000) done = false; } } for (int h = 0; h < divisorLen; h++) dividendPart[h] = remainder[pos - h]; BigInteger kk = new BigInteger(dividendPart); BigInteger ss = bi2 * (long)q_hat; //Console.WriteLine("ss before = " + ss); while (ss > kk) { q_hat--; ss -= bi2; //Console.WriteLine(ss); } BigInteger yy = kk - ss; //Console.WriteLine("ss = " + ss); //Console.WriteLine("kk = " + kk); //Console.WriteLine("yy = " + yy); for (int h = 0; h < divisorLen; h++) remainder[pos - h] = yy.data[bi2.dataLength - h]; /* Console.WriteLine("dividend = "); for(int q = remainderLen - 1; q >= 0; q--) Console.Write("{0:x2}", remainder[q]); Console.WriteLine("\n************ q_hat = {0:X}\n", q_hat); */ result[resultPos++] = (uint)q_hat; pos--; j--; } outQuotient.dataLength = resultPos; int y = 0; for (int x = outQuotient.dataLength - 1; x >= 0; x--, y++) outQuotient.data[y] = result[x]; for (; y < maxLength; y++) outQuotient.data[y] = 0; while (outQuotient.dataLength > 1 && outQuotient.data[outQuotient.dataLength - 1] == 0) outQuotient.dataLength--; if (outQuotient.dataLength == 0) outQuotient.dataLength = 1; outRemainder.dataLength = shiftRight(remainder, shift); for (y = 0; y < outRemainder.dataLength; y++) outRemainder.data[y] = remainder[y]; for (; y < maxLength; y++) outRemainder.data[y] = 0; } //*********************************************************************** // Private function that supports the division of two numbers with // a divisor that has only 1 digit. //*********************************************************************** private static void singleByteDivide(BigInteger bi1, BigInteger bi2, BigInteger outQuotient, BigInteger outRemainder) { uint[] result = new uint[maxLength]; int resultPos = 0; // copy dividend to reminder for (int i = 0; i < maxLength; i++) outRemainder.data[i] = bi1.data[i]; outRemainder.dataLength = bi1.dataLength; while (outRemainder.dataLength > 1 && outRemainder.data[outRemainder.dataLength - 1] == 0) outRemainder.dataLength--; ulong divisor = (ulong)bi2.data[0]; int pos = outRemainder.dataLength - 1; ulong dividend = (ulong)outRemainder.data[pos]; //Console.WriteLine("divisor = " + divisor + " dividend = " + dividend); //Console.WriteLine("divisor = " + bi2 + "\ndividend = " + bi1); if (dividend >= divisor) { ulong quotient = dividend / divisor; result[resultPos++] = (uint)quotient; outRemainder.data[pos] = (uint)(dividend % divisor); } pos--; while (pos >= 0) { //Console.WriteLine(pos); dividend = ((ulong)outRemainder.data[pos + 1] << 32) + (ulong)outRemainder.data[pos]; ulong quotient = dividend / divisor; result[resultPos++] = (uint)quotient; outRemainder.data[pos + 1] = 0; outRemainder.data[pos--] = (uint)(dividend % divisor); //Console.WriteLine(">>>> " + bi1); } outQuotient.dataLength = resultPos; int j = 0; for (int i = outQuotient.dataLength - 1; i >= 0; i--, j++) outQuotient.data[j] = result[i]; for (; j < maxLength; j++) outQuotient.data[j] = 0; while (outQuotient.dataLength > 1 && outQuotient.data[outQuotient.dataLength - 1] == 0) outQuotient.dataLength--; if (outQuotient.dataLength == 0) outQuotient.dataLength = 1; while (outRemainder.dataLength > 1 && outRemainder.data[outRemainder.dataLength - 1] == 0) outRemainder.dataLength--; } //*********************************************************************** // Overloading of division operator //*********************************************************************** public static BigInteger operator /(BigInteger bi1, BigInteger bi2) { BigInteger quotient = new BigInteger(); BigInteger remainder = new BigInteger(); int lastPos = maxLength - 1; bool divisorNeg = false, dividendNeg = false; if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative { bi1 = -bi1; dividendNeg = true; } if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative { bi2 = -bi2; divisorNeg = true; } if (bi1 < bi2) { return quotient; } else { if (bi2.dataLength == 1) singleByteDivide(bi1, bi2, quotient, remainder); else multiByteDivide(bi1, bi2, quotient, remainder); if (dividendNeg != divisorNeg) return -quotient; return quotient; } } //*********************************************************************** // Overloading of modulus operator //*********************************************************************** public static BigInteger operator %(BigInteger bi1, BigInteger bi2) { BigInteger quotient = new BigInteger(); BigInteger remainder = new BigInteger(bi1); int lastPos = maxLength - 1; bool dividendNeg = false; if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative { bi1 = -bi1; dividendNeg = true; } if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative bi2 = -bi2; if (bi1 < bi2) { return remainder; } else { if (bi2.dataLength == 1) singleByteDivide(bi1, bi2, quotient, remainder); else multiByteDivide(bi1, bi2, quotient, remainder); if (dividendNeg) return -remainder; return remainder; } } //*********************************************************************** // Overloading of bitwise AND operator //*********************************************************************** public static BigInteger operator &(BigInteger bi1, BigInteger bi2) { BigInteger result = new BigInteger(); int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; for (int i = 0; i < len; i++) { uint sum = (uint)(bi1.data[i] & bi2.data[i]); result.data[i] = sum; } result.dataLength = maxLength; while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; return result; } //*********************************************************************** // Overloading of bitwise OR operator //*********************************************************************** public static BigInteger operator |(BigInteger bi1, BigInteger bi2) { BigInteger result = new BigInteger(); int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; for (int i = 0; i < len; i++) { uint sum = (uint)(bi1.data[i] | bi2.data[i]); result.data[i] = sum; } result.dataLength = maxLength; while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; return result; } //*********************************************************************** // Overloading of bitwise XOR operator //*********************************************************************** public static BigInteger operator ^(BigInteger bi1, BigInteger bi2) { BigInteger result = new BigInteger(); int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; for (int i = 0; i < len; i++) { uint sum = (uint)(bi1.data[i] ^ bi2.data[i]); result.data[i] = sum; } result.dataLength = maxLength; while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; return result; } //*********************************************************************** // Returns max(this, bi) //*********************************************************************** public BigInteger max(BigInteger bi) { if (this > bi) return (new BigInteger(this)); else return (new BigInteger(bi)); } //*********************************************************************** // Returns min(this, bi) //*********************************************************************** public BigInteger min(BigInteger bi) { if (this < bi) return (new BigInteger(this)); else return (new BigInteger(bi)); } //*********************************************************************** // Returns the absolute value //*********************************************************************** public BigInteger abs() { if ((this.data[maxLength - 1] & 0x80000000) != 0) return (-this); else return (new BigInteger(this)); } //*********************************************************************** // Returns a string representing the BigInteger in base 10. //*********************************************************************** public override string ToString() { return ToString(10); } //*********************************************************************** // Returns a string representing the BigInteger in sign-and-magnitude // format in the specified radix. // // Example // ------- // If the value of BigInteger is -255 in base 10, then // ToString(16) returns "-FF" // //*********************************************************************** public string ToString(int radix) { if (radix < 2 || radix > 36) throw (new ArgumentException("Radix must be >= 2 and <= 36")); string charSet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; string result = ""; BigInteger a = this; bool negative = false; if ((a.data[maxLength - 1] & 0x80000000) != 0) { negative = true; try { a = -a; } catch (Exception) { } } BigInteger quotient = new BigInteger(); BigInteger remainder = new BigInteger(); BigInteger biRadix = new BigInteger(radix); if (a.dataLength == 1 && a.data[0] == 0) result = "0"; else { while (a.dataLength > 1 || (a.dataLength == 1 && a.data[0] != 0)) { singleByteDivide(a, biRadix, quotient, remainder); if (remainder.data[0] < 10) result = remainder.data[0] + result; else result = charSet[(int)remainder.data[0] - 10] + result; a = quotient; } if (negative) result = "-" + result; } return result; } //*********************************************************************** // Returns a hex string showing the contains of the BigInteger // // Examples // ------- // 1) If the value of BigInteger is 255 in base 10, then // ToHexString() returns "FF" // // 2) If the value of BigInteger is -255 in base 10, then // ToHexString() returns ".....FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF01", // which is the 2's complement representation of -255. // //*********************************************************************** public string ToHexString() { string result = data[dataLength - 1].ToString("X"); for (int i = dataLength - 2; i >= 0; i--) { result += data[i].ToString("X8"); } return result; } //*********************************************************************** // Modulo Exponentiation //*********************************************************************** public BigInteger modPow(BigInteger exp, BigInteger n) { if ((exp.data[maxLength - 1] & 0x80000000) != 0) throw (new ArithmeticException("Positive exponents only.")); BigInteger resultNum = 1; BigInteger tempNum; bool thisNegative = false; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative this { tempNum = -this % n; thisNegative = true; } else tempNum = this % n; // ensures (tempNum * tempNum) < b^(2k) if ((n.data[maxLength - 1] & 0x80000000) != 0) // negative n n = -n; // calculate constant = b^(2k) / m BigInteger constant = new BigInteger(); int i = n.dataLength << 1; constant.data[i] = 0x00000001; constant.dataLength = i + 1; constant = constant / n; int totalBits = exp.bitCount(); int count = 0; // perform squaring and multiply exponentiation for (int pos = 0; pos < exp.dataLength; pos++) { uint mask = 0x01; //Console.WriteLine("pos = " + pos); for (int index = 0; index < 32; index++) { if ((exp.data[pos] & mask) != 0) resultNum = BarrettReduction(resultNum * tempNum, n, constant); mask <<= 1; tempNum = BarrettReduction(tempNum * tempNum, n, constant); if (tempNum.dataLength == 1 && tempNum.data[0] == 1) { if (thisNegative && (exp.data[0] & 0x1) != 0) //odd exp return -resultNum; return resultNum; } count++; if (count == totalBits) break; } } if (thisNegative && (exp.data[0] & 0x1) != 0) //odd exp return -resultNum; return resultNum; } //*********************************************************************** // Fast calculation of modular reduction using Barrett's reduction. // Requires x < b^(2k), where b is the base. In this case, base is // 2^32 (uint). // // Reference [4] //*********************************************************************** private BigInteger BarrettReduction(BigInteger x, BigInteger n, BigInteger constant) { int k = n.dataLength, kPlusOne = k + 1, kMinusOne = k - 1; BigInteger q1 = new BigInteger(); // q1 = x / b^(k-1) for (int i = kMinusOne, j = 0; i < x.dataLength; i++, j++) q1.data[j] = x.data[i]; q1.dataLength = x.dataLength - kMinusOne; if (q1.dataLength <= 0) q1.dataLength = 1; BigInteger q2 = q1 * constant; BigInteger q3 = new BigInteger(); // q3 = q2 / b^(k+1) for (int i = kPlusOne, j = 0; i < q2.dataLength; i++, j++) q3.data[j] = q2.data[i]; q3.dataLength = q2.dataLength - kPlusOne; if (q3.dataLength <= 0) q3.dataLength = 1; // r1 = x mod b^(k+1) // i.e. keep the lowest (k+1) words BigInteger r1 = new BigInteger(); int lengthToCopy = (x.dataLength > kPlusOne) ? kPlusOne : x.dataLength; for (int i = 0; i < lengthToCopy; i++) r1.data[i] = x.data[i]; r1.dataLength = lengthToCopy; // r2 = (q3 * n) mod b^(k+1) // partial multiplication of q3 and n BigInteger r2 = new BigInteger(); for (int i = 0; i < q3.dataLength; i++) { if (q3.data[i] == 0) continue; ulong mcarry = 0; int t = i; for (int j = 0; j < n.dataLength && t < kPlusOne; j++, t++) { // t = i + j ulong val = ((ulong)q3.data[i] * (ulong)n.data[j]) + (ulong)r2.data[t] + mcarry; r2.data[t] = (uint)(val & 0xFFFFFFFF); mcarry = (val >> 32); } if (t < kPlusOne) r2.data[t] = (uint)mcarry; } r2.dataLength = kPlusOne; while (r2.dataLength > 1 && r2.data[r2.dataLength - 1] == 0) r2.dataLength--; r1 -= r2; if ((r1.data[maxLength - 1] & 0x80000000) != 0) // negative { BigInteger val = new BigInteger(); val.data[kPlusOne] = 0x00000001; val.dataLength = kPlusOne + 1; r1 += val; } while (r1 >= n) r1 -= n; return r1; } //*********************************************************************** // Returns gcd(this, bi) //*********************************************************************** public BigInteger gcd(BigInteger bi) { BigInteger x; BigInteger y; if ((data[maxLength - 1] & 0x80000000) != 0) // negative x = -this; else x = this; if ((bi.data[maxLength - 1] & 0x80000000) != 0) // negative y = -bi; else y = bi; BigInteger g = y; while (x.dataLength > 1 || (x.dataLength == 1 && x.data[0] != 0)) { g = x; x = y % x; y = g; } return g; } //*********************************************************************** // Populates "this" with the specified amount of random bits //*********************************************************************** public void genRandomBits(int bits, Random rand) { int dwords = bits >> 5; int remBits = bits & 0x1F; if (remBits != 0) dwords++; if (dwords > maxLength) throw (new ArithmeticException("Number of required bits > maxLength.")); for (int i = 0; i < dwords; i++) data[i] = (uint)(rand.NextDouble() * 0x100000000); for (int i = dwords; i < maxLength; i++) data[i] = 0; if (remBits != 0) { uint mask = (uint)(0x01 << (remBits - 1)); data[dwords - 1] |= mask; mask = (uint)(0xFFFFFFFF >> (32 - remBits)); data[dwords - 1] &= mask; } else data[dwords - 1] |= 0x80000000; dataLength = dwords; if (dataLength == 0) dataLength = 1; } //*********************************************************************** // Returns the position of the most significant bit in the BigInteger. // // Eg. The result is 0, if the value of BigInteger is 0...0000 0000 // The result is 1, if the value of BigInteger is 0...0000 0001 // The result is 2, if the value of BigInteger is 0...0000 0010 // The result is 2, if the value of BigInteger is 0...0000 0011 // //*********************************************************************** public int bitCount() { while (dataLength > 1 && data[dataLength - 1] == 0) dataLength--; uint value = data[dataLength - 1]; uint mask = 0x80000000; int bits = 32; while (bits > 0 && (value & mask) == 0) { bits--; mask >>= 1; } bits += ((dataLength - 1) << 5); return bits; } //*********************************************************************** // Probabilistic prime test based on Fermat's little theorem // // for any a < p (p does not divide a) if // a^(p-1) mod p != 1 then p is not prime. // // Otherwise, p is probably prime (pseudoprime to the chosen base). // // Returns // ------- // True if "this" is a pseudoprime to randomly chosen // bases. The number of chosen bases is given by the "confidence" // parameter. // // False if "this" is definitely NOT prime. // // Note - this method is fast but fails for Carmichael numbers except // when the randomly chosen base is a factor of the number. // //*********************************************************************** public bool FermatLittleTest(int confidence) { BigInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; int bits = thisVal.bitCount(); BigInteger a = new BigInteger(); BigInteger p_sub1 = thisVal - (new BigInteger(1)); Random rand = new Random(); for (int round = 0; round < confidence; round++) { bool done = false; while (!done)// generate a < n { int testBits = 0; // make sure "a" has at least 2 bits while (testBits < 2) testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0 if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1)) done = true; } // check whether a factor exists (fix for version 1.03) BigInteger gcdTest = a.gcd(thisVal); if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1) return false; // calculate a^(p-1) mod p BigInteger expResult = a.modPow(p_sub1, thisVal); int resultLen = expResult.dataLength; // is NOT prime is a^(p-1) mod p != 1 if (resultLen > 1 || (resultLen == 1 && expResult.data[0] != 1)) { //Console.WriteLine("a = " + a.ToString()); return false; } } return true; } //*********************************************************************** // Probabilistic prime test based on Rabin-Miller's // // for any p > 0 with p - 1 = 2^s * t // // p is probably prime (strong pseudoprime) if for any a < p, // 1) a^t mod p = 1 or // 2) a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1 // // Otherwise, p is composite. // // Returns // ------- // True if "this" is a strong pseudoprime to randomly chosen // bases. The number of chosen bases is given by the "confidence" // parameter. // // False if "this" is definitely NOT prime. // //*********************************************************************** public bool RabinMillerTest(int confidence) { BigInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; // calculate values of s and t BigInteger p_sub1 = thisVal - (new BigInteger(1)); int s = 0; for (int index = 0; index < p_sub1.dataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((p_sub1.data[index] & mask) != 0) { index = p_sub1.dataLength; // to break the outer loop break; } mask <<= 1; s++; } } BigInteger t = p_sub1 >> s; int bits = thisVal.bitCount(); BigInteger a = new BigInteger(); Random rand = new Random(); for (int round = 0; round < confidence; round++) { bool done = false; while (!done)// generate a < n { int testBits = 0; // make sure "a" has at least 2 bits while (testBits < 2) testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0 if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1)) done = true; } // check whether a factor exists (fix for version 1.03) BigInteger gcdTest = a.gcd(thisVal); if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1) return false; BigInteger b = a.modPow(t, thisVal); /* Console.WriteLine("a = " + a.ToString(10)); Console.WriteLine("b = " + b.ToString(10)); Console.WriteLine("t = " + t.ToString(10)); Console.WriteLine("s = " + s); */ bool result = false; if (b.dataLength == 1 && b.data[0] == 1) // a^t mod p = 1 result = true; for (int j = 0; result == false && j < s; j++) { if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1 { result = true; break; } b = (b * b) % thisVal; } if (result == false) return false; } return true; } //*********************************************************************** // Probabilistic prime test based on Solovay-Strassen (Euler Criterion) // // p is probably prime if for any a < p (a is not multiple of p), // a^((p-1)/2) mod p = J(a, p) // // where J is the Jacobi symbol. // // Otherwise, p is composite. // // Returns // ------- // True if "this" is a Euler pseudoprime to randomly chosen // bases. The number of chosen bases is given by the "confidence" // parameter. // // False if "this" is definitely NOT prime. // //*********************************************************************** public bool SolovayStrassenTest(int confidence) { BigInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; int bits = thisVal.bitCount(); BigInteger a = new BigInteger(); BigInteger p_sub1 = thisVal - 1; BigInteger p_sub1_shift = p_sub1 >> 1; Random rand = new Random(); for (int round = 0; round < confidence; round++) { bool done = false; while (!done)// generate a < n { int testBits = 0; // make sure "a" has at least 2 bits while (testBits < 2) testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0 if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1)) done = true; } // check whether a factor exists (fix for version 1.03) BigInteger gcdTest = a.gcd(thisVal); if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1) return false; // calculate a^((p-1)/2) mod p BigInteger expResult = a.modPow(p_sub1_shift, thisVal); if (expResult == p_sub1) expResult = -1; // calculate Jacobi symbol BigInteger jacob = Jacobi(a, thisVal); //Console.WriteLine("a = " + a.ToString(10) + " b = " + thisVal.ToString(10)); //Console.WriteLine("expResult = " + expResult.ToString(10) + " Jacob = " + jacob.ToString(10)); // if they are different then it is not prime if (expResult != jacob) return false; } return true; } //*********************************************************************** // Implementation of the Lucas Strong Pseudo Prime test. // // Let n be an odd number with gcd(n,D) = 1, and n - J(D, n) = 2^s * d // with d odd and s >= 0. // // If Ud mod n = 0 or V2^r*d mod n = 0 for some 0 <= r < s, then n // is a strong Lucas pseudoprime with parameters (P, Q). We select // P and Q based on Selfridge. // // Returns True if number is a strong Lucus pseudo prime. // Otherwise, returns False indicating that number is composite. //*********************************************************************** public bool LucasStrongTest() { BigInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; return LucasStrongTestHelper(thisVal); } private bool LucasStrongTestHelper(BigInteger thisVal) { // Do the test (selects D based on Selfridge) // Let D be the first element of the sequence // 5, -7, 9, -11, 13, ... for which J(D,n) = -1 // Let P = 1, Q = (1-D) / 4 long D = 5, sign = -1, dCount = 0; bool done = false; while (!done) { int Jresult = BigInteger.Jacobi(D, thisVal); if (Jresult == -1) done = true; // J(D, this) = 1 else { if (Jresult == 0 && Math.Abs(D) < thisVal) // divisor found return false; if (dCount == 20) { // check for square BigInteger root = thisVal.sqrt(); if (root * root == thisVal) return false; } //Console.WriteLine(D); D = (Math.Abs(D) + 2) * sign; sign = -sign; } dCount++; } long Q = (1 - D) >> 2; /* Console.WriteLine("D = " + D); Console.WriteLine("Q = " + Q); Console.WriteLine("(n,D) = " + thisVal.gcd(D)); Console.WriteLine("(n,Q) = " + thisVal.gcd(Q)); Console.WriteLine("J(D|n) = " + BigInteger.Jacobi(D, thisVal)); */ BigInteger p_add1 = thisVal + 1; int s = 0; for (int index = 0; index < p_add1.dataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((p_add1.data[index] & mask) != 0) { index = p_add1.dataLength; // to break the outer loop break; } mask <<= 1; s++; } } BigInteger t = p_add1 >> s; // calculate constant = b^(2k) / m // for Barrett Reduction BigInteger constant = new BigInteger(); int nLen = thisVal.dataLength << 1; constant.data[nLen] = 0x00000001; constant.dataLength = nLen + 1; constant = constant / thisVal; BigInteger[] lucas = LucasSequenceHelper(1, Q, t, thisVal, constant, 0); bool isPrime = false; if ((lucas[0].dataLength == 1 && lucas[0].data[0] == 0) || (lucas[1].dataLength == 1 && lucas[1].data[0] == 0)) { // u(t) = 0 or V(t) = 0 isPrime = true; } for (int i = 1; i < s; i++) { if (!isPrime) { // doubling of index lucas[1] = thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal, constant); lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal; //lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal; if ((lucas[1].dataLength == 1 && lucas[1].data[0] == 0)) isPrime = true; } lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant); //Q^k } if (isPrime) // additional checks for composite numbers { // If n is prime and gcd(n, Q) == 1, then // Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n BigInteger g = thisVal.gcd(Q); if (g.dataLength == 1 && g.data[0] == 1) // gcd(this, Q) == 1 { if ((lucas[2].data[maxLength - 1] & 0x80000000) != 0) lucas[2] += thisVal; BigInteger temp = (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal; if ((temp.data[maxLength - 1] & 0x80000000) != 0) temp += thisVal; if (lucas[2] != temp) isPrime = false; } } return isPrime; } //*********************************************************************** // Determines whether a number is probably prime, using the Rabin-Miller's // test. Before applying the test, the number is tested for divisibility // by primes < 2000 // // Returns true if number is probably prime. //*********************************************************************** public bool isProbablePrime(int confidence) { BigInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; // test for divisibility by primes < 2000 for (int p = 0; p < primesBelow2000.Length; p++) { BigInteger divisor = primesBelow2000[p]; if (divisor >= thisVal) break; BigInteger resultNum = thisVal % divisor; if (resultNum.IntValue() == 0) { /* Console.WriteLine("Not prime! Divisible by {0}\n", primesBelow2000[p]); */ return false; } } if (thisVal.RabinMillerTest(confidence)) return true; else { //Console.WriteLine("Not prime! Failed primality test\n"); return false; } } //*********************************************************************** // Determines whether this BigInteger is probably prime using a // combination of base 2 strong pseudoprime test and Lucas strong // pseudoprime test. // // The sequence of the primality test is as follows, // // 1) Trial divisions are carried out using prime numbers below 2000. // if any of the primes divides this BigInteger, then it is not prime. // // 2) Perform base 2 strong pseudoprime test. If this BigInteger is a // base 2 strong pseudoprime, proceed on to the next step. // // 3) Perform strong Lucas pseudoprime test. // // Returns True if this BigInteger is both a base 2 strong pseudoprime // and a strong Lucas pseudoprime. // // For a detailed discussion of this primality test, see [6]. // //*********************************************************************** public bool isProbablePrime() { BigInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; // test for divisibility by primes < 2000 for (int p = 0; p < primesBelow2000.Length; p++) { BigInteger divisor = primesBelow2000[p]; if (divisor >= thisVal) break; BigInteger resultNum = thisVal % divisor; if (resultNum.IntValue() == 0) { //Console.WriteLine("Not prime! Divisible by {0}\n", // primesBelow2000[p]); return false; } } // Perform BASE 2 Rabin-Miller Test // calculate values of s and t BigInteger p_sub1 = thisVal - (new BigInteger(1)); int s = 0; for (int index = 0; index < p_sub1.dataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((p_sub1.data[index] & mask) != 0) { index = p_sub1.dataLength; // to break the outer loop break; } mask <<= 1; s++; } } BigInteger t = p_sub1 >> s; int bits = thisVal.bitCount(); BigInteger a = 2; // b = a^t mod p BigInteger b = a.modPow(t, thisVal); bool result = false; if (b.dataLength == 1 && b.data[0] == 1) // a^t mod p = 1 result = true; for (int j = 0; result == false && j < s; j++) { if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1 { result = true; break; } b = (b * b) % thisVal; } // if number is strong pseudoprime to base 2, then do a strong lucas test if (result) result = LucasStrongTestHelper(thisVal); return result; } //*********************************************************************** // Returns the lowest 4 bytes of the BigInteger as an int. //*********************************************************************** public int IntValue() { return (int)data[0]; } //*********************************************************************** // Returns the lowest 8 bytes of the BigInteger as a long. //*********************************************************************** public long LongValue() { long val = 0; val = (long)data[0]; try { // exception if maxLength = 1 val |= (long)data[1] << 32; } catch (Exception) { if ((data[0] & 0x80000000) != 0) // negative val = (int)data[0]; } return val; } //*********************************************************************** // Computes the Jacobi Symbol for a and b. // Algorithm adapted from [3] and [4] with some optimizations //*********************************************************************** public static int Jacobi(BigInteger a, BigInteger b) { // Jacobi defined only for odd integers if ((b.data[0] & 0x1) == 0) throw (new ArgumentException("Jacobi defined only for odd integers.")); if (a >= b) a %= b; if (a.dataLength == 1 && a.data[0] == 0) return 0; // a == 0 if (a.dataLength == 1 && a.data[0] == 1) return 1; // a == 1 if (a < 0) { if ((((b - 1).data[0]) & 0x2) == 0) //if( (((b-1) >> 1).data[0] & 0x1) == 0) return Jacobi(-a, b); else return -Jacobi(-a, b); } int e = 0; for (int index = 0; index < a.dataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((a.data[index] & mask) != 0) { index = a.dataLength; // to break the outer loop break; } mask <<= 1; e++; } } BigInteger a1 = a >> e; int s = 1; if ((e & 0x1) != 0 && ((b.data[0] & 0x7) == 3 || (b.data[0] & 0x7) == 5)) s = -1; if ((b.data[0] & 0x3) == 3 && (a1.data[0] & 0x3) == 3) s = -s; if (a1.dataLength == 1 && a1.data[0] == 1) return s; else return (s * Jacobi(b % a1, a1)); } //*********************************************************************** // Generates a positive BigInteger that is probably prime. //*********************************************************************** public static BigInteger genPseudoPrime(int bits, int confidence, Random rand) { BigInteger result = new BigInteger(); bool done = false; while (!done) { result.genRandomBits(bits, rand); result.data[0] |= 0x01;// make it odd // prime test done = result.isProbablePrime(confidence); } return result; } //*********************************************************************** // Generates a random number with the specified number of bits such // that gcd(number, this) = 1 //*********************************************************************** public BigInteger genCoPrime(int bits, Random rand) { bool done = false; BigInteger result = new BigInteger(); while (!done) { result.genRandomBits(bits, rand); //Console.WriteLine(result.ToString(16)); // gcd test BigInteger g = result.gcd(this); if (g.dataLength == 1 && g.data[0] == 1) done = true; } return result; } //*********************************************************************** // Returns the modulo inverse of this. Throws ArithmeticException if // the inverse does not exist. (i.e. gcd(this, modulus) != 1) //*********************************************************************** public BigInteger modInverse(BigInteger modulus) { BigInteger[] p = { 0, 1 }; BigInteger[] q = new BigInteger[2]; // quotients BigInteger[] r = { 0, 0 }; // remainders int step = 0; BigInteger a = modulus; BigInteger b = this; while (b.dataLength > 1 || (b.dataLength == 1 && b.data[0] != 0)) { BigInteger quotient = new BigInteger(); BigInteger remainder = new BigInteger(); if (step > 1) { BigInteger pval = (p[0] - (p[1] * q[0])) % modulus; p[0] = p[1]; p[1] = pval; } if (b.dataLength == 1) singleByteDivide(a, b, quotient, remainder); else multiByteDivide(a, b, quotient, remainder); /* Console.WriteLine(quotient.dataLength); Console.WriteLine("{0} = {1}({2}) + {3} p = {4}", a.ToString(10), b.ToString(10), quotient.ToString(10), remainder.ToString(10), p[1].ToString(10)); */ q[0] = q[1]; r[0] = r[1]; q[1] = quotient; r[1] = remainder; a = b; b = remainder; step++; } if (r[0].dataLength > 1 || (r[0].dataLength == 1 && r[0].data[0] != 1)) throw (new ArithmeticException("No inverse!")); BigInteger result = ((p[0] - (p[1] * q[0])) % modulus); if ((result.data[maxLength - 1] & 0x80000000) != 0) result += modulus; // get the least positive modulus return result; } //*********************************************************************** // Returns the value of the BigInteger as a byte array. The lowest // index contains the MSB. //*********************************************************************** public byte[] getBytes() { int numBits = bitCount(); int numBytes = numBits >> 3; if ((numBits & 0x7) != 0) numBytes++; byte[] result = new byte[numBytes]; //Console.WriteLine(result.Length); int pos = 0; uint tempVal, val = data[dataLength - 1]; if ((tempVal = (val >> 24 & 0xFF)) != 0) result[pos++] = (byte)tempVal; if ((tempVal = (val >> 16 & 0xFF)) != 0) result[pos++] = (byte)tempVal; if ((tempVal = (val >> 8 & 0xFF)) != 0) result[pos++] = (byte)tempVal; if ((tempVal = (val & 0xFF)) != 0) result[pos++] = (byte)tempVal; for (int i = dataLength - 2; i >= 0; i--, pos += 4) { val = data[i]; result[pos + 3] = (byte)(val & 0xFF); val >>= 8; result[pos + 2] = (byte)(val & 0xFF); val >>= 8; result[pos + 1] = (byte)(val & 0xFF); val >>= 8; result[pos] = (byte)(val & 0xFF); } return result; } //*********************************************************************** // Sets the value of the specified bit to 1 // The Least Significant Bit position is 0. //*********************************************************************** public void setBit(uint bitNum) { uint bytePos = bitNum >> 5; // divide by 32 byte bitPos = (byte)(bitNum & 0x1F); // get the lowest 5 bits uint mask = (uint)1 << bitPos; this.data[bytePos] |= mask; if (bytePos >= this.dataLength) this.dataLength = (int)bytePos + 1; } //*********************************************************************** // Sets the value of the specified bit to 0 // The Least Significant Bit position is 0. //*********************************************************************** public void unsetBit(uint bitNum) { uint bytePos = bitNum >> 5; if (bytePos < this.dataLength) { byte bitPos = (byte)(bitNum & 0x1F); uint mask = (uint)1 << bitPos; uint mask2 = 0xFFFFFFFF ^ mask; this.data[bytePos] &= mask2; if (this.dataLength > 1 && this.data[this.dataLength - 1] == 0) this.dataLength--; } } //*********************************************************************** // Returns a value that is equivalent to the integer square root // of the BigInteger. // // The integer square root of "this" is defined as the largest integer n // such that (n * n) <= this // //*********************************************************************** public BigInteger sqrt() { uint numBits = (uint)this.bitCount(); if ((numBits & 0x1) != 0) // odd number of bits numBits = (numBits >> 1) + 1; else numBits = (numBits >> 1); uint bytePos = numBits >> 5; byte bitPos = (byte)(numBits & 0x1F); uint mask; BigInteger result = new BigInteger(); if (bitPos == 0) mask = 0x80000000; else { mask = (uint)1 << bitPos; bytePos++; } result.dataLength = (int)bytePos; for (int i = (int)bytePos - 1; i >= 0; i--) { while (mask != 0) { // guess result.data[i] ^= mask; // undo the guess if its square is larger than this if ((result * result) > this) result.data[i] ^= mask; mask >>= 1; } mask = 0x80000000; } return result; } //*********************************************************************** // Returns the k_th number in the Lucas Sequence reduced modulo n. // // Uses index doubling to speed up the process. For example, to calculate V(k), // we maintain two numbers in the sequence V(n) and V(n+1). // // To obtain V(2n), we use the identity // V(2n) = (V(n) * V(n)) - (2 * Q^n) // To obtain V(2n+1), we first write it as // V(2n+1) = V((n+1) + n) // and use the identity // V(m+n) = V(m) * V(n) - Q * V(m-n) // Hence, // V((n+1) + n) = V(n+1) * V(n) - Q^n * V((n+1) - n) // = V(n+1) * V(n) - Q^n * V(1) // = V(n+1) * V(n) - Q^n * P // // We use k in its binary expansion and perform index doubling for each // bit position. For each bit position that is set, we perform an // index doubling followed by an index addition. This means that for V(n), // we need to update it to V(2n+1). For V(n+1), we need to update it to // V((2n+1)+1) = V(2*(n+1)) // // This function returns // [0] = U(k) // [1] = V(k) // [2] = Q^n // // Where U(0) = 0 % n, U(1) = 1 % n // V(0) = 2 % n, V(1) = P % n //*********************************************************************** public static BigInteger[] LucasSequence(BigInteger P, BigInteger Q, BigInteger k, BigInteger n) { if (k.dataLength == 1 && k.data[0] == 0) { BigInteger[] result = new BigInteger[3]; result[0] = 0; result[1] = 2 % n; result[2] = 1 % n; return result; } // calculate constant = b^(2k) / m // for Barrett Reduction BigInteger constant = new BigInteger(); int nLen = n.dataLength << 1; constant.data[nLen] = 0x00000001; constant.dataLength = nLen + 1; constant = constant / n; // calculate values of s and t int s = 0; for (int index = 0; index < k.dataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((k.data[index] & mask) != 0) { index = k.dataLength; // to break the outer loop break; } mask <<= 1; s++; } } BigInteger t = k >> s; //Console.WriteLine("s = " + s + " t = " + t); return LucasSequenceHelper(P, Q, t, n, constant, s); } //*********************************************************************** // Performs the calculation of the kth term in the Lucas Sequence. // For details of the algorithm, see reference [9]. // // k must be odd. i.e LSB == 1 //*********************************************************************** private static BigInteger[] LucasSequenceHelper(BigInteger P, BigInteger Q, BigInteger k, BigInteger n, BigInteger constant, int s) { BigInteger[] result = new BigInteger[3]; if ((k.data[0] & 0x00000001) == 0) throw (new ArgumentException("Argument k must be odd.")); int numbits = k.bitCount(); uint mask = (uint)0x1 << ((numbits & 0x1F) - 1); // v = v0, v1 = v1, u1 = u1, Q_k = Q^0 BigInteger v = 2 % n, Q_k = 1 % n, v1 = P % n, u1 = Q_k; bool flag = true; for (int i = k.dataLength - 1; i >= 0; i--) // iterate on the binary expansion of k { //Console.WriteLine("round"); while (mask != 0) { if (i == 0 && mask == 0x00000001) // last bit break; if ((k.data[i] & mask) != 0) // bit is set { // index doubling with addition u1 = (u1 * v1) % n; v = ((v * v1) - (P * Q_k)) % n; v1 = n.BarrettReduction(v1 * v1, n, constant); v1 = (v1 - ((Q_k * Q) << 1)) % n; if (flag) flag = false; else Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); Q_k = (Q_k * Q) % n; } else { // index doubling u1 = ((u1 * v) - Q_k) % n; v1 = ((v * v1) - (P * Q_k)) % n; v = n.BarrettReduction(v * v, n, constant); v = (v - (Q_k << 1)) % n; if (flag) { Q_k = Q % n; flag = false; } else Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); } mask >>= 1; } mask = 0x80000000; } // at this point u1 = u(n+1) and v = v(n) // since the last bit always 1, we need to transform u1 to u(2n+1) and v to v(2n+1) u1 = ((u1 * v) - Q_k) % n; v = ((v * v1) - (P * Q_k)) % n; if (flag) flag = false; else Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); Q_k = (Q_k * Q) % n; for (int i = 0; i < s; i++) { // index doubling u1 = (u1 * v) % n; v = ((v * v) - (Q_k << 1)) % n; if (flag) { Q_k = Q % n; flag = false; } else Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); } result[0] = u1; result[1] = v; result[2] = Q_k; return result; } //*********************************************************************** // Tests the correct implementation of the /, %, * and + operators //*********************************************************************** public static void MulDivTest(int rounds) { Random rand = new Random(); byte[] val = new byte[64]; byte[] val2 = new byte[64]; for (int count = 0; count < rounds; count++) { // generate 2 numbers of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 65); int t2 = 0; while (t2 == 0) t2 = (int)(rand.NextDouble() * 65); bool done = false; while (!done) { for (int i = 0; i < 64; i++) { if (i < t1) val[i] = (byte)(rand.NextDouble() * 256); else val[i] = 0; if (val[i] != 0) done = true; } } done = false; while (!done) { for (int i = 0; i < 64; i++) { if (i < t2) val2[i] = (byte)(rand.NextDouble() * 256); else val2[i] = 0; if (val2[i] != 0) done = true; } } while (val[0] == 0) val[0] = (byte)(rand.NextDouble() * 256); while (val2[0] == 0) val2[0] = (byte)(rand.NextDouble() * 256); Console.WriteLine(count); BigInteger bn1 = new BigInteger(val, t1); BigInteger bn2 = new BigInteger(val2, t2); // Determine the quotient and remainder by dividing // the first number by the second. BigInteger bn3 = bn1 / bn2; BigInteger bn4 = bn1 % bn2; // Recalculate the number BigInteger bn5 = (bn3 * bn2) + bn4; // Make sure they're the same if (bn5 != bn1) { Console.WriteLine("Error at " + count); Console.WriteLine(bn1 + "\n"); Console.WriteLine(bn2 + "\n"); Console.WriteLine(bn3 + "\n"); Console.WriteLine(bn4 + "\n"); Console.WriteLine(bn5 + "\n"); return; } } } //*********************************************************************** // Tests the correct implementation of the modulo exponential function // using RSA encryption and decryption (using pre-computed encryption and // decryption keys). //*********************************************************************** public static void RSATest(int rounds) { Random rand = new Random(1); byte[] val = new byte[64]; // private and public key BigInteger bi_e = new BigInteger("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7", 16); BigInteger bi_d = new BigInteger("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7", 16); BigInteger bi_n = new BigInteger("e8e77781f36a7b3188d711c2190b560f205a52391b3479cdb99fa010745cbeba5f2adc08e1de6bf38398a0487c4a73610d94ec36f17f3f46ad75e17bc1adfec99839589f45f95ccc94cb2a5c500b477eb3323d8cfab0c8458c96f0147a45d27e45a4d11d54d77684f65d48f15fafcc1ba208e71e921b9bd9017c16a5231af7f", 16); Console.WriteLine("e =\n" + bi_e.ToString(10)); Console.WriteLine("\nd =\n" + bi_d.ToString(10)); Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n"); for (int count = 0; count < rounds; count++) { // generate data of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 65); bool done = false; while (!done) { for (int i = 0; i < 64; i++) { if (i < t1) val[i] = (byte)(rand.NextDouble() * 256); else val[i] = 0; if (val[i] != 0) done = true; } } while (val[0] == 0) val[0] = (byte)(rand.NextDouble() * 256); Console.Write("Round = " + count); // encrypt and decrypt data BigInteger bi_data = new BigInteger(val, t1); BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n); BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n); // compare if (bi_decrypted != bi_data) { Console.WriteLine("\nError at round " + count); Console.WriteLine(bi_data + "\n"); return; } Console.WriteLine(" <PASSED>."); } } //*********************************************************************** // Tests the correct implementation of the modulo exponential and // inverse modulo functions using RSA encryption and decryption. The two // pseudoprimes p and q are fixed, but the two RSA keys are generated // for each round of testing. //*********************************************************************** public static void RSATest2(int rounds) { Random rand = new Random(); byte[] val = new byte[64]; byte[] pseudoPrime1 = { (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, }; byte[] pseudoPrime2 = { (byte)0x99, (byte)0x98, (byte)0xCA, (byte)0xB8, (byte)0x5E, (byte)0xD7, (byte)0xE5, (byte)0xDC, (byte)0x28, (byte)0x5C, (byte)0x6F, (byte)0x0E, (byte)0x15, (byte)0x09, (byte)0x59, (byte)0x6E, (byte)0x84, (byte)0xF3, (byte)0x81, (byte)0xCD, (byte)0xDE, (byte)0x42, (byte)0xDC, (byte)0x93, (byte)0xC2, (byte)0x7A, (byte)0x62, (byte)0xAC, (byte)0x6C, (byte)0xAF, (byte)0xDE, (byte)0x74, (byte)0xE3, (byte)0xCB, (byte)0x60, (byte)0x20, (byte)0x38, (byte)0x9C, (byte)0x21, (byte)0xC3, (byte)0xDC, (byte)0xC8, (byte)0xA2, (byte)0x4D, (byte)0xC6, (byte)0x2A, (byte)0x35, (byte)0x7F, (byte)0xF3, (byte)0xA9, (byte)0xE8, (byte)0x1D, (byte)0x7B, (byte)0x2C, (byte)0x78, (byte)0xFA, (byte)0xB8, (byte)0x02, (byte)0x55, (byte)0x80, (byte)0x9B, (byte)0xC2, (byte)0xA5, (byte)0xCB, }; BigInteger bi_p = new BigInteger(pseudoPrime1); BigInteger bi_q = new BigInteger(pseudoPrime2); BigInteger bi_pq = (bi_p - 1) * (bi_q - 1); BigInteger bi_n = bi_p * bi_q; for (int count = 0; count < rounds; count++) { // generate private and public key BigInteger bi_e = bi_pq.genCoPrime(512, rand); BigInteger bi_d = bi_e.modInverse(bi_pq); Console.WriteLine("\ne =\n" + bi_e.ToString(10)); Console.WriteLine("\nd =\n" + bi_d.ToString(10)); Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n"); // generate data of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 65); bool done = false; while (!done) { for (int i = 0; i < 64; i++) { if (i < t1) val[i] = (byte)(rand.NextDouble() * 256); else val[i] = 0; if (val[i] != 0) done = true; } } while (val[0] == 0) val[0] = (byte)(rand.NextDouble() * 256); Console.Write("Round = " + count); // encrypt and decrypt data BigInteger bi_data = new BigInteger(val, t1); BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n); BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n); // compare if (bi_decrypted != bi_data) { Console.WriteLine("\nError at round " + count); Console.WriteLine(bi_data + "\n"); return; } Console.WriteLine(" <PASSED>."); } } //*********************************************************************** // Tests the correct implementation of sqrt() method. //*********************************************************************** public static void SqrtTest(int rounds) { Random rand = new Random(); for (int count = 0; count < rounds; count++) { // generate data of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 1024); Console.Write("Round = " + count); BigInteger a = new BigInteger(); a.genRandomBits(t1, rand); BigInteger b = a.sqrt(); BigInteger c = (b + 1) * (b + 1); // check that b is the largest integer such that b*b <= a if (c <= a) { Console.WriteLine("\nError at round " + count); Console.WriteLine(a + "\n"); return; } Console.WriteLine(" <PASSED>."); } } }}using System;using System.Collections.Generic;using System.Linq;using System.Security.Cryptography;using System.Text;namespace RSATest{ /// <summary> /// 非对称RSA加密类 可以参考 /// http://www.cnblogs.com/hhh/archive/2011/06/03/2070692.html /// http://blog.csdn.net/zhilunchen/article/details/2943158 /// 若是私匙加密 则需公钥解密 /// 反正公钥加密 私匙来解密 /// 需要BigInteger类来辅助 /// </summary> public static class RSAHelper { /// <summary> /// RSA的容器 可以解密的源字符串长度为 DWKEYSIZE/8-11 /// </summary> public const int DWKEYSIZE = 1024; /// <summary> /// RSA加密的密匙结构 公钥和私匙 /// </summary> public struct RSAKey { public string PublicKey { get; set; } public string PrivateKey { get; set; } } #region 得到RSA的解谜的密匙对 /// <summary> /// 得到RSA的解谜的密匙对 /// </summary> /// <returns></returns> public static RSAKey GetRASKey() { RSACryptoServiceProvider.UseMachineKeyStore = true; //声明一个指定大小的RSA容器 RSACryptoServiceProvider rsaProvider = new RSACryptoServiceProvider(DWKEYSIZE); //取得RSA容易里的各种参数 RSAParameters p = rsaProvider.ExportParameters(true); return new RSAKey() { PublicKey = ComponentKey(p.Exponent,p.Modulus), PrivateKey = ComponentKey(p.D,p.Modulus) }; } #endregion #region 检查明文的有效性 DWKEYSIZE/8-11 长度之内为有效 中英文都算一个字符 /// <summary> /// 检查明文的有效性 DWKEYSIZE/8-11 长度之内为有效 中英文都算一个字符 /// </summary> /// <param name="source"></param> /// <returns></returns> public static bool CheckSourceValidate(string source) { return (DWKEYSIZE / 8 - 11) >= source.Length; } #endregion #region 组合解析密匙 /// <summary> /// 组合成密匙字符串 /// </summary> /// <param name="b1"></param> /// <param name="b2"></param> /// <returns></returns> private static string ComponentKey(byte[] b1, byte[] b2) { List<byte> list = new List<byte>(); //在前端加上第一个数组的长度值 这样今后可以根据这个值分别取出来两个数组 list.Add((byte)b1.Length); list.AddRange(b1); list.AddRange(b2); byte[] b = list.ToArray<byte>(); return Convert.ToBase64String(b); } /// <summary> /// 解析密匙 /// </summary> /// <param name="key">密匙</param> /// <param name="b1">RSA的相应参数1</param> /// <param name="b2">RSA的相应参数2</param> private static void ResolveKey(string key, out byte[] b1, out byte[] b2) { //从base64字符串 解析成原来的字节数组 byte[] b = Convert.FromBase64String(key); //初始化参数的数组长度 b1=new byte[b[0]]; b2=new byte[b.Length-b[0]-1]; //将相应位置是值放进相应的数组 for (int n = 1, i = 0, j = 0; n < b.Length; n++) { if (n <= b[0]) { b1[i++] = b[n]; } else { b2[j++] = b[n]; } } } #endregion #region 字符串加密解密 公开方法 /// <summary> /// 字符串加密 /// </summary> /// <param name="source">源字符串 明文</param> /// <param name="key">密匙</param> /// <returns>加密遇到错误将会返回原字符串</returns> public static string EncryptString(string source,string key) { string encryptString = string.Empty; byte[] d; byte[] n; try { if (!CheckSourceValidate(source)) { throw new Exception("source string too long"); } //解析这个密钥 ResolveKey(key, out d, out n); BigInteger biN = new BigInteger(n); BigInteger biD = new BigInteger(d); encryptString= EncryptString(source, biD, biN); } catch { encryptString = source; } return encryptString; } /// <summary> /// 字符串解密 /// </summary> /// <param name="encryptString">密文</param> /// <param name="key">密钥</param> /// <returns>遇到解密失败将会返回原字符串</returns> public static string DecryptString(string encryptString, string key) { string source = string.Empty; byte[] e; byte[] n; try { //解析这个密钥 ResolveKey(key, out e, out n); BigInteger biE = new BigInteger(e); BigInteger biN = new BigInteger(n); source = DecryptString(encryptString, biE, biN); } catch { source = encryptString; } return source; } #endregion #region 字符串加密解密 私有 实现加解密的实现方法 /// <summary> /// 用指定的密匙加密 /// </summary> /// <param name="source">明文</param> /// <param name="d">可以是RSACryptoServiceProvider生成的D</param> /// <param name="n">可以是RSACryptoServiceProvider生成的Modulus</param> /// <returns>返回密文</returns> private static string EncryptString(string source, BigInteger d, BigInteger n) { int len = source.Length; int len1 = 0; int blockLen = 0; if ((len % 128) == 0) len1 = len / 128; else len1 = len / 128 + 1; string block = ""; StringBuilder result = new StringBuilder(); for (int i = 0; i < len1; i++) { if (len >= 128) blockLen = 128; else blockLen = len; block = source.Substring(i * 128, blockLen); byte[] oText = System.Text.Encoding.Default.GetBytes(block); BigInteger biText = new BigInteger(oText); BigInteger biEnText = biText.modPow(d, n); string temp = biEnText.ToHexString(); result.Append(temp).Append("@"); len -= blockLen; } return result.ToString().TrimEnd('@'); } /// <summary> /// 用指定的密匙加密 /// </summary> /// <param name="source">密文</param> /// <param name="e">可以是RSACryptoServiceProvider生成的Exponent</param> /// <param name="n">可以是RSACryptoServiceProvider生成的Modulus</param> /// <returns>返回明文</returns> private static string DecryptString(string encryptString, BigInteger e, BigInteger n) { StringBuilder result = new StringBuilder(); string[] strarr1 = encryptString.Split(new char[] { '@' }, StringSplitOptions.RemoveEmptyEntries); for (int i = 0; i < strarr1.Length; i++) { string block = strarr1[i]; BigInteger biText = new BigInteger(block, 16); BigInteger biEnText = biText.modPow(e, n); string temp = System.Text.Encoding.Default.GetString(biEnText.getBytes()); result.Append(temp); } return result.ToString(); } #endregion }}测试程序：
using System;using System.Collections.Generic;using System.Linq;using System.Text;namespace RSATest{ class Program { static void Main(string[] args) { string str = "{\"sc\":\"his51\",\"no\":\"1\",\"na\":\"管理员\"}{\"sc\":\"@his51\",\"no\":\"1\",\"na\":\"管理员\"}{\"sc\":\"his51\",\"no\":\"1\",\"na\":\"管员\"}{\"sc\":\"his522"; RSAHelper.RSAKey keyPair = RSAHelper.GetRASKey(); Console.WriteLine("加密前："+str+"\r\n"); Console.WriteLine("公钥:" + keyPair.PublicKey + "\r\n"); Console.WriteLine("私钥:" + keyPair.PrivateKey + "\r\n"); string en = RSAHelper.EncryptString(str, keyPair.PrivateKey); Console.WriteLine("加密后："+en + "\r\n"); Console.WriteLine("解密："+RSAHelper.DecryptString(en, keyPair.PublicKey) + "\r\n"); Console.ReadLine(); } }} 0 0
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