From d6fb0646531172f23648441c224cdcccd721b894 Mon Sep 17 00:00:00 2001
From: xm <1271024303@qq.com>
Date: 星期一, 14 十二月 2020 09:59:01 +0800
Subject: [PATCH] 请合并代码，完成晾衣架最终功能。
---
ZigbeeApp/Shared/Phone/ZigBee/Common/BigInteger.cs | 3126 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
1 files changed, 3,126 insertions(+), 0 deletions(-)
diff --git a/ZigbeeApp/Shared/Phone/ZigBee/Common/BigInteger.cs b/ZigbeeApp/Shared/Phone/ZigBee/Common/BigInteger.cs
new file mode 100755
index 0000000..6e96ac4
--- /dev/null
+++ b/ZigbeeApp/Shared/Phone/ZigBee/Common/BigInteger.cs
@@ -0,0 +1,3126 @@
+锘縰sing System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+namespace ZigBee.Common
+{
+ 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>.");
+ }
+ }
+ }
+}
--
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