//***********************************************************************
// 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
var constant = new BigInteger(0);
int i = n.Length << 1;
constant.Data[i] = 0x00000001;
constant.Length = i + 1;
constant.Divide(n);
//constant /= n;
int totalBits = exp.bitCount();
int count = 0;
var temp = new BigInteger(0);
// perform squaring and multiply exponentiation
for (var pos = 0; pos < exp.Length; pos++)
{
uint mask = 0x01;
//Console.WriteLine("pos = " + pos);
for (var index = 0; index < 32; index++)
{
if ((exp.Data[pos] & mask) != 0)
{
BarrettReduction(ref resultNum, tempNum, n, constant, ref temp);
}
mask <<= 1;
BarrettReduction(ref tempNum, tempNum, n, constant, ref temp);
if (tempNum.Length == 1 && tempNum.Data[0] == 1)
{
if (thisNegative && (exp.Data[0] & 0x1) != 0) //odd exp
{
resultNum.Negative();
}
return(resultNum);
}
count++;
if (count == totalBits)
{
break;
}
}
}
constant.Recycle();
temp.Recycle();
if (thisNegative && (exp.Data[0] & 0x1) != 0) //odd exp
{
resultNum.Negative();
}
return(resultNum);
}
public static void Multiply(BigInteger bi1, BigInteger bi2, ref BigInteger result)
{
const 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) { }
result.Clear();
// multiply the absolute values
try
{
for (int i = 0; i < bi1.Length; i++)
{
if (bi1.Data[i] == 0)
{
continue;
}
ulong mcarry = 0;
for (int j = 0, k = i; j < bi2.Length; 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;
mcarry = (val >> 32);
}
if (mcarry != 0)
{
result.Data[i + bi2.Length] = (uint)mcarry;
}
}
}
catch (Exception)
{
throw (new ArithmeticException("Multiplication overflow."));
}
result.Length = bi1.Length + bi2.Length;
if (result.Length > maxLength)
{
result.Length = maxLength;
}
while (result.Length > 1 && result.Data[result.Length - 1] == 0)
{
result.Length--;
}
// 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.Length == 1)
{
return;
}
else
{
bool isMaxNeg = true;
for (int i = 0; i < result.Length - 1 && isMaxNeg; i++)
{
if (result.Data[i] != 0)
{
isMaxNeg = false;
}
}
if (isMaxNeg)
{
return;
}
}
}
throw (new ArithmeticException("Multiplication overflow."));
}
// if input has different signs, then result is -ve
if (bi1Neg != bi2Neg)
{
result.Negative();
}
return;
}
public static void Multiply(BigInteger bi1, BigInteger bi2,ref BigInteger result)
{
const 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) { }
result.Clear();
// multiply the absolute values
try
{
for (int i = 0; i < bi1.Length; i++)
{
if (bi1.Data[i] == 0) continue;
ulong mcarry = 0;
for (int j = 0, k = i; j < bi2.Length; 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;
mcarry = (val >> 32);
}
if (mcarry != 0)
result.Data[i + bi2.Length] = (uint)mcarry;
}
}
catch (Exception)
{
throw (new ArithmeticException("Multiplication overflow."));
}
result.Length = bi1.Length + bi2.Length;
if (result.Length > maxLength)
result.Length = maxLength;
while (result.Length > 1 && result.Data[result.Length - 1] == 0)
result.Length--;
// 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.Length == 1)
return;
else
{
bool isMaxNeg = true;
for (int i = 0; i < result.Length - 1 && isMaxNeg; i++)
{
if (result.Data[i] != 0)
isMaxNeg = false;
}
if (isMaxNeg)
return;
}
}
throw (new ArithmeticException("Multiplication overflow."));
}
// if input has different signs, then result is -ve
if (bi1Neg != bi2Neg) result.Negative();
return;
}