/// <summary>
/// M.
/// Computes x to the power of y at mod z.
/// </summary>
/// <returns></returns>
public static BigNum Power(BigNum x, BigNum y, BigNum z)
{
BigNum result = new BigNum();
if (y.CompNumWithoutPrint(GlobalVariables.zero))
{
result = new BigNum(GlobalVariables.one);
}
else
{
if (y.IsEven())
{
// x^y = [x^(y/2)]^2 mod z.
BigNum yDividedBy2 = new BigNum();
DivNum(y, GlobalVariables.two, yDividedBy2, result); // y = y/2.
result = Power(x, yDividedBy2, z);
result.MultNum(new BigNum(result));
DivNum(result, z, new BigNum(), result);
}
else
{
BigNum yMinus1DividedBy2 = new BigNum(y);
yMinus1DividedBy2.SubNum(GlobalVariables.one); // y = y-1.
DivNum(y, GlobalVariables.two, yMinus1DividedBy2, result); // y = y-1/2.
result = Power(x, yMinus1DividedBy2, z);
result.MultNum(new BigNum(result));
DivNum(result, z, new BigNum(), result);
result.MultNum(x);
DivNum(result, z, new BigNum(), result);
}
}
return(result);
}
/// <summary>
/// Gets a number m.
/// Finds p >= 0 and k (k is odd), where m = 2^p * k.
/// Return p and k by ref.
///
/// p = 0;
/// if (!IsEven(m))
/// {
/// k = m;
/// }
/// else // m is even.
/// {
/// while(IsEven(m))
/// {
/// m /= 2;
/// p++;
/// }
/// k = m;
/// }
/// </summary>
/// <param name=""></param>
/// <param name=""></param>
public static void FindExpressionOfGivenNumberByPowerOfTwoTimesOddNumber(BigNum m, BigNum p, BigNum k)
{
if (!m.IsEven())
{
k.Set(m);
}
else
{
while (m.IsEven())
{
DivNum(m, GlobalVariables.two, m, new BigNum());
p.AddNum(GlobalVariables.one);
}
k.Set(m);
}
}