//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//Convertations
//Format the polyValue to the classic polynom-looking string (x^a + x^b + ...)
public static string ToPolyString(this BigInteger num)
{
StringBuilder bld = new StringBuilder();
//Go thru given num and check for the bit set, and format the string for each iteration
for (int i = num.GetBitLength(); i >= 0; i--)
{
if (num.CheckBit(i))
{
if (bld.Length > 0)
{
bld.Append(" + ");
}
bld.Append((i > 0) ? "x" : "1");
if (i > 1)
{
bld.Append("^");
bld.Append(i);
}
}
}
if (bld.Length == 0)
{
bld.Append("0");
}
return(bld.ToString());
}
//Operator *. Represents multiplication of two finite field polynoms using modified AncientEgyptian/Russian peasant multiplication method.
//It decomposes one of the multiplicands (preferably the smaller) into a sum of powers of two and creates a table of doublings
//of the second multiplicand. This method may be called mediation and duplation, where mediation means halving one number,
//and duplation means doubling the other number.
public static FFPolynom operator *(FFPolynom left, FFPolynom right)
{
//Invariant is (b * a + p) is product. Continue to 2*a and taking b/2.
//If b is odd number => calculate a + p
BigInteger a = left._polynomCoefficients;
BigInteger b = right._polynomCoefficients;
BigInteger product = BigInteger.Zero; //p
//Degree is a length of the entered phrase in bytes * 8
int degree = left.PrimePolynom.Degree;
//Shift a BigInt value a specified number of bits to the left (preserves the sign)
//"BigInteger.One << degree" means 1 * 2^degree
//- BigInteger.One means to invert all bits
// 2^degree -1 => length in bits w/o sign
BigInteger mask = (BigInteger.One << degree) - BigInteger.One;
for (int i = 0; i < degree; i++)
{
if ((a == BigInteger.Zero) || (b == BigInteger.Zero))
{
break;
}
//Take lowest bit of b, and check if it set meaning b is odd
if (b.CheckBit(0))
{
//b odd, do a + product
product = product ^ a;
}
//Check if the highest bit set for a
bool isHighBitSet = a.CheckBit(degree - 1);
a = a << 1; // a*2
a = a & mask; // remove the highest bit
if (isHighBitSet)
{
a = a ^ left.PrimePolynom.PolynomValue;
a = a & mask;
}
b = b >> 1; // b/2
}
product = product & mask;
return(new FFPolynom(left.PrimePolynom, product));
}