public BigIntegerPoint SummarizePoints(BigIntegerPoint first, BigIntegerPoint second)
{
if (first.X == 0 && first.Y == 0)
{
return(second);
}
if (first.X == 0 && second.Y == 0)
{
return(first);
}
if (first.X == second.X && (first.X == 0 || first.Y != second.Y))
{
return(new BigIntegerPoint(0, 0));
}
BigInteger numerator;
BigInteger denominator;
if (first.X != second.X)
{
numerator = second.Y ^ first.Y;
denominator = second.X ^ first.X;
}
else
{
numerator = PolynominalService.MultiplyPolynominal(first.X, first.X) ^
PolynominalService.MultiplyPolynominal(A, first.Y);
denominator = PolynominalService.MultiplyPolynominal(first.X, A);
}
denominator = PolynominalService.InversePolynominal(denominator, Polynome);
var k = PolynominalService.MultiplyPolynominal(numerator, denominator);
k = PolynominalService.ModPolynominal(k, Polynome);
var x = PolynominalService.MultiplyPolynominal(k, k);
x ^= PolynominalService.MultiplyPolynominal(A, k);
x ^= B;
if (first.X != second.X)
{
x ^= first.X;
x ^= second.X;
}
x = PolynominalService.ModPolynominal(x, Polynome);
var y = x ^ first.X;
y = PolynominalService.MultiplyPolynominal(y, k);
y ^= first.Y;
y ^= PolynominalService.MultiplyPolynominal(A, x);
y = PolynominalService.ModPolynominal(y, Polynome);
return(new BigIntegerPoint(x, y));
}
public BigIntegerPoint MultiplyPointByNumber(BigIntegerPoint point, BigInteger number)
{
var newPoint = new BigIntegerPoint(point.X, point.Y);
var binaryNumber = number.ToBinaryString();
foreach (var bit in binaryNumber.Substring(2))
{
newPoint = SummarizePoints(newPoint, newPoint);
if (bit == '1')
{
newPoint = SummarizePoints(newPoint, point);
}
}
return(newPoint);
}
public BigIntegerPoint SummarizePoints(BigIntegerPoint first, BigIntegerPoint second)
{
if (first.X == second.X && first.Y == second.Y)
{
return(new BigIntegerPoint(0, 0));
}
BigInteger numerator;
BigInteger denominator;
if (first.X != second.X)
{
numerator = second.Y ^ first.Y;
denominator = second.X ^ first.X;
}
else
{
numerator = PolynominalService.MultiplyPolynominal(first.X, second.X);
numerator ^= B;
denominator = A;
}
denominator = PolynominalService.InversePolynominal(denominator, Polynome);
var k = PolynominalService.MultiplyPolynominal(numerator, denominator);
k = PolynominalService.ModPolynominal(k, Polynome);
var x = PolynominalService.MultiplyPolynominal(k, k);
if (first.X != second.X)
{
x ^= first.X;
x ^= second.X;
}
x = PolynominalService.ModPolynominal(x, Polynome);
var y = first.X ^ x;
y = PolynominalService.MultiplyPolynominal(y, k);
y ^= first.Y;
y ^= A;
y = PolynominalService.ModPolynominal(y, Polynome);
return(new BigIntegerPoint(x, y));
}
public BigIntegerPoint SummarizePoints(BigIntegerPoint first, BigIntegerPoint second)
{
BigInteger k = 0;
if (first.X != second.X)
{
k = (second.Y - first.Y) * MulInv(second.X - first.X, P);
}
else
{
k = (3 * first.X * first.X + A) * MulInv(2 * first.Y, P);
}
var d = first.Y - k * first.X;
var newX = k * k - first.X - second.X;
return(new BigIntegerPoint(newX.Mod(P), (-(k * newX + d)).Mod(P)));
}