public AffineEdwardsCurve(BigInteger parameterD, BigInteger fieldOrder)
{
ParameterD = parameterD;
FieldOrder = fieldOrder;
NeitralPoint = new AffineEdwardsCurvePoint(0, 1, this);
}
/// <summary> Sum two points of the same curve </summary>
/// <param name="point1">First point</param>
/// <param name="point2">Second point</param>
/// <returns>Sum point</returns>
/// <exception cref="InvalidOperationException">If points belong to different curves</exception>
public AffineEdwardsCurvePoint Sum(AffineEdwardsCurvePoint point1, AffineEdwardsCurvePoint point2)
{
if (point1.EdwardsCurve != point2.EdwardsCurve)
{
throw new InvalidOperationException("It's not allowed to sum points of two different curves");
}
var(xSum, ySum) = CalcSum(point1, point2);
return(new AffineEdwardsCurvePoint(xSum, ySum, point1.EdwardsCurve));
}
public AffineEdwardsCurvePoint Mult(BigInteger k, AffineEdwardsCurvePoint p)
{
if (k.IsZero)
{
throw new Exception("Попытка умножить на 0");
}
var b = p;
var q = ((AffineEdwardsCurve)p.EdwardsCurve).NeitralPoint;
while (!k.IsZero)
{
if (k % 2 == 1)
{
q = Sum(q, b);
}
b = Sum(b, b);
k /= 2;
}
return(q);
}
private (BigInteger xSum, BigInteger ySum) CalcSum(AffineEdwardsCurvePoint point1,
AffineEdwardsCurvePoint point2)
{
var x1 = point1.ParameterX;
var x2 = point2.ParameterX;
var y1 = point1.ParameterY;
var y2 = point2.ParameterY;
var d = point1.EdwardsCurve.ParameterD;
var znam = d * x1 * x2 * y1 * y2;
var fieldOrder = point1.EdwardsCurve.FieldOrder;
var znam1 = (1 + znam).Mod(fieldOrder).Inverse(fieldOrder).Mod(fieldOrder);
var znam2 = (1 - znam).Mod(fieldOrder).Inverse(fieldOrder).Mod(fieldOrder);
var chisl1 = x1 * y2 + y1 * x2;
var chisl2 = y1 * y2 - x1 * x2;
var xSum = chisl1 * znam1;
return(xSum, chisl2 *znam2);
}