public ProjectiveEdwardsCurve(BigInteger parameterD, BigInteger fieldOrder)
{
ParameterD = parameterD;
FieldOrder = fieldOrder;
NeitralPoint = new ProjectiveEdwardsCurvePoint(0, 1, 1, this);
}
private (BigInteger, BigInteger, BigInteger) AdvancedCalc(ProjectiveEdwardsCurvePoint point1,
ProjectiveEdwardsCurvePoint point2)
{
var x1 = point1.ParameterX;
var x2 = point2.ParameterX;
var y1 = point1.ParameterY;
var y2 = point2.ParameterY;
var z1 = point1.ParameterZ;
var z2 = point2.ParameterZ;
var parameterD = point1.ProjectiveEdwardsCurve.ParameterD;
var a = z1 * z2;
var b = a * a;
var c = x1 * x2;
var d = y1 * y2;
var e = parameterD * c * d;
var f = b - e;
var g = b + e;
var xSum = a * f * ((x1 + y1) * (x2 + y2) - c - d);
var ySum = a * g * (d - c);
var zSum = 1 * f * g;
return(xSum, ySum, zSum);
}
/// <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 ProjectiveEdwardsCurvePoint Sum(ProjectiveEdwardsCurvePoint point1, ProjectiveEdwardsCurvePoint point2)
{
if (point1.ProjectiveEdwardsCurve != point2.ProjectiveEdwardsCurve)
{
throw new InvalidOperationException("It's not allowed to sum points of two different curves");
}
var(xSum, ySum, zSum) = AdvancedCalc(point1, point2);
return(new ProjectiveEdwardsCurvePoint(xSum, ySum, zSum, point1.ProjectiveEdwardsCurve));
}
public ProjectiveEdwardsCurvePoint Mult(BigInteger k, ProjectiveEdwardsCurvePoint p)
{
if (k.IsZero)
{
throw new Exception("Попытка умножить на 0");
}
var b = p;
var q = ((ProjectiveEdwardsCurve)p.ProjectiveEdwardsCurve).NeitralPoint;
while (!k.IsZero)
{
if (k % 2 == 1)
{
q = Sum(q, b);
}
b = Sum(b, b);
k /= 2;
}
return(q);
}
