internal static ProjectivePoint Identity()
{
return(new ProjectivePoint
{
X = FieldElement51.Zero(),
Y = FieldElement51.One(),
Z = FieldElement51.One()
});
}
/// Compress this point using the Ristretto encoding.
public CompressedRistretto Compress()
{
var invsqrt =
new Func <FieldElement51, (bool, FieldElement51)>((el) => {
return(FieldElement51.SqrtRatioI(FieldElement51.One(), el));
});
var X = Ep.X;
var Y = Ep.Y;
var Z = Ep.Z;
var T = Ep.T;
var u1 = Z.Add(Y).Mul(Z.Sub(Y));
var u2 = X.Mul(Y);
// Ignore return value since this is always square
var inv = invsqrt(u1.Mul(u2.Square()));
var i1 = inv.Item2.Mul(u1);
var i2 = inv.Item2.Mul(u2);
var z_inv = i1.Mul(i2.Mul(T));
var den_inv = i2;
var iX = X.Mul(Consts.SQRT_M1);
var iY = Y.Mul(Consts.SQRT_M1);
var ristretto_magic = (Consts.INVSQRT_A_MINUS_D);
var enchanted_denominator = i1.Mul(ristretto_magic);
var rotate = T.Mul(z_inv).IsNegative();
X.ConditionalAssign(iY, rotate);
Y.ConditionalAssign(iX, rotate);
den_inv.ConditionalAssign(enchanted_denominator, rotate);
Y.ConditionalNegate(X.Mul(z_inv).IsNegative());
var s = den_inv.Mul(Z.Sub(Y));
var s_is_negative = s.IsNegative();
s.ConditionalNegate(s_is_negative);
return(new CompressedRistretto(s.ToBytes()));
}
internal static EdwardsPoint Decompress(byte[] bytes)
{
var invsqrt =
new Func <FieldElement51, (bool, FieldElement51)>((el) => {
return(FieldElement51.SqrtRatioI(FieldElement51.One(), el));
});
var s = FieldElement51.FromBytes(bytes);
// Step 2. Compute (X:Y:Z:T).
var one = FieldElement51.One();
var ss = s.Square();
var u1 = one - ss; // 1 + as²
var u2 = one + ss; // 1 - as² where a=-1
var u2_sqr = u2.Square(); // (1 - as²)²
// v == ad(1+as²)² - (1-as²)² where d=-121665/121666
var nEdwardsD = Consts.EDWARDS_D.Negate();
var v = nEdwardsD * u1.Square() - u2_sqr;
var I = invsqrt(v * u2_sqr); // 1/sqrt(v*u_2²)
var Dx = I.Item2 * u2; // 1/sqrt(v)
var Dy = I.Item2 * Dx * v; // 1/u2
// x == | 2s/sqrt(v) | == + sqrt(4s²/(ad(1+as²)² - (1-as²)²))
var x = (s + s) * Dx;
var x_neg = x.IsNegative();
x.ConditionalNegate(x_neg);
// y == (1-as²)/(1+as²)
var y = u1 * Dy;
// t == ((1+as²) sqrt(4s²/(ad(1+as²)² - (1-as²)²)))/(1-as²)
var t = x * y;
return(new EdwardsPoint(x, y, one, t));
}
public AffineNielsPoint()
{
Y_plus_X = FieldElement51.One();
Y_minus_X = FieldElement51.One();
XY2d = FieldElement51.Zero();
}