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Add optimized Edwards addition and doubling algorithms #1313

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Add optimized Edwards addition and doubling algorithms #1313

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60 changes: 30 additions & 30 deletions ed448-goldilocks/src/edwards/extended.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -597,41 +597,41 @@ impl EdwardsPoint {
}

/// Add two points
//https://iacr.org/archive/asiacrypt2008/53500329/53500329.pdf (3.1)
// These formulas are unified, so for now we can use it for doubling. Will refactor later for speed
// (3.1) https://iacr.org/archive/asiacrypt2008/53500329/53500329.pdf
pub fn add(&self, other: &EdwardsPoint) -> Self {
let aXX = self.X * other.X; // aX1X2
let dTT = FieldElement::EDWARDS_D * self.T * other.T; // dT1T2
let ZZ = self.Z * other.Z; // Z1Z2
let YY = self.Y * other.Y;

let X = {
let x_1 = (self.X * other.Y) + (self.Y * other.X);
let x_2 = ZZ - dTT;
x_1 * x_2
};
let Y = {
let y_1 = YY - aXX;
let y_2 = ZZ + dTT;
y_1 * y_2
};

let T = {
let t_1 = YY - aXX;
let t_2 = (self.X * other.Y) + (self.Y * other.X);
t_1 * t_2
};

let Z = { (ZZ - dTT) * (ZZ + dTT) };

EdwardsPoint { X, Y, Z, T }
let A = self.X * other.X;
let B = self.Y * other.Y;
let C = self.T * other.T * FieldElement::EDWARDS_D;
let D = self.Z * other.Z;
let E = (self.X + self.Y) * (other.X + other.Y) - A - B;
let F = D - C;
let G = D + C;
let H = B - A;
Self {
X: E * F,
Y: G * H,
Z: F * G,
T: E * H,
}
}

/// Double this point
// XXX: See comment on addition, the formula is unified, so this will do for now
//https://iacr.org/archive/asiacrypt2008/53500329/53500329.pdf (3.1)
// (3.3) https://iacr.org/archive/asiacrypt2008/53500329/53500329.pdf
pub fn double(&self) -> Self {
self.add(self)
let A = self.X.square();
let B = self.Y.square();
let C = self.Z.square().double();
let D = A;
let E = (self.X + self.Y).square() - A - B;
let G = D + B;
let F = G - C;
let H = D - B;
Self {
X: E * F,
Y: G * H,
Z: F * G,
T: E * H,
}
}

/// Check if this point is on the curve
Expand Down