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Use Decaf448 specific addition algorithm #1314

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44 changes: 5 additions & 39 deletions ed448-goldilocks/src/curve/twedwards/extended.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -80,11 +80,11 @@ impl ExtendedPoint {
/// Returns an extensible point
/// (3.1) https://iacr.org/archive/asiacrypt2008/53500329/53500329.pdf
pub fn add_extended(&self, other: &ExtendedPoint) -> ExtensiblePoint {
let A = self.X * other.X;
let B = self.Y * other.Y;
let C = self.T * other.T * FieldElement::TWISTED_D;
let D = self.Z * other.Z;
let E = (self.X + self.Y) * (other.X + other.Y) - A - B;
let A = (self.Y - self.X) * (other.Y - other.X);
let B = (self.Y + self.X) * (other.Y + other.X);
let C = FieldElement::TWO_TIMES_TWISTED_D * self.T * other.T;
let D = (self.Z * other.Z).double();
let E = B - A;
let F = D - C;
let G = D + C;
let H = B + A;
Expand All @@ -97,27 +97,6 @@ impl ExtendedPoint {
}
}

/// Subtracts an extensible point from an extended point
/// Returns an extensible point
/// This is a direct modification of the addition formula to the negation of `other`
pub fn sub_extended(&self, other: &ExtendedPoint) -> ExtensiblePoint {
let A = self.X * other.X;
let B = self.Y * other.Y;
let C = self.T * other.T * FieldElement::TWISTED_D;
let D = self.Z * other.Z;
let E = (self.X + self.Y) * (other.Y - other.X) + A - B;
let F = D + C;
let G = D - C;
let H = B - A;
ExtensiblePoint {
X: E * F,
Y: G * H,
T1: E,
T2: H,
Z: F * G,
}
}

/// Adds an extensible point to an AffineNiels point
/// Returns an Extensible point
pub fn add_affine_niels(&self, other: AffineNielsPoint) -> ExtensiblePoint {
Expand Down Expand Up @@ -297,19 +276,6 @@ mod tests {
assert!(c == c_1);
}

#[test]
fn test_point_sub() {
let a = TWISTED_EDWARDS_BASE_POINT;
let b = a.to_extensible().double().to_extended();

// A - B = C
let c_1 = a.sub_extended(&b).to_extended();

// -B + A = C
let c_2 = b.negate().add_extended(&a).to_extended();
assert!(c_1 == c_2);
}

#[test]
fn test_negate() {
let a = TWISTED_EDWARDS_BASE_POINT;
Expand Down
2 changes: 1 addition & 1 deletion ed448-goldilocks/src/decaf/ops.rs
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Expand Up @@ -101,7 +101,7 @@ impl Sub<&DecafPoint> for &DecafPoint {
type Output = DecafPoint;

fn sub(self, other: &DecafPoint) -> DecafPoint {
DecafPoint(self.0.sub_extended(&other.0).to_extended())
DecafPoint(self.0.add_extended(&other.0.negate()).to_extended())
}
}

Expand Down
2 changes: 1 addition & 1 deletion ed448-goldilocks/src/decaf/points.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -320,7 +320,7 @@ impl DecafPoint {

/// Subtract two points
pub fn sub(&self, other: &DecafPoint) -> DecafPoint {
DecafPoint(self.0.sub_extended(&other.0).to_extended())
DecafPoint(self.0.add_extended(&other.0.negate()).to_extended())
}

/// Compress this point
Expand Down