Module point_edwards 

Point representation and group law for Edwards curves.

A single EdwardsPoint<F> type handles both odd and even characteristic via runtime dispatch on $F::characteristic()$.

Odd characteristic

The curve is given by

$$ x^2 + y^2 = 1 + d x^2 y^2 $$

• Identity: $(0, 1)$
• Negation: $-(x, y) = (-x, y)$
• Addition:

$$ x_3 = \frac{x_1 y_2 + y_1 x_2}{1 + d x_1 x_2 y_1 y_2}, \quad y_3 = \frac{y_1 y_2 - x_1 x_2}{1 - d x_1 x_2 y_1 y_2} $$

Characteristic $2$

The curve is given by

$$ d_1(x + y) + d_2(x^2 + y^2) = xy + xy(x + y) + x^2 y^2 $$

• Identity: $(0, 0)$
• Negation: $-(x, y) = (y, x)$
• Addition: Bernstein–Lange–Rezaeian Farashahi §3 formulas (strongly unified — works for doubling too)

Structs

EdwardsPoint

An affine point on an Edwards curve, for any characteristic.