garaga-rs / wasm - Implement Twisted Edwards to Weirstrass bijection for point representation

[feltroidprime]

Using the reference formulas in

garaga/hydra/garaga/definitions.py

Lines 196 to 221 in 7e16413

	def to_weierstrass(self, x_twisted, y_twisted):
	a = self.a_twisted
	d = self.d_twisted
	return (
	(5 * a + a * y_twisted - 5 * d * y_twisted - d)
	* pow(12 - 12 * y_twisted, -1, self.p)
	% self.p,
	(a + a * y_twisted - d * y_twisted - d)
	* pow(4 * x_twisted - 4 * x_twisted * y_twisted, -1, self.p)
	% self.p,
	)
	def to_twistededwards(self, x_weirstrass: int, y_weirstrass: int):
	a = self.a_twisted
	d = self.d_twisted
	y = (
	(5 * a - 12 * x_weirstrass - d)
	* pow(-12 * x_weirstrass - a + 5 * d, -1, self.p)
	% self.p
	)
	x = (
	(a + a * y - d * y - d)
	* pow(4 * y_weirstrass - 4 * y_weirstrass * y, -1, self.p)
	% self.p
	)
	return (x, y)

implement in tools/garaga-rs/definitions.rs the two conversion function

• to_weirstrass(x:X25519PrimeField, y: X25519PrimeField)- > (X25519PrimeField, X25519PrimeField)
• to_twisted(x:X25519PrimeField, y:X25519PrimeField) -> (X25519PrimeField, X25519PrimeField)

Test them simply similarly to

garaga/tests/hydra/test_g1_point.py

Lines 16 to 26 in 7e16413

	def test_weierstrass_to_twistededwards_and_back(curve_id):
	curve: TwistedEdwardsCurve = CURVES[curve_id.value]
	# Define a point in Weierstrass form
	x_weierstrass = curve.Gx
	y_weierstrass = curve.Gy
	x_twisted, y_twisted = curve.to_twistededwards(x_weierstrass, y_weierstrass)
	x_weierstrass_back, y_weierstrass_back = curve.to_weierstrass(x_twisted, y_twisted)
	assert x_weierstrass == x_weierstrass_back
	assert y_weierstrass == y_weierstrass_back

using the generator point Gx, Gy.

Then, create a wasm binding for it and add it to the npm package.