Module elliptic_curve_functions

Elliptic curve functions

This module defines jets that replicate the functional behavior of (a specific version of) libsecp256k1’s elliptic curve operations https://github.com/bitcoin-core/secp256k1/tree/v0.3.0. The functions defined here return precisely the same field and point representatives that the corresponding libsecp256k1’s functions do, with a few exceptions with the way the point at infinity is handled.

Functions

decompress

Decompress a point into affine coordinates.

fe_add

Add two field elements.

fe_invert

Compute the modular inverse of a field element.

fe_is_odd

Check if the canonical representative of the field element is odd.

fe_is_zero

Check if the field element represents zero.

fe_multiply

Multiply two field elements.

fe_multiply_beta

Multiply a field element by the canonical primitive cube root of unity (beta).

fe_negate

Negate a field element.

fe_normalize

Return the canonical representation of a field element.

fe_square

Square a field element.

fe_square_root

Compute the modular square root of a field element if it exists.

ge_is_on_curve

Check if the given point satisfies the curve equation y² = x³ + 7.

ge_negate

Negate a point.

gej_add

Add two points.

gej_double

Double a point. If the result is the point at infinity, it is returned in canonical form.

gej_equiv

Check if two points represent the same point.

gej_ge_add

Add two points. If the result is the point at infinity, it is returned in canonical form.

gej_ge_add_ex

Add two points. Also return the ration of the as z-coordinate and the result’s z-coordinate. If the result is the point at infinity, it is returned in canonical form.

gej_ge_equiv

Check if two points represent the same point.

gej_infinity

Return the canonical representation of the point at infinity.

gej_is_infinity

Check if the point represents infinity.

gej_is_on_curve

Check if the given point satisfies the curve equation y² = x³ + 7.

gej_negate

Negate a point.

gej_normalize

Convert the point into affine coordinates with canonical field representatives. If the result is the point at infinity, it is returned in canonical form.

gej_rescale

Change the representatives of a point by multiplying the z-coefficient by the given value.

gej_x_equiv

Check if the point represents an affine point with the given x-coordinate.

gej_y_is_odd

Check if the point represents an affine point with odd y-coordinate.

generate

Multiply the generator point with the given scalar.

hash_to_curve

A cryptographic hash function that results in a point on the secp256k1 curve.

linear_combination_1

Compute the linear combination b * a + c * g for point b and scalars a and c, where g is the generator point.

linear_verify_1

Assert that a point b is equal to the linear combination a.0 * a.1 + a.2 * g, where g is the generator point.

point_verify_1

Assert that a point b is equal to the linear combination a.0 * a.1 + a.2 * g, where g is the generator point.

scalar_add

Add two scalars.

scalar_invert

Compute the modular inverse of a scalar.

scalar_is_zero

Check if the scalar represents zero.

scalar_multiply

Multiply two scalars.

scalar_multiply_lambda

Multiply a scalar with the canonical primitive cube of unity (lambda)

scalar_negate

Negate a scalar.

scalar_normalize

Return the canonical representation of the scalar.

scalar_square

Square a scalar.

scale

Multiply a point by a scalar.

swu

Algebraically distribute a field element over the secp256k1 curve as defined in “Indifferentiable Hashing to Barreto-Naehrig Curves” by Pierre-Alain Fouque, Mehdi Tibouchi.