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.