The type of the element in the elliptic curve

The size of a point representation, in bytes

Create an empty value to store an element of the curve. DO NOT USE THIS TO DO COMPUTATIONS WITH, UNDEFINED BEHAVIORS MAY HAPPEN

Check if a point, represented as a byte array, is on the curve *

Attempt to construct a point from a byte array of length size_in_bytes.

Attempt to construct a point from a byte array of length size_in_bytes. Raise Not_on_curve if the point is not on the curve

Allocates a new point from a byte of length size_in_bytes / 2 array representing a point in compressed form.

Allocates a new point from a byte array of length size_in_bytes / 2 representing a point in compressed form. Raise Not_on_curve if the point is not on the curve.

Return a representation in bytes

Return a compressed bytes representation

Zero of the elliptic curve

A fixed generator of the elliptic curve

Return true if the given element is zero

Generate a random element. The element is on the curve and in the prime subgroup.

Return the addition of two element

double g returns 2g

Return the opposite of the element

Return true if the two elements are algebraically the same

Multiply an element by a scalar

fft ~domain ~points performs a Fourier transform on points using domain The domain should be of the form w^{i} where w is a principal root of unity. If the domain is of size n, w must be a n-th principal root of unity. The number of points can be smaller than the domain size, but not larger. The complexity is in O(n log(m)) where n is the domain size and m the number of points.

ifft ~domain ~points performs an inverse Fourier transform on points using domain. The domain should be of the form w^{-i} (i.e the "inverse domain") where w is a principal root of unity. If the domain is of size n, w must be a n-th principal root of unity. The domain size must be exactly the same than the number of points. The complexity is O(n log(n)) where n is the domain size.