package bls12-381

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in-package search v0.2.0

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include Bls12_381_gen.Elliptic_curve_sig.T with type Scalar.t = Fr.t

exception Not_on_curve of Stdlib.Bytes.t

type t

The type of the element in the elliptic curve

val size_in_bytes : int

The size of a point representation, in bytes

module Scalar : Ff_sig.PRIME with type t = Fr.t

val empty : unit -> t

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

val check_bytes : Stdlib.Bytes.t -> bool

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

val of_bytes_opt : Stdlib.Bytes.t -> t option

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

val of_bytes_exn : Stdlib.Bytes.t -> t

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

val of_compressed_bytes_opt : Stdlib.Bytes.t -> t option

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

val of_compressed_bytes_exn : Stdlib.Bytes.t -> t

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.

val to_bytes : t -> Stdlib.Bytes.t

Return a representation in bytes

val to_compressed_bytes : t -> Stdlib.Bytes.t

Return a compressed bytes representation

val zero : t

Zero of the elliptic curve

val one : t

A fixed generator of the elliptic curve

val is_zero : t -> bool

Return true if the given element is zero

val random : ?state:Stdlib.Random.State.t -> unit -> t

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

val add : t -> t -> t

Return the addition of two element

val double : t -> t

double g returns 2g

val negate : t -> t

Return the opposite of the element

val eq : t -> t -> bool

Return true if the two elements are algebraically the same

val mul : t -> Scalar.t -> t

Multiply an element by a scalar

val fft : domain:Scalar.t array -> points:t list -> t list

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.

val ifft : domain:Scalar.t array -> points:t list -> t list

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.

val of_z_opt : x:(Z.t * Z.t) -> y:(Z.t * Z.t) -> t option

Create a point from the coordinates. If the point is not on the curve, None is return. The points must be given modulo the order of Fq. The points are in the form (c0, c1) where x = c1 * X + c0 and y = c1 * X + c0. To create the point at infinity, use zero ()