Module arithmetic

This module provides common utilities, traits and structures for group, field and polynomial arithmetic.

Traits

CurveAffine

This trait is the affine counterpart to Curve and is used for serialization, storage in memory, and inspection of $x$ and $y$ coordinates.

CurveExt

This trait is a common interface for dealing with elements of an elliptic curve group in a “projective” form, where that arithmetic is usually more efficient.

FftGroup

This represents an element of a group with basic operations that can be performed. This allows an FFT implementation (for example) to operate generically over either a field or elliptic curve group.

Field

This trait represents an element of a field.

Functions

best_fft

Dispatcher

best_multiexp

Performs a multi-exponentiation operation.

bitreverse

Reverse l LSBs of bitvector n

compute_inner_product

This computes the inner product of two vectors a and b.

eval_polynomial

This evaluates a provided polynomial (in coefficient form) at point.

g_to_lagrange

Convert coefficient bases group elements to lagrange basis by inverse FFT.

kate_division

Divides polynomial a in X by X - b with no remainder.

lagrange_interpolate

Returns coefficients of an n - 1 degree polynomial given a set of n points and their evaluations. This function will panic if two values in points are the same.

log2_floor

parallelize

This utility function will parallelize an operation that is to be performed over a mutable slice.