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.
• small_multiexp
  Performs a small multi-exponentiation operation. Uses the double-and-add algorithm with doublings shared across points.