Module fp 

This module contains the implementation of a prime field element Fp, altogether with exact implementations Fp64 for 64-bit, Fp128 for 128-bit elements and so on.

Finite field element Fp wraps a biginteger element in motgomery form, which is used for efficient multiplication and division.

Note that implementation of Ord for Fp compares field elements viewing them as integers in the range 0, 1, ..., P::MODULUS - 1. However, other implementations of PrimeField might choose a different ordering, and as such, users should use this Ord for applications where any ordering suffices (like in a BTreeMap), and not in applications where a particular ordering is required.

Structs

Fp

Represents an element of the prime field F_p, where p == P::MODULUS.

Constants

LIMBS_64

Number of limbs in the field with 64 bits size element.

LIMBS_128

Number of limbs in the field with 128 bits size element.

LIMBS_192

Number of limbs in the field with 192 bits size element.

LIMBS_256

Number of limbs in the field with 256 bits size element.

LIMBS_320

Number of limbs in the field with 320 bits size element.

LIMBS_384

Number of limbs in the field with 384 bits size element.

LIMBS_448

Number of limbs in the field with 448 bits size element.

LIMBS_512

Number of limbs in the field with 512 bits size element.

LIMBS_576

Number of limbs in the field with 576 bits size element.

LIMBS_640

Number of limbs in the field with 640 bits size element.

LIMBS_704

Number of limbs in the field with 704 bits size element.

LIMBS_768

Number of limbs in the field with 768 bits size element.

LIMBS_832

Number of limbs in the field with 832 bits size element.

Traits

FpParams

A trait that specifies the configuration of a prime field. Also specifies how to perform arithmetic on field elements.

Functions

inv

Compute -M^{-1} mod 2^64.

Type Aliases

Fp64

Finite field with max 64 bits size element.

Fp128

Finite field with max 128 bits size element.

Fp192

Finite field with max 192 bits size element.

Fp256

Finite field with max 256 bits size element.

Fp320

Finite field with max 320 bits size element.

Fp384

Finite field with max 384 bits size element.

Fp448

Finite field with max 448 bits size element.

Fp512

Finite field with max 512 bits size element.

Fp576

Finite field with max 576 bits size element.

Fp640

Finite field with max 640 bits size element.

Fp704

Finite field with max 704 bits size element.

Fp768

Finite field with max 768 bits size element.

Fp832

Finite field with max 832 bits size element.