Crate finitelib 

finitelib is a library for advanced maths over finite groups, fields, their extensions, multi precision operations and related things.

At the moment the library supports:

• Finite groups
• Finite fields (prime - GF(p), splitting - GF(p^m), binary - GF(2^m), Montgomery representation)
• Euclidean rings (including modular operations)
• Polynomials
• Multi precision operations over unsigned integers
  • Converting
  • Formatting
  • Basic operations: addition, subtraction, product, division, bitwise operations
  • Prime numbers: Fermat test, Miller-Rabin test, Legendre symbol, Tonelli–Shanks algorithm

Usage

Installation command:

cargo add finitelib

Basic example

use finitelib::prelude::*;
use finitelib::gf::prime::Prime as GF;

// Define 256-bit unsigned integer type
type U256 = bigi_of_bits!(256);

// Define an Euclidean ring over U256, that contains the correct basic
// math operations like addition, multiplication, Euclidean extended
// algorithm and so on.
let R256 = bigi_ring_for_bigi!(U256);

// Define a 256-bit prime number
let p = U256::from_decimal("67096435317933606252190858377894931905843553631817376158639971807689379094463");

// Define a finite field `GF(p)` with the prime characteristic `p`
let gf = GF::new(R256, p);

// Define two arbitrary numbers
let a = U256::from(3);
let b = U256::from(2);

// Perform division a / b inside the field
let c = gf.div(&a, &b).unwrap();

// Print the result as a decimal string
println!("{:?}", c.to_decimal());

// Perform multiplication
let d = gf.mul(&c, &b);

// Since multiplication is opposite to division `d` must be equal to `a`
assert_eq!(d, a);

Modules

bigi

A module for multi precision arithmetic.

common

Some common implementations for groups and fields over the standard integer and float data types.

complex

Field for complex extension implemented as linear polynomials with the irreducible 1 + x^2.

field

A module that contains a trait for mathematical field objects.

gf

This module contains implementations of Galois fields such that prime field (GF(p)), splitting field (GF(p^m)), binary field (GF(2^m)).

group

A module that contains a trait for mathematical group objects.

polynomial

This module implements operations over polynomials over a field.

prelude

Default basic imports for traits.

ring

A module that contains a trait for Euclidean rings.

signed

Signed is a wrapper that attaches a sign bit to a type that is supposed to be unsigned originally.

utils

Additional functions and algorithms.

Macros

bigi_of_bits

A macros that generates a Bigi data type calculating the size of the inner array from given number of bits that should be multiple of 64 (bit size of u64 unit).

bigi_ring_for_bigi

Define BigiRing (a ring for Bigi numbers) from the type Bigi.

bigi_ring_of_bits

Define BigiRing (a ring for Bigi numbers) from the number of bits.

bigi_xor_ring_for_bigi

Define BigiXorRing (a ring for Bigi numbers) from the type Bigi.

bigi_xor_ring_of_bits

Define BigiXorRing (a ring for Bigi numbers) from the number of bits.