# [−][src]Crate g2poly

# g2poly

A small library to handle polynomials of degree < 64 over the finite field GF(2).

The main motivation for this library is generating finite fields of the form GF(2^p). Elements of GF(2^p) can be expressed as polynomials over GF(2) with degree < p. These finite fields are used in cryptographic algorithms as well as error detecting / correcting codes.

# Example

use g2poly; let a = g2poly::G2Poly(0b10011); assert_eq!(format!("{}", a), "G2Poly { x^4 + x + 1 }"); let b = g2poly::G2Poly(0b1); assert_eq!(a + b, g2poly::G2Poly(0b10010)); // Since products could overflow in u64, the product is defined as a u128 assert_eq!(a * a, g2poly::G2PolyProd(0b100000101)); // This can be reduced using another polynomial let s = a * a % g2poly::G2Poly(0b1000000); assert_eq!(s, g2poly::G2Poly(0b101));

## Structs

G2Poly | Main type exported by this library |

G2PolyProd | The result of multiplying two |

## Functions

extended_gcd | Calculate the greatest common divisor with Bézout coefficients |

gcd | Calculate the greatest common divisor of |