Finite Field Arithmetic in Rust

This Rust implementation provides a basic abstraction for performing arithmetic operations in a finite field (also known as a Galois Field). Finite fields are mathematical structures that play a vital role in cryptography, error correction, and algebraic geometry.

Features

• Finite Field Representation: Encapsulates the finite field element as a struct with a value and a prime modulus.
• Arithmetic Operations:
  • Addition: Adds two finite field elements and reduces the result modulo the prime.
  • (Extendable) Framework for additional operations like subtraction, multiplication, division, and exponentiation.

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Code Design

Core Struct

The FieldElement struct represents an element in a finite field:

#[derive(Debug, PartialEq)]
struct FieldElement {
    value: u32,
    prime: u32,
}

Examples

Creating a finite field

use finite_field::FieldElement;

let fe = FieldElement::new(7, 13);
println!("{:?}", fe); // Output: FieldElement { value: 7, prime: 13 }

Adding two finite field elements

use finite_field::FieldElement;

let fe1 = FieldElement::new(7, 13);
let fe2 = FieldElement::new(6, 13);
let sum = fe1.add(&fe2);
println!("{:?}", sum); // Output: FieldElement { value: 0, prime: 13 }

Tests

To run the tests

cargo test

License

This project is open-source and licensed under the MIT License. Feel free to use, modify, and distribute