ec_generic

This crate is a minimal and easy-to-use elliptic curve library. This library allows to perform the following operations over an elliptic curve finite cyclic group:

• Point Addition: R = P + Q
• Point Doubling: R = P + P = 2 * P
• Scalar Multiplication: R = d * P

A generic elliptic curve is defined as y^2 = x^3 + ax + b mod p, and in this particular library the constrains are:

• p should be a prime number bigger than 3
• 4 a^3 + 27 b^2 != 0

The library could be use in any cryptographic algorithm that requires elliptic curve groups, for example:

• Digital Signature Algorithm (DSA)
• Zero-Knowledge Proofs (ZKP)

Usage

This crate is on crates.io and can be used by adding regex to your dependencies in your project's Cargo.toml.

toml [dependencies] ec_generic = "0.1.12"

Example: y^2 = x^3 + 2x + 2 mod 17

```rust use ecgeneric::{EllipticCurve, Point}; use numbigint::BigUint;

let ec = EllipticCurve { a: BigUint::from(2u32), b: BigUint::from(2u32), p: BigUint::from(17u32), };

// (6,3) + (5,1) = (10,6) let p1 = Point::Coor(BigUint::from(6u32), BigUint::from(3u32)); let p2 = Point::Coor(BigUint::from(5u32), BigUint::from(1u32)); let pr = Ok(Point::Coor(BigUint::from(10u32), BigUint::from(6u32)));

let res = ec.add(&p1, &p2); assert_eq!(res, pr);