User Guide

Installation

dlog-group is published on crates.io. Add via Cargo:

cargo add dlog-group --features p256

Or add entries manually to your Cargo.toml (replace the version with the latest on crates.io):

[dependencies]
dlog-group = { version = "x.y.z", features = ["p256"] }

Available feature flags include: "ristretto", "p256", "k256" and "p384".

Usage

Once a group $\mathbb{G}$ is selected (following standard elliptic-curve conventions, $\mathbb{G}$ is considered an additive group), we can distinguish two main components:

1. Points: Elements of $\mathbb{G}$. If $P,Q\in \mathbb{G}$, then $P+Q\in \mathbb{G}$ as well. Operations on points (e.g. addition, scalar multiplication) are typically more expensive than on scalars.

2. Scalars: Elements of ${\mathbb{Z}}_n$, where $n$ is the order of the group $\mathbb{G}$. Scalars represent integer multipliers. For example, multiplying a point $P$ by $2$ (i.e., $[2]P$) is defined as $P+P$, and more generally $[r]P$ represents the sum of $P$ added to itself $r$-times.

These two structures support standard algebraic operations and are the basis for cryptographic schemes like Diffie–Hellman and digital signatures.

Example

First, we import a backend implementation (in this case, RistrettoGroup) as well as the traits GroupPoint and GroupScalar, which provide operations over points and scalars, respectively:

use dlog_group::{
    ristretto::{RistrettoGroup}, 
    group::{GroupPoint, GroupScalar}
};

We additionally import the rand crate to generate a random seed (rng) which we are going to use to generate a scalar r.

use rand;
let mut rng = rand::thread_rng();

Finally, let’s use the standard generator $G$ of the RistrettoGroup, perform some basic operations, and verify that the following holds: $$G=[1+r]G-[r]G$$

let G = RistrettoGroup::generator();
let r = RistrettoGroup::scalar_random(&mut rng);

let r_G = G * &r;
let r1_G = G + &r_G;

assert_eq!(r1_G - &r_G, G);