Bls12 381 Curve

Pairing friendly bls12-381 curve.

This crate partly uses https://github.com/dusk-network/bls12_381 and https://github.com/dusk-network/bls12_381 implementation designed by Dusk-Network team and, @str4d and @ebfull. We replace field and curve implementation with zero-crypto to make this compatible with Substrate.

Overview

This crate includes field and extension fields, curve implementation. There are two curve $G1$ and $G2$ described as following.

$G1: y^2 = x^3 + 4$
$G2: y^2 = x^3 + 4(u + 1)$

These two group supports bilinearity by pairing. Let $G$ and $H$ be generator of $G1$, and $G2$, and $e$ be pairing function. The relationship is described as following.

$e(aG, bH) = e(G, H)^{ab}$