# Explaining BLS12–381 … The “Zero Knowledge Proof” Curve

## What’s “BLS”, “12” and “381” in BLS12–381?

## Introduction

A good deal of my work involves using elliptic curves, along with implementing **pairing-based cryptography** for things like zero knowledge proofs (ZKPs). At the core of this is often the magical **BLS12–381** curve, and which has not one curve, but two. If you want a little bit of the basics on elliptic curve cryptography (ECC), try here:

Well, the “BLS” part is easy, as it is named after its creators: Barreto, Lynn and Scott (BLS) [1]:

## The first curve (G1)

The first curve on BLS12–381 is just **y²=x³+4** (mod p) over a finite field defined by:

`p= 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab`