# Crate bls12_381_plus

Expand description

## bls12_381

This crate provides an implementation of the BLS12-381 pairing-friendly elliptic curve construction.

• This implementation has not been reviewed or audited. Use at your own risk.
• This implementation targets Rust 1.36 or later.
• This implementation does not require the Rust standard library.
• All operations are constant time unless explicitly noted.

## Modules

Notes about how the BLS12-381 elliptic curve is designed, specified and implemented by this library.

## Structs

A pairing::Engine for BLS12-381 pairing operations.

Placeholder type for implementing expand_message_xmd based on a hash function

Placeholder type for implementing expand_message_xof based on a hash function

This is an element of $\mathbb{G}_1$ represented in the affine coordinate space. It is ideal to keep elements in this representation to reduce memory usage and improve performance through the use of mixed curve model arithmetic.

This is an element of $\mathbb{G}_1$ represented in the projective coordinate space.

This is an element of $\mathbb{G}_2$ represented in the affine coordinate space. It is ideal to keep elements in this representation to reduce memory usage and improve performance through the use of mixed curve model arithmetic.

This structure contains cached computations pertaining to a $\mathbb{G}_2$ element as part of the pairing function (specifically, the Miller loop) and so should be computed whenever a $\mathbb{G}_2$ element is being used in multiple pairings or is otherwise known in advance. This should be used in conjunction with the multi_miller_loop function provided by this crate.

This is an element of $\mathbb{G}_2$ represented in the projective coordinate space.

This is an element of $\mathbb{G}_T$, the target group of the pairing function. As with $\mathbb{G}_1$ and $\mathbb{G}_2$ this group has order $q$.

Represents results of a Miller loop, one of the most expensive portions of the pairing function. MillerLoopResults cannot be compared with each other until .final_exponentiation() is called, which is also expensive.

Represents an element of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.

## Traits

Trait for types implementing expand_message interface for hash_to_field

## Functions

Computes $$\sum_{i=1}^n \textbf{ML}(a_i, b_i)$$ given a series of terms $$(a_1, b_1), (a_2, b_2), …, (a_n, b_n).$$

Invoke the pairing function without the use of precomputation and other optimizations.