# Crate fullcodec_bls12_381[−][src]

## 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

Multiscalar multiplication implementation using pippenger algorithm.

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

## Structs

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

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. `MillerLoopResult`

s cannot be compared with each
other until `.final_exponentiation()`

is called, which is also expensive.

## Constants

Generator of the Scalar field

GENERATOR^t where t * 2^s + 1 = q with t odd. In other words, this is a 2^s root of unity.

Two adacity

## 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.