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

## 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.