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

## Structs

 G1Affine 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. G1Projective This is an element of $\mathbb{G}_1$ represented in the projective coordinate space. G2Affine 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. G2Projective This is an element of $\mathbb{G}_2$ represented in the projective coordinate space. G2Prepared 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. Gt 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 $q$. MillerLoopResult 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. Scalar Represents an element of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.

## Functions

 multi_miller_loop Computes $$\sum_{i=1}^n \textbf{ML}(a_i, b_i)$$ given a series of terms $$(a_1, b_1), (a_2, b_2), ..., (a_n, b_n).$$ pairing Invoke the pairing function without the use of precomputation and other optimizations.