Crate dusk_bls12_381

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_mul
  Multiscalar multiplication implementation using pippenger algorithm.
• notes
  Notes about how the BLS12-381 elliptic curve is designed, specified and implemented by this library.

Structs

• Bls12
  A pairing::Engine for BLS12-381 pairing operations.
• BlsScalar
  Represents an element of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.
• 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.
• 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.
• G2Projective
  This is an element of $\mathbb{G}_2$ represented in the projective coordinate space.
• 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.

Constants

• GENERATOR
  GENERATOR = 7 (multiplicative generator of r-1 order, that is also quadratic nonresidue)
• ROOT_OF_UNITY
  GENERATOR^t where t * 2^s + 1 = q with t odd. In other words, this is a 2^s root of unity.
• TWO_ADACITY
  2^TWO_ADACITY * t = MODULUS - 1 with t odd

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.