This is a [pairing cryptography](https://en.wikipedia.org/wiki/Pairing-based_cryptography) library written in pure Rust. It makes use of the Barreto-Naehrig (BN) curve construction from [[BCTV2015]](https://eprint.iacr.org/2013/879.pdf) to provide two cyclic groups **G<sub>1</sub>** and **G<sub>2</sub>**, with an efficient bilinear pairing:
*`G1` is a point on the BN curve E/Fq : y^2 = x^3 + b
*`G2` is a point on the twisted BN curve E'/Fq2 : y^2 = x^3 + b/xi
*`Gt` is a group element (written multiplicatively) obtained with the `pairing` function over `G1` and `G2`.
### Examples
#### Joux's key agreement protocol
In a typical Diffie-Hellman key exchange, relying on ECDLP, a three-party key exchange requires two rounds. A single round protocol is possible through the use of a bilinear pairing: given Alice's public key *a*P<sub>1</sub> and Bob's public key *b*P<sub>2</sub>, Carol can compute the shared secret with her private key *c* by *e*(*a*P<sub>1</sub>, *b*P<sub>2</sub>)<sup>c</sup>.
* MIT license, ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
* Apache License, Version 2.0 ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
at your option.
Copyright 2016 [Zcash Electric Coin Company](https://z.cash/). The Zcash Company promises to maintain the "bn" crate on crates.io under this MIT/Apache-2.0 dual license.
### Authors
* [Sean Bowe](https://github.com/ebfull)
### Contribution
Unless you explicitly state otherwise, any contribution intentionally
submitted for inclusion in the work by you, as defined in the Apache-2.0
license, shall be dual licensed as above, without any additional terms or