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https://github.com/paritytech/bn
Pairing cryptography library in Rust
https://github.com/paritytech/bn
Last synced: 1 day ago
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Pairing cryptography library in Rust
- Host: GitHub
- URL: https://github.com/paritytech/bn
- Owner: paritytech
- License: apache-2.0
- Fork: true (zcash-hackworks/bn)
- Created: 2017-03-21T21:01:13.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2024-01-18T22:54:25.000Z (10 months ago)
- Last Synced: 2024-09-09T14:13:25.296Z (about 2 months ago)
- Language: Rust
- Homepage:
- Size: 6.62 MB
- Stars: 32
- Watchers: 16
- Forks: 45
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE-APACHE
Awesome Lists containing this project
- awesome-cryptography-rust - bn - hackworks/bn) Pairing cryptography library in Rust. Barreto-Naehrig (BN). (Cryptography / Theorem)
README
# bn [](https://crates.io/crates/bn) [](https://travis-ci.org/zcash/bn)
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 **G1** and **G2**, with an efficient bilinear pairing:
*e: G1 × G2 → GT*
## Security warnings
This library, like other pairing cryptography libraries implementing this construction, is not resistant to side-channel attacks.
## Usage
Add the `bn` crate to your dependencies in `Cargo.toml`...
```toml
[dependencies]
bn = "0.4.2"
```
...and add an `extern crate` declaration to your crate root:
```rust
extern crate bn;
```
## API
* `Fr` is an element of Fr
* `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*P1 and Bob's public key *b*P2, Carol can compute the shared secret with her private key *c* by *e*(*a*P1, *b*P2)c.
(See `examples/joux.rs` for the full example.)
```rust
// Generate private keys
let alice_sk = Fr::random(rng);
let bob_sk = Fr::random(rng);
let carol_sk = Fr::random(rng);
// Generate public keys in G1 and G2
let (alice_pk1, alice_pk2) = (G1::one() * alice_sk, G2::one() * alice_sk);
let (bob_pk1, bob_pk2) = (G1::one() * bob_sk, G2::one() * bob_sk);
let (carol_pk1, carol_pk2) = (G1::one() * carol_sk, G2::one() * carol_sk);
// Each party computes the shared secret
let alice_ss = pairing(bob_pk1, carol_pk2).pow(alice_sk);
let bob_ss = pairing(carol_pk1, alice_pk2).pow(bob_sk);
let carol_ss = pairing(alice_pk1, bob_pk2).pow(carol_sk);
assert!(alice_ss == bob_ss && bob_ss == carol_ss);
```
## License
Licensed under either of
* 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
conditions.