78456041cc | ||
---|---|---|

benches | ||

examples | ||

shootout | ||

src | ||

tests | ||

.gitignore | ||

.travis.yml | ||

Cargo.toml | ||

LICENSE-APACHE | ||

LICENSE-MIT | ||

README.md |

####
**README.md**

**README.md**

# bn

This is a pairing cryptography library written in pure Rust. It makes use of the Barreto-Naehrig (BN) curve construction from [BCTV2015] to provide two cyclic groups **G _{1}** and

**G**, with an efficient bilinear pairing:

_{2}*e: G _{1} × G_{2} → G_{T}*

## 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`

...

```
[dependencies]
bn = "0.4.3"
```

...and add an `extern crate`

declaration to your crate root:

```
extern crate bn;
```

## API

`Fr`

is an element of F_{r}`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_{1} and Bob's public key *b*P_{2}, Carol can compute the shared secret with her private key *c* by *e*(*a*P_{1}, *b*P_{2})^{c}.

(See `examples/joux.rs`

for the full example.)

```
// 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 or http://opensource.org/licenses/MIT)
- Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)

at your option.

Copyright 2016 Zcash Electric Coin Company. The Zcash Company promises to maintain the "bn" crate on crates.io under this MIT/Apache-2.0 dual license.

### Authors

### 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.