extern crate bn;
extern crate rand;
use bn::{Group, Fr, G1, G2, pairing};

fn main() {
    let rng = &mut rand::thread_rng();

    // 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);
}