BBS signatures demo (https://eprint.iacr.org/2023/275.pdf)

bbs_sig.rs

use bls12_381::{G1Affine, G2Affine, G2Prepared, Scalar, multi_miller_loop, pairing};
use group::Group;

fn main() {
    // secret key
    let x: Scalar = 1234u64.into();

    // public key
    let x_g: G2Affine = (G2Affine::generator() * x).into();

    // message
    let m: Scalar = 420u64.into();

    // signature
    let s: G1Affine = (G1Affine::generator() * (x + m).invert().unwrap()).into();

    let x_g_plus_m_g: G2Affine = (x_g + G2Affine::generator() * m).into();

    assert_eq!(
        pairing(&s, &x_g_plus_m_g),
        pairing(&G1Affine::generator(), &G2Affine::generator()),
    );

    println!("verified pairing equation 1");

    let g2_neg: G2Affine = (-G2Affine::generator()).into();
    let g2_neg: G2Prepared = g2_neg.into();

    assert!(
        multi_miller_loop(&[
            (&s, &x_g_plus_m_g.into()),
            (&G1Affine::generator(), &g2_neg),
        ])
        .final_exponentiation()
        .is_identity()
        .unwrap_u8()
            == 1
    );

    println!("verified pairing equation 2");
}