libbolt/src/ccs08.rs

/*
Implementation of the ZK Range Proof scheme, based on:
Efficient Protocols for Set Membership and Range Proofs
Jan Camenisch, Rafik Chaabouni, and abhi shelat
Asiacrypt 2008
*/
extern crate pairing;
extern crate rand;

use rand::{thread_rng, Rng};
use super::*;
use cl::{KeyPair, Signature, PublicParams, setup};
use ped92::{CSPublicKey, Commitment};
use pairing::{Engine, CurveProjective};
use ff::PrimeField;
use std::collections::HashMap;
use std::fmt::Display;
use std::mem::transmute;

/*
paramsUL contains elements generated by the verifier, which are necessary for the prover.
This must be computed in a trusted setup.
*/
#[derive(Clone)]
struct ParamsUL<E: Engine> {
    pub mpk: PublicParams<E>,
    pub signatures: HashMap<String, Signature<E>>,
    pub com: CSPublicKey<E>,
    kp: KeyPair<E>,
    // u determines the amount of signatures we need in the public params.
    // Each signature can be compressed to just 1 field element of 256 bits.
    // Then the parameters have minimum size equal to 256*u bits.
    u: i64,
    // l determines how many pairings we need to compute, then in order to improve
    // verifier`s performance we want to minize it.
    // Namely, we have 2*l pairings for the prover and 3*l for the verifier.
    l: i64,
}

/*
proofUL contains the necessary elements for the ZK range proof.
*/
#[derive(Clone)]
struct ProofUL<E: Engine> {
    v: Vec<E::G1>,
    d: E::G2,
    comm: Commitment<E>,
    a: Vec<E::Fqk>,
    s: Vec<E::Fr>,
    t: Vec<E::Fr>,
    zsig: Vec<E::Fr>,
    zv: Vec<E::Fr>,
    ch: E::Fr,
    m: E::Fr,
    zr: E::Fr,
}

#[derive(Clone)]
pub struct RangeProof<E: Engine> {
    p1: ProofUL<E>,
    p2: ProofUL<E>,
}
/*
params contains elements generated by the verifier, which are necessary for the prover.
This must be computed in a trusted setup.
*/
#[derive(Clone)]
pub struct RPPublicParams<E: Engine> {
    p: ParamsUL<E>,
    a: i64,
    b: i64,
}

impl<E: Engine> ParamsUL<E> {
    /*
setup_ul generates the signature for the interval [0,u^l).
The value of u should be roughly b/log(b), but we can choose smaller values in
order to get smaller parameters, at the cost of having worse performance.
*/
    pub fn setup_ul<R: Rng>(rng: &mut R, u: i64, l: i64) -> ParamsUL<E> {
        let mpk = setup(rng);
        let kp = KeyPair::<E>::generate(rng, &mpk, 1);

        let mut signatures: HashMap<String, Signature<E>> = HashMap::new();
        for i in 0..u {
            let sig_i = kp.sign(rng, &vec! {E::Fr::from_str(i.to_string().as_str()).unwrap()});
            signatures.insert(i.to_string(), sig_i);
        }

        let com = CSPublicKey::setup(rng);
        return ParamsUL { mpk, signatures, com, kp, u, l };
    }

    /*
prove_ul method is used to produce the ZKRP proof that secret x belongs to the interval [0,U^L].
*/
    pub fn prove_ul<R: Rng>(&self, rng: &mut R, x: i64, r: E::Fr) -> ProofUL<E> {
        let mut mutr = r.clone();

        let decx = decompose(x, self.u);
        let modx = E::Fr::from_str(&(x.to_string())).unwrap();

// Initialize variables
        let mut v = Vec::<E::Fr>::with_capacity(self.l as usize);
        let mut V = Vec::<E::G1>::with_capacity(self.l as usize);
        let mut a = Vec::<E::Fqk>::with_capacity(self.l as usize);
        let mut s = Vec::<E::Fr>::with_capacity(self.l as usize);
        let mut t = Vec::<E::Fr>::with_capacity(self.l as usize);
        let mut zsig = Vec::<E::Fr>::with_capacity(self.l as usize);
        let mut zv = Vec::<E::Fr>::with_capacity(self.l as usize);
        let mut one = E::G2::one();
        let mut D = E::G2::zero();
        one.negate();
        D.add_assign(&one);
        let mut m = E::Fr::rand(rng);

// D = H^m
        let mut Dnew = self.com.h;
        Dnew.mul_assign(m);
        for i in 0..self.l as usize {
            v.push(E::Fr::rand(rng));
            let mut A = self.signatures.get(&decx[i].to_string()).unwrap().H;
            A.mul_assign(v[i]);
            V.push(A);
            s.push(E::Fr::rand(rng));
            t.push(E::Fr::rand(rng));
            a.push(E::pairing(V[i], self.mpk.g2));
            a[i].pow(s[i].into_repr());
            a[i] = a[i].inverse().unwrap();
            let mut E = E::pairing(self.mpk.g1, self.mpk.g2);
            E.pow(t[i].into_repr());
            a[i].add_assign(&E);

            let ui = self.u.pow(i as u32);
            let mut muisi = s[i].clone();
            muisi.mul_assign(&E::Fr::from_str(&ui.to_string()).unwrap());
            let mut aux = self.mpk.g2.clone();
            aux.mul_assign(muisi);
            D.add_assign(&aux);
        }
        D.add_assign(&Dnew);

        let C = self.com.commit(rng, modx, Some(mutr));
// Fiat-Shamir heuristic
        let c = Hash::<E>(a.clone(), D.clone());

        let mut zr = m.clone();
        mutr.mul_assign(&c);
        zr.sub_assign(&mutr);
        for i in 0..self.l as usize {
            zsig.push(s[i].clone());
            let mut dx = E::Fr::from_str(&decx[i].to_string()).unwrap();
            dx.mul_assign(&c);
            zsig[i].sub_assign(&dx);
            let mut vi = v[i].clone();
            vi.mul_assign(&c);
            let mut ti = t[i].clone();
            ti.sub_assign(&vi);
            zv.push(ti.clone());
        }
        return ProofUL { v: V, d: D, comm: C, a, s, t, zsig, zv, ch: c, m, zr };
    }
}

fn Hash<E: Engine>(a: Vec<E::Fqk>, D: E::G2) -> E::Fr {
    // create a Sha256 object
    let mut a_vec: Vec<u8> = Vec::new();
    for a_el in a {
        a_vec.extend(format!("{}", a_el).bytes());
    }

    let mut x_vec: Vec<u8> = Vec::new();
    x_vec.extend(format!("{}", D).bytes());
    a_vec.extend(x_vec);
    let sha2_digest = sha512::hash(a_vec.as_slice());

    let mut hash_buf: [u8; 64] = [0; 64];
    hash_buf.copy_from_slice(&sha2_digest[0..64]);
    let mut hexresult = fmt_bytes_to_int(hash_buf);
    let result = E::Fr::from_str(&hexresult);
    return result.unwrap();
}

/*
Decompose receives as input an integer x and outputs an array of integers such that
x = sum(xi.u^i), i.e. it returns the decomposition of x into base u.
*/
fn decompose(x: i64, u: i64) -> Vec<i64> {
    let l = (x as f64).log(u as f64).ceil() as usize;
    let mut result = Vec::with_capacity(l as usize);
    let mut decomposer = x.clone();
    for i in 0..l {
        result.push(decomposer % u);
        decomposer = decomposer / u;
    }
    return result;
}

fn fmt_bytes_to_int(bytearray: [u8; 64]) -> String {
    let mut result: String = "".to_string();
    for byte in bytearray.iter() {
        // Decide if you want upper- or lowercase results,
        // padding the values to two characters, spaces
        // between bytes, etc.
        result = result + &format!("{}", *byte as u8);
    }
    result.to_string()
}

impl<E: Engine> RPPublicParams<E> {
    /*
    Setup receives integers a and b, and configures the parameters for the rangeproof scheme.
    */
    pub fn setup<R: Rng>(rng: &mut R, a: i64, b: i64) -> RPPublicParams<E> {
        // Compute optimal values for u and l
        if a > b {
            panic!("a must be less than or equal to b");
        }
        let p: PublicParams<E>;
        let logb = (b as f64).log10();
        if logb != 0.0 {
            let u = b / logb as i64;
            if u != 0 {
                let l = (b as f64).log(u as f64).ceil() as i64;
                let params_out: ParamsUL<E> = ParamsUL::<E>::setup_ul(rng, u, l);
                return RPPublicParams { p: params_out, a, b };
            } else {
                panic!("u is zero");
            }
        } else {
            panic!("log(b) is zero");
        }
    }
}


#[cfg(test)]
mod tests {
    use super::*;
    use pairing::bls12_381::{Bls12, G2, Fq12, Fr};

    #[test]
    fn setup_ul_works() {
        let rng = &mut rand::thread_rng();
        let params = ParamsUL::<Bls12>::setup_ul(rng, 2, 3);
        assert_eq!(2, params.signatures.len());
        for (m, s) in params.signatures {
            assert_eq!(true, params.kp.verify(&params.mpk, &vec! {Fr::from_str(m.to_string().as_str()).unwrap()}, &s));
        }
    }

    #[test]
    fn prove_ul_works() {
        let rng = &mut rand::thread_rng();
        let params = ParamsUL::<Bls12>::setup_ul(rng, 2, 3);
        let fr = Fr::rand(rng);
        let proof = params.prove_ul(rng, 10, fr);

    }

    #[test]
    fn decompose_works() {
        assert_eq!(vec! {1, 2, 2}, decompose(25, 3));
        assert_eq!(vec! {0, 6, 6}, decompose(336, 7));
        assert_eq!(vec! {5, 3, 4}, decompose(285, 8));
        assert_eq!(vec! {8, 9}, decompose(125, 13));
        assert_eq!(vec! {5, 2, 0, 3, 2, 0, 3}, decompose(143225, 6));
    }

    #[test]
    fn setup_works() {
        let rng = &mut rand::thread_rng();
        let public_params = RPPublicParams::<Bls12>::setup(rng, 2, 10);
        assert_eq!(2, public_params.a);
        assert_eq!(10, public_params.b);
        assert_eq!(10, public_params.p.signatures.len());
        assert_eq!(10 / ((10 as f64).log10() as i64), public_params.p.u);
        assert_eq!(((10 / (10 / ((10 as f64).log10() as i64))) as f64).ceil() as i64, public_params.p.l);
        for (m, s) in public_params.p.signatures {
            assert_eq!(true, public_params.p.kp.verify(&public_params.p.mpk, &vec! {Fr::from_str(m.to_string().as_str()).unwrap()}, &s));
        }
    }

    #[test]
    #[should_panic(expected = "a must be less than or equal to b")]
    fn setup_wrong_a_and_b() {
        let rng = &mut rand::thread_rng();
        let public_params = RPPublicParams::<Bls12>::setup(rng, 10, 2);
    }

    #[test]
    #[should_panic(expected = "u is zero")]
    fn setup_wrong_b() {
        let rng = &mut rand::thread_rng();
        let public_params = RPPublicParams::<Bls12>::setup(rng, -1, 0);
    }

    #[test]
    #[should_panic(expected = "log(b) is zero")]
    fn setup_wrong_logb() {
        let rng = &mut rand::thread_rng();
        let public_params = RPPublicParams::<Bls12>::setup(rng, -1, 1);
    }

    #[test]
    fn fmt_byte_to_int_works() {
        assert_eq!("122352312313431223523123134312235231231343122352312313431223523123134312235231231343122352312313431223523123134312235231231343122352312313431223523123",
                   fmt_bytes_to_int([12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123, 13, 43, 12, 235, 23, 123]));
    }

    #[test]
    fn hash_works() {
        let rng = &mut rand::thread_rng();
        let D = G2::rand(rng);
        let D2 = G2::rand(rng);
        let a = vec! {Fq12::rand(rng), Fq12::rand(rng), Fq12::rand(rng)};
        let a2 = vec! {Fq12::rand(rng), Fq12::rand(rng), Fq12::rand(rng)};
        assert_eq!(false, Hash::<Bls12>(a.clone(), D.clone()).is_zero());
        assert_ne!(Hash::<Bls12>(a2.clone(), D.clone()), Hash::<Bls12>(a.clone(), D.clone()));
        assert_ne!(Hash::<Bls12>(a.clone(), D2.clone()), Hash::<Bls12>(a.clone(), D.clone()));
        assert_ne!(Hash::<Bls12>(a2.clone(), D2.clone()), Hash::<Bls12>(a.clone(), D.clone()));
    }
}