Merge pull request #1 from arnaucube/feature/opt

Add [ff](https://github.com/matter-labs/ff) for internal finite field operations, and add `add-2008-bbjlp` for point addition.

Benchmarks (On a Intel(R) Core(TM) i7-8705G CPU @ 3.10GHz, with 32 GB of RAM):
```
- before:
add               time:   [53.447 us 53.467 us 53.492 us]
mul_scalar        time:   [121.19 ms 121.22 ms 121.25 ms]
sign              time:   [383.01 ms 384.46 ms 385.98 ms]
verify            time:   [250.56 ms 251.46 ms 252.43 ms]

- current:
add               time:   [317.34 ns 317.44 ns 317.54 ns]
mul_scalar        time:   [131.05 us 131.28 us 131.58 us]
sign              time:   [973.38 us 973.83 us 974.41 us]
verify            time:   [835.34 us 839.94 us 845.29 us]
```

add: `168x` improvement
mul_scalar: `923x` improvement
sign: `394x` improvement
verify: `300x` improvement

Still needs a refactor.

Cargo.toml

@@ -9,15 +9,25 @@ repository = "https://github.com/arnaucube/babyjubjub-rs"
 readme = "README.md"
 
 [dependencies]
+ff = {package="ff_ce" , version="0.11", features = ["derive"]}
+rand = "0.4"
+rand6 = {package="rand", version="0.6.5"}
 num = "0.2.0"
 num-bigint = {version = "0.2.2", features = ["rand"]}
 num-traits = "0.2.8"
-rand = "0.6.5"
 blake2 = "0.8"
 generic-array = "0.13.2"
 tiny-keccak = "1.5"
 rustc-hex = "1.0.0"
 mimc-rs = "0.0.2"
-poseidon-rs = "0.0.1"
+poseidon-rs = "0.0.3"
 arrayref = "0.3.5"
 lazy_static = "1.4.0"
+
+[dev-dependencies]
+criterion = "0.3"
+
+[[bench]]
+name = "bench_babyjubjub"
+harness = false
+

README.md

@@ -1,13 +1,14 @@
 # babyjubjub-rs [![Crates.io](https://img.shields.io/crates/v/babyjubjub-rs.svg)](https://crates.io/crates/babyjubjub-rs) [![Build Status](https://travis-ci.org/arnaucube/babyjubjub-rs.svg?branch=master)](https://travis-ci.org/arnaucube/babyjubjub-rs)
-BabyJubJub elliptic curve implementation in Rust. A twisted edwards curve embedded in the curve of BN128.
+BabyJubJub elliptic curve implementation in Rust. A twisted edwards curve embedded in the curve of BN128/BN256.
 
 BabyJubJub curve explanation: https://medium.com/zokrates/efficient-ecc-in-zksnarks-using-zokrates-bd9ae37b8186
 
 Uses:
-- MiMC7 hash function: https://github.com/arnaucube/mimc-rs
 - Poseidon hash function https://github.com/arnaucube/poseidon-rs
 
-Compatible with the BabyJubJub Go implementation from https://github.com/iden3/go-iden3-crypto
+Compatible with the BabyJubJub implementations in:
+- Go, from https://github.com/iden3/go-iden3-crypto
+- circom & javascript, from https://github.com/iden3/circomlib
 
 ## Warning
 Doing this in my free time to get familiar with Rust, **do not use in production**.

benches/bench_babyjubjub.rs

@@ -0,0 +1,57 @@
+use criterion::{criterion_group, criterion_main, Criterion};
+
+extern crate rand;
+#[macro_use]
+extern crate ff;
+use ff::*;
+
+extern crate num;
+extern crate num_bigint;
+use num_bigint::{BigInt, ToBigInt};
+
+use babyjubjub_rs::{utils, Point};
+
+fn criterion_benchmark(c: &mut Criterion) {
+    let p: Point = Point {
+        x: babyjubjub_rs::Fr::from_str(
+            "17777552123799933955779906779655732241715742912184938656739573121738514868268",
+        )
+        .unwrap(),
+        y: babyjubjub_rs::Fr::from_str(
+            "2626589144620713026669568689430873010625803728049924121243784502389097019475",
+        )
+        .unwrap(),
+    };
+    let q = p.clone();
+
+    let p_projective = p.projective();
+    let q_projective = q.projective();
+
+    c.bench_function("add", |b| b.iter(|| p_projective.add(&q_projective)));
+    let r: BigInt = BigInt::parse_bytes(b"3", 10).unwrap();
+    c.bench_function("mul_scalar_small", |b| b.iter(|| p.mul_scalar(&r)));
+    let r: BigInt = BigInt::parse_bytes(
+        b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
+        10,
+    )
+    .unwrap();
+    c.bench_function("mul_scalar", |b| b.iter(|| p.mul_scalar(&r)));
+
+    c.bench_function("point compress", |b| b.iter(|| p.compress()));
+    let p_comp = p.compress();
+    c.bench_function("point decompress", |b| {
+        b.iter(|| babyjubjub_rs::decompress_point(p_comp))
+    });
+
+    let sk = babyjubjub_rs::new_key();
+    let pk = sk.public().unwrap();
+    let msg = 5.to_bigint().unwrap();
+    c.bench_function("sign", |b| b.iter(|| sk.sign(msg.clone())));
+    let sig = sk.sign(msg.clone()).unwrap();
+    c.bench_function("verify", |b| {
+        b.iter(|| babyjubjub_rs::verify(pk.clone(), sig.clone(), msg.clone()))
+    });
+}
+
+criterion_group!(benches, criterion_benchmark);
+criterion_main!(benches);

src/lib.rs

@@ -1,3 +1,13 @@
+// WARNING still updating the code, it works, but is still in process the refactor.
+
+extern crate rand;
+#[macro_use]
+extern crate ff;
+use ff::*;
+
+use poseidon_rs::Poseidon;
+pub type Fr = poseidon_rs::Fr; // alias
+
 #[macro_use]
 extern crate arrayref;
 extern crate generic_array;
@@ -5,48 +15,58 @@ extern crate mimc_rs;
 extern crate num;
 extern crate num_bigint;
 extern crate num_traits;
-extern crate rand;
+
+extern crate rand6;
+use rand6::Rng;
 
 use blake2::{Blake2b, Digest};
 use mimc_rs::Mimc7;
-use poseidon_rs::Poseidon;
 use std::cmp::min;
 
-use num_bigint::{BigInt, RandBigInt, Sign, ToBigInt};
+use num_bigint::{BigInt, RandBigInt, RandomBits, Sign, ToBigInt};
 use num_traits::{One, Zero};
 
 use generic_array::GenericArray;
 
-mod utils;
+pub mod utils;
 
 #[macro_use]
 extern crate lazy_static;
 
 lazy_static! {
-    static ref D: BigInt = BigInt::parse_bytes(b"168696", 10).unwrap();
+    static ref D: Fr = Fr::from_str("168696").unwrap();
-    static ref A: BigInt = BigInt::parse_bytes(b"168700", 10).unwrap();
+    static ref D_big: BigInt = BigInt::parse_bytes(b"168696", 10).unwrap();
-    static ref Q: BigInt = BigInt::parse_bytes(
+    static ref A: Fr = Fr::from_str("168700").unwrap();
-        b"21888242871839275222246405745257275088548364400416034343698204186575808495617",
+    static ref A_big: BigInt = BigInt::parse_bytes(b"168700", 10).unwrap();
-        10,
+    pub static ref Q: BigInt = BigInt::parse_bytes(
+        b"21888242871839275222246405745257275088548364400416034343698204186575808495617",10
     )
     .unwrap();
+    // pub static ref Q: Fr = Fr::from_str(
+    //     "21888242871839275222246405745257275088548364400416034343698204186575808495617"
+    // )
+    // .unwrap();
     static ref B8: Point = Point {
-        x: BigInt::parse_bytes(
+        x: Fr::from_str(
-            b"5299619240641551281634865583518297030282874472190772894086521144482721001553",
+            "5299619240641551281634865583518297030282874472190772894086521144482721001553",
-            10,
         )
         .unwrap(),
-        y: BigInt::parse_bytes(
+        y: Fr::from_str(
-            b"16950150798460657717958625567821834550301663161624707787222815936182638968203",
+            "16950150798460657717958625567821834550301663161624707787222815936182638968203",
-            10,
         )
         .unwrap(),
+            // z: Fr::one(),
     };
-    static ref ORDER: BigInt = BigInt::parse_bytes(
+    static ref ORDER: Fr = Fr::from_str(
-        b"21888242871839275222246405745257275088614511777268538073601725287587578984328",
+        "21888242871839275222246405745257275088614511777268538073601725287587578984328",
-        10,
     )
     .unwrap();
+
+    // SUBORDER = ORDER >> 3
+    // static ref SUBORDER: Fr = Fr::from_str(
+    //     "i2736030358979909402780800718157159386076813972158567259200215660948447373041",
+    // )
+    // .unwrap();
     static ref SUBORDER: BigInt = &BigInt::parse_bytes(
                 b"21888242871839275222246405745257275088614511777268538073601725287587578984328",
                         10,
@@ -55,62 +75,120 @@ lazy_static! {
                     >> 3;
 }
 
+#[derive(Clone, Debug)]
+pub struct PointProjective {
+    pub x: Fr,
+    pub y: Fr,
+    pub z: Fr,
+}
+
+impl PointProjective {
+    pub fn affine(&self) -> Point {
+        if self.z.is_zero() {
+            return Point {
+                x: Fr::zero(),
+                y: Fr::zero(),
+            };
+        }
+
+        let mut zinv = self.z.inverse().unwrap();
+        let mut x = self.x;
+        x.mul_assign(&zinv);
+        let mut y = self.y;
+        y.mul_assign(&zinv);
+
+        Point {
+            x: x.clone(),
+            y: y.clone(),
+        }
+    }
+    pub fn add(&self, q: &PointProjective) -> Result<PointProjective, String> {
+        // add-2008-bbjlp https://hyperelliptic.org/EFD/g1p/auto-twisted-projective.html#doubling-dbl-2008-bbjlp
+        let mut a = self.z;
+        a.mul_assign(&q.z);
+        let mut b = a;
+        b.square();
+        let mut c = self.x;
+        c.mul_assign(&q.x);
+        let mut d = self.y;
+        d.mul_assign(&q.y);
+        let mut e = D.clone();
+        e.mul_assign(&c);
+        e.mul_assign(&d);
+        let mut f = b;
+        f.sub_assign(&e);
+        let mut g = b;
+        g.add_assign(&e);
+        let mut x1y1 = self.x;
+        x1y1.add_assign(&self.y);
+        let mut x2y2 = q.x;
+        x2y2.add_assign(&q.y);
+        let mut aux = x1y1;
+        aux.mul_assign(&x2y2);
+        aux.sub_assign(&c);
+        aux.sub_assign(&d);
+        let mut x3 = a;
+        x3.mul_assign(&f);
+        x3.mul_assign(&aux);
+        let mut ac = A.clone();
+        ac.mul_assign(&c);
+        let mut dac = d;
+        dac.sub_assign(&ac);
+        let mut y3 = a;
+        y3.mul_assign(&g);
+        y3.mul_assign(&dac);
+        let mut z3 = f;
+        z3.mul_assign(&g);
+
+        Ok(PointProjective {
+            x: x3.clone(),
+            y: y3.clone(),
+            z: z3.clone(),
+        })
+    }
+}
+
 #[derive(Clone, Debug)]
 pub struct Point {
-    pub x: BigInt,
+    pub x: Fr,
-    pub y: BigInt,
+    pub y: Fr,
 }
 
 impl Point {
-    pub fn add(&self, q: &Point) -> Result<Point, String> {
+    pub fn projective(&self) -> PointProjective {
-        // x = (x1*y2+y1*x2)/(c*(1+d*x1*x2*y1*y2))
+        PointProjective {
-        // y = (y1*y2-x1*x2)/(c*(1-d*x1*x2*y1*y2))
+            x: self.x.clone(),
-
+            y: self.y.clone(),
-        // x = (x1 * y2 + y1 * x2) / (1 + d * x1 * y1 * y2)
+            z: Fr::one(),
-        let one: BigInt = One::one();
+        }
-        let x_num: BigInt = &self.x * &q.y + &self.y * &q.x;
-        let x_den: BigInt = &one + &D.clone() * &self.x * &q.x * &self.y * &q.y;
-        let x_den_inv = utils::modinv(&x_den, &Q)?;
-        let x: BigInt = utils::modulus(&(&x_num * &x_den_inv), &Q);
-
-        // y = (y1 * y2 - a * x1 * x2) / (1 - d * x1 * x2 * y1 * y2)
-        let y_num = &self.y * &q.y - &A.clone() * &self.x * &q.x;
-        let y_den = utils::modulus(&(&one - &D.clone() * &self.x * &q.x * &self.y * &q.y), &Q);
-        let y_den_inv = utils::modinv(&y_den, &Q)?;
-        let y: BigInt = utils::modulus(&(&y_num * &y_den_inv), &Q);
-
-        Ok(Point { x: x, y: y })
     }
 
     pub fn mul_scalar(&self, n: &BigInt) -> Result<Point, String> {
-        let mut r: Point = Point {
+        let mut r: PointProjective = PointProjective {
-            x: Zero::zero(),
+            x: Fr::zero(),
-            y: One::one(),
+            y: Fr::one(),
+            z: Fr::one(),
         };
-        let mut rem: BigInt = n.clone();
+        let mut exp: PointProjective = self.projective();
-        let mut exp: Point = self.clone();
+        let (_, b) = n.to_bytes_le();
-
+        for i in 0..n.bits() {
-        let zero: BigInt = Zero::zero();
+            if test_bit(&b, i) {
-        let one: BigInt = One::one();
-        while rem != zero {
-            let is_odd = &rem & &one == one;
-            if is_odd == true {
                 r = r.add(&exp)?;
             }
             exp = exp.add(&exp)?;
-            rem = rem >> 1;
         }
-        r.x = utils::modulus(&r.x, &Q);
+        Ok(r.affine())
-        r.y = utils::modulus(&r.y, &Q);
-        Ok(r)
     }
 
     pub fn compress(&self) -> [u8; 32] {
+        let p = &self;
         let mut r: [u8; 32] = [0; 32];
-        let (_, y_bytes) = self.y.to_bytes_le();
+        let x_big = BigInt::parse_bytes(to_hex(&p.x).as_bytes(), 16).unwrap();
+        let y_big = BigInt::parse_bytes(to_hex(&p.y).as_bytes(), 16).unwrap();
+        let (_, y_bytes) = y_big.to_bytes_le();
         let len = min(y_bytes.len(), r.len());
         r[..len].copy_from_slice(&y_bytes[..len]);
-        if &self.x > &(&Q.clone() >> 1) {
+        if &x_big > &(&Q.clone() >> 1) {
             r[31] = r[31] | 0x80;
         }
         r
@@ -124,6 +202,10 @@ impl Point {
     }
 }
 
+pub fn test_bit(b: &Vec<u8>, i: usize) -> bool {
+    return b[i / 8] & (1 << (i % 8)) != 0;
+}
+
 pub fn decompress_point(bb: [u8; 32]) -> Result<Point, String> {
     // https://tools.ietf.org/html/rfc8032#section-5.2.3
     let mut sign: bool = false;
@@ -141,7 +223,7 @@ pub fn decompress_point(bb: [u8; 32]) -> Result<Point, String> {
     // x^2 = (1 - y^2) / (a - d * y^2) (mod p)
     let den = utils::modinv(
         &utils::modulus(
-            &(&A.clone() - utils::modulus(&(&D.clone() * (&y * &y)), &Q)),
+            &(&A_big.clone() - utils::modulus(&(&D_big.clone() * (&y * &y)), &Q)),
             &Q,
         ),
         &Q,
@@ -153,9 +235,12 @@ pub fn decompress_point(bb: [u8; 32]) -> Result<Point, String> {
         x = x * -1.to_bigint().unwrap();
     }
     x = utils::modulus(&x, &Q);
-    Ok(Point { x: x, y: y })
+    let x_fr: Fr = Fr::from_str(&x.to_string()).unwrap();
+    let y_fr: Fr = Fr::from_str(&y.to_string()).unwrap();
+    Ok(Point { x: x_fr, y: y_fr })
 }
 
+#[derive(Debug, Clone)]
 pub struct Signature {
     r_b8: Point,
     s: BigInt,
@@ -200,56 +285,33 @@ impl PrivateKey {
         Ok(pk.clone())
     }
 
-    pub fn sign_mimc(&self, msg: BigInt) -> Result<Signature, String> {
+    pub fn sign(&self, msg: BigInt) -> Result<Signature, String> {
-        // https://tools.ietf.org/html/rfc8032#section-5.1.6
+        if msg > Q.clone() {
-        let mut hasher = Blake2b::new();
+            return Err("msg outside the Finite Field".to_string());
-        let (_, sk_bytes) = self.key.to_bytes_be();
-        hasher.input(sk_bytes);
-        let mut h = hasher.result(); // h: hash(sk)
-                                     // s: h[32:64]
-        let s = GenericArray::<u8, generic_array::typenum::U32>::from_mut_slice(&mut h[32..64]);
-        let (_, msg_bytes) = msg.to_bytes_be();
-        let r_bytes = utils::concatenate_arrays(s, &msg_bytes);
-        let mut r = BigInt::from_bytes_be(Sign::Plus, &r_bytes[..]);
-        r = utils::modulus(&r, &SUBORDER);
-        let r8: Point = B8.mul_scalar(&r)?;
-        let a = &self.public()?;
-
-        let hm_input = vec![r8.x.clone(), r8.y.clone(), a.x.clone(), a.y.clone(), msg];
-        let mimc7 = Mimc7::new();
-        let hm = mimc7.hash(hm_input)?;
-
-        let mut s = &self.key << 3;
-        s = hm * s;
-        s = r + s;
-        s = s % &SUBORDER.clone();
-
-        Ok(Signature {
-            r_b8: r8.clone(),
-            s: s,
-        })
         }
-    pub fn sign_poseidon(&self, msg: BigInt) -> Result<Signature, String> {
         // https://tools.ietf.org/html/rfc8032#section-5.1.6
         let mut hasher = Blake2b::new();
         let (_, sk_bytes) = self.key.to_bytes_be();
         hasher.input(sk_bytes);
         let mut h = hasher.result(); // h: hash(sk)
                                      // s: h[32:64]
-        let s = GenericArray::<u8, generic_array::typenum::U32>::from_mut_slice(&mut h[32..64]);
         let (_, msg_bytes) = msg.to_bytes_be();
+        let msgFr: Fr = Fr::from_str(&msg.to_string()).unwrap();
+
+        let s = GenericArray::<u8, generic_array::typenum::U32>::from_mut_slice(&mut h[32..64]);
         let r_bytes = utils::concatenate_arrays(s, &msg_bytes);
         let mut r = BigInt::from_bytes_be(Sign::Plus, &r_bytes[..]);
         r = utils::modulus(&r, &SUBORDER);
         let r8: Point = B8.mul_scalar(&r)?;
         let a = &self.public()?;
 
-        let hm_input = vec![r8.x.clone(), r8.y.clone(), a.x.clone(), a.y.clone(), msg];
+        let hm_input = vec![r8.x.clone(), r8.y.clone(), a.x.clone(), a.y.clone(), msgFr];
         let poseidon = Poseidon::new();
         let hm = poseidon.hash(hm_input)?;
 
         let mut s = &self.key << 3;
-        s = hm * s;
+        let hmB = BigInt::parse_bytes(to_hex(&hm).as_bytes(), 16).unwrap();
+        s = hmB * s;
         s = r + s;
         s = s % &SUBORDER.clone();
 
@@ -259,9 +321,9 @@ impl PrivateKey {
         })
     }
 
-    pub fn sign_schnorr(&self, m: Vec<u8>) -> Result<(Point, BigInt), String> {
+    pub fn sign_schnorr(&self, m: BigInt) -> Result<(Point, BigInt), String> {
         // random r
-        let mut rng = rand::thread_rng();
+        let mut rng = rand6::thread_rng();
         let k = rng.gen_biguint(1024).to_bigint().unwrap();
 
         // r = k·G
@@ -277,35 +339,34 @@ impl PrivateKey {
     }
 }
 
-pub fn schnorr_hash(pk: &Point, m: Vec<u8>, c: &Point) -> Result<BigInt, String> {
+pub fn schnorr_hash(pk: &Point, msg: BigInt, c: &Point) -> Result<BigInt, String> {
-    let b: &mut Vec<u8> = &mut Vec::new();
+    if msg > Q.clone() {
-
+        return Err("msg outside the Finite Field".to_string());
-    // other option could be to do it without compressing the points, and concatenating x|y
+    }
-    b.append(&mut pk.compress().to_vec());
+    let msgFr: Fr = Fr::from_str(&msg.to_string()).unwrap();
-    b.append(&mut c.compress().to_vec());
+    let hm_input = vec![pk.x.clone(), pk.y.clone(), c.x.clone(), c.y.clone(), msgFr];
-    b.append(&mut m.clone());
-
     let poseidon = Poseidon::new();
-    let h = poseidon.hash_bytes(b.to_vec())?;
+    let h = poseidon.hash(hm_input)?;
     println!("h {:?}", h.to_string());
-    Ok(h)
+    let hB = BigInt::parse_bytes(to_hex(&h).as_bytes(), 16).unwrap();
+    Ok(hB)
 }
 
-pub fn verify_schnorr(pk: Point, m: Vec<u8>, r: Point, s: BigInt) -> Result<bool, String> {
+pub fn verify_schnorr(pk: Point, m: BigInt, r: Point, s: BigInt) -> Result<bool, String> {
     // sG = s·G
     let sg = B8.mul_scalar(&s)?;
 
     // r + h · x
     let h = schnorr_hash(&pk, m, &r)?;
     let pk_h = pk.mul_scalar(&h)?;
-    let right = r.add(&pk_h)?;
+    let right = r.projective().add(&pk_h.projective())?;
 
-    Ok(sg.equals(right))
+    Ok(sg.equals(right.affine()))
 }
 
 pub fn new_key() -> PrivateKey {
     // https://tools.ietf.org/html/rfc8032#section-5.1.5
-    let mut rng = rand::thread_rng();
+    let mut rng = rand6::thread_rng();
     let sk_raw = rng.gen_biguint(1024).to_bigint().unwrap();
 
     let mut hasher = Blake2b::new();
@@ -322,39 +383,18 @@ pub fn new_key() -> PrivateKey {
     PrivateKey { key: sk }
 }
 
-pub fn verify_mimc(pk: Point, sig: Signature, msg: BigInt) -> bool {
+pub fn verify(pk: Point, sig: Signature, msg: BigInt) -> bool {
+    if msg > Q.clone() {
+        return false;
+    }
+    let (_, msg_bytes) = msg.to_bytes_be();
+    let msgFr: Fr = Fr::from_str(&msg.to_string()).unwrap();
     let hm_input = vec![
         sig.r_b8.x.clone(),
         sig.r_b8.y.clone(),
         pk.x.clone(),
         pk.y.clone(),
-        msg,
+        msgFr,
-    ];
-    let mimc7 = Mimc7::new();
-    let hm = match mimc7.hash(hm_input) {
-        Result::Err(_) => return false,
-        Result::Ok(hm) => hm,
-    };
-    let l = match B8.mul_scalar(&sig.s) {
-        Result::Err(_) => return false,
-        Result::Ok(l) => l,
-    };
-    let r = match sig
-        .r_b8
-        .add(&pk.mul_scalar(&(8.to_bigint().unwrap() * hm)).unwrap())
-    {
-        Result::Err(_) => return false,
-        Result::Ok(r) => r,
-    };
-    l.equals(r)
-}
-pub fn verify_poseidon(pk: Point, sig: Signature, msg: BigInt) -> bool {
-    let hm_input = vec![
-        sig.r_b8.x.clone(),
-        sig.r_b8.y.clone(),
-        pk.x.clone(),
-        pk.y.clone(),
-        msg,
     ];
     let poseidon = Poseidon::new();
     let hm = match poseidon.hash(hm_input) {
@@ -365,14 +405,16 @@ pub fn verify_poseidon(pk: Point, sig: Signature, msg: BigInt) -> bool {
         Result::Err(_) => return false,
         Result::Ok(l) => l,
     };
-    let r = match sig
+    let hmB = BigInt::parse_bytes(to_hex(&hm).as_bytes(), 16).unwrap();
-        .r_b8
+    let r = match sig.r_b8.projective().add(
-        .add(&pk.mul_scalar(&(8.to_bigint().unwrap() * hm)).unwrap())
+        &pk.mul_scalar(&(8.to_bigint().unwrap() * hmB))
-    {
+            .unwrap()
+            .projective(),
+    ) {
         Result::Err(_) => return false,
         Result::Ok(r) => r,
     };
-    l.equals(r)
+    l.equals(r.affine())
 }
 
 #[cfg(test)]
@@ -383,102 +425,114 @@ mod tests {
 
     #[test]
     fn test_add_same_point() {
-        let p: Point = Point {
+        let p: PointProjective = PointProjective {
-            x: BigInt::parse_bytes(
+            x: Fr::from_str(
-                b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
+                "17777552123799933955779906779655732241715742912184938656739573121738514868268",
-                10,
             )
             .unwrap(),
-            y: BigInt::parse_bytes(
+            y: Fr::from_str(
-                b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
+                "2626589144620713026669568689430873010625803728049924121243784502389097019475",
-                10,
             )
             .unwrap(),
+            z: Fr::one(),
         };
-        let q: Point = Point {
+        let q: PointProjective = PointProjective {
-            x: BigInt::parse_bytes(
+            x: Fr::from_str(
-                b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
+                "17777552123799933955779906779655732241715742912184938656739573121738514868268",
-                10,
             )
             .unwrap(),
-            y: BigInt::parse_bytes(
+            y: Fr::from_str(
-                b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
+                "2626589144620713026669568689430873010625803728049924121243784502389097019475",
-                10,
             )
             .unwrap(),
+            z: Fr::one(),
         };
-        let res = p.add(&q).unwrap();
+        let res = p.add(&q).unwrap().affine();
         assert_eq!(
-            res.x.to_string(),
+            res.x,
+            Fr::from_str(
                 "6890855772600357754907169075114257697580319025794532037257385534741338397365"
+            )
+            .unwrap()
         );
         assert_eq!(
-            res.y.to_string(),
+            res.y,
+            Fr::from_str(
                 "4338620300185947561074059802482547481416142213883829469920100239455078257889"
+            )
+            .unwrap()
         );
     }
     #[test]
     fn test_add_different_points() {
-        let p: Point = Point {
+        let p: PointProjective = PointProjective {
-            x: BigInt::parse_bytes(
+            x: Fr::from_str(
-                b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
+                "17777552123799933955779906779655732241715742912184938656739573121738514868268",
-                10,
             )
             .unwrap(),
-            y: BigInt::parse_bytes(
+            y: Fr::from_str(
-                b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
+                "2626589144620713026669568689430873010625803728049924121243784502389097019475",
-                10,
             )
             .unwrap(),
+            z: Fr::one(),
         };
-        let q: Point = Point {
+        let q: PointProjective = PointProjective {
-            x: BigInt::parse_bytes(
+            x: Fr::from_str(
-                b"16540640123574156134436876038791482806971768689494387082833631921987005038935",
+                "16540640123574156134436876038791482806971768689494387082833631921987005038935",
-                10,
             )
             .unwrap(),
-            y: BigInt::parse_bytes(
+            y: Fr::from_str(
-                b"20819045374670962167435360035096875258406992893633759881276124905556507972311",
+                "20819045374670962167435360035096875258406992893633759881276124905556507972311",
-                10,
             )
             .unwrap(),
+            z: Fr::one(),
         };
-        let res = p.add(&q).unwrap();
+        let res = p.add(&q).unwrap().affine();
         assert_eq!(
-            res.x.to_string(),
+            res.x,
+            Fr::from_str(
                 "7916061937171219682591368294088513039687205273691143098332585753343424131937"
+            )
+            .unwrap()
         );
         assert_eq!(
-            res.y.to_string(),
+            res.y,
+            Fr::from_str(
                 "14035240266687799601661095864649209771790948434046947201833777492504781204499"
+            )
+            .unwrap()
         );
     }
 
     #[test]
     fn test_mul_scalar() {
         let p: Point = Point {
-            x: BigInt::parse_bytes(
+            x: Fr::from_str(
-                b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
+                "17777552123799933955779906779655732241715742912184938656739573121738514868268",
-                10,
             )
             .unwrap(),
-            y: BigInt::parse_bytes(
+            y: Fr::from_str(
-                b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
+                "2626589144620713026669568689430873010625803728049924121243784502389097019475",
-                10,
             )
             .unwrap(),
         };
         let res_m = p.mul_scalar(&3.to_bigint().unwrap()).unwrap();
-        let res_a = p.add(&p).unwrap();
+        let res_a = p.projective().add(&p.projective()).unwrap();
-        let res_a = res_a.add(&p).unwrap();
+        let res_a = res_a.add(&p.projective()).unwrap().affine();
         assert_eq!(res_m.x, res_a.x);
         assert_eq!(
-            res_m.x.to_string(),
+            res_m.x,
+            Fr::from_str(
                 "19372461775513343691590086534037741906533799473648040012278229434133483800898"
+            )
+            .unwrap()
         );
         assert_eq!(
-            res_m.y.to_string(),
+            res_m.y,
+            Fr::from_str(
                 "9458658722007214007257525444427903161243386465067105737478306991484593958249"
+            )
+            .unwrap()
         );
 
         let n = BigInt::parse_bytes(
@@ -488,65 +542,70 @@ mod tests {
         .unwrap();
         let res2 = p.mul_scalar(&n).unwrap();
         assert_eq!(
-            res2.x.to_string(),
+            res2.x,
+            Fr::from_str(
                 "17070357974431721403481313912716834497662307308519659060910483826664480189605"
+            )
+            .unwrap()
         );
         assert_eq!(
-            res2.y.to_string(),
+            res2.y,
+            Fr::from_str(
                 "4014745322800118607127020275658861516666525056516280575712425373174125159339"
+            )
+            .unwrap()
         );
     }
 
+    // #[test]
+    // fn test_new_key_sign_verify_mimc_0() {
+    //     let sk = new_key();
+    //     let pk = sk.public().unwrap();
+    //     let msg = 5.to_bigint().unwrap();
+    //     let sig = sk.sign_mimc(msg.clone()).unwrap();
+    //     let v = verify_mimc(pk, sig, msg);
+    //     assert_eq!(v, true);
+    // }
+    //
+    // #[test]
+    // fn test_new_key_sign_verify_mimc_1() {
+    //     let sk = new_key();
+    //     let pk = sk.public().unwrap();
+    //     let msg = BigInt::parse_bytes(b"123456789012345678901234567890", 10).unwrap();
+    //     let sig = sk.sign_mimc(msg.clone()).unwrap();
+    //     let v = verify_mimc(pk, sig, msg);
+    //     assert_eq!(v, true);
+    // }
+
     #[test]
-    fn test_new_key_sign_verify_mimc_0() {
+    fn test_new_key_sign_verify_0() {
         let sk = new_key();
         let pk = sk.public().unwrap();
         let msg = 5.to_bigint().unwrap();
-        let sig = sk.sign_mimc(msg.clone()).unwrap();
+        let sig = sk.sign(msg.clone()).unwrap();
-        let v = verify_mimc(pk, sig, msg);
+        let v = verify(pk, sig, msg);
         assert_eq!(v, true);
     }
 
     #[test]
-    fn test_new_key_sign_verify_mimc_1() {
+    fn test_new_key_sign_verify_1() {
         let sk = new_key();
         let pk = sk.public().unwrap();
         let msg = BigInt::parse_bytes(b"123456789012345678901234567890", 10).unwrap();
-        let sig = sk.sign_mimc(msg.clone()).unwrap();
+        let sig = sk.sign(msg.clone()).unwrap();
-        let v = verify_mimc(pk, sig, msg);
+        let v = verify(pk, sig, msg);
-        assert_eq!(v, true);
-    }
-    #[test]
-    fn test_new_key_sign_verify_poseidon_0() {
-        let sk = new_key();
-        let pk = sk.public().unwrap();
-        let msg = 5.to_bigint().unwrap();
-        let sig = sk.sign_poseidon(msg.clone()).unwrap();
-        let v = verify_poseidon(pk, sig, msg);
-        assert_eq!(v, true);
-    }
-
-    #[test]
-    fn test_new_key_sign_verify_poseidon_1() {
-        let sk = new_key();
-        let pk = sk.public().unwrap();
-        let msg = BigInt::parse_bytes(b"123456789012345678901234567890", 10).unwrap();
-        let sig = sk.sign_poseidon(msg.clone()).unwrap();
-        let v = verify_poseidon(pk, sig, msg);
         assert_eq!(v, true);
     }
 
     #[test]
     fn test_point_compress_decompress() {
         let p: Point = Point {
-            x: BigInt::parse_bytes(
+            x: Fr::from_str(
-                b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
+                "17777552123799933955779906779655732241715742912184938656739573121738514868268",
-                10,
             )
             .unwrap(),
-            y: BigInt::parse_bytes(
+            y: Fr::from_str(
-                b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
+                "2626589144620713026669568689430873010625803728049924121243784502389097019475",
-                10,
             )
             .unwrap(),
         };
@@ -574,7 +633,8 @@ mod tests {
             .unwrap();
         let mut e_px_bytes: [u8; 32] = [0; 32];
         e_px_bytes.copy_from_slice(&expected_px_raw);
-        let expected_px: BigInt = BigInt::from_bytes_le(Sign::Plus, &e_px_bytes);
+        let expected_px: Fr =
+            Fr::from_str(&BigInt::from_bytes_le(Sign::Plus, &e_px_bytes).to_string()).unwrap();
         assert_eq!(&p.x, &expected_px);
     }
 
@@ -592,15 +652,16 @@ mod tests {
             .unwrap();
         let mut e_px_bytes: [u8; 32] = [0; 32];
         e_px_bytes.copy_from_slice(&expected_px_raw);
-        let expected_px: BigInt = BigInt::from_bytes_le(Sign::Plus, &e_px_bytes);
+        let expected_px: Fr =
+            Fr::from_str(&BigInt::from_bytes_le(Sign::Plus, &e_px_bytes).to_string()).unwrap();
         assert_eq!(&p.x, &expected_px);
     }
 
     #[test]
     fn test_point_decompress_loop() {
         for _ in 0..5 {
-            let mut rng = rand::thread_rng();
+            let random_bytes = rand6::thread_rng().gen::<[u8; 32]>();
-            let sk_raw = rng.gen_biguint(1024).to_bigint().unwrap();
+            let sk_raw: BigInt = BigInt::from_bytes_le(Sign::Plus, &random_bytes[..]);
             let mut hasher = Blake2b::new();
             let (_, sk_raw_bytes) = sk_raw.to_bytes_be();
             hasher.input(sk_raw_bytes);
@@ -628,7 +689,7 @@ mod tests {
         for i in 0..5 {
             let msg_raw = "123456".to_owned() + &i.to_string();
             let msg = BigInt::parse_bytes(msg_raw.as_bytes(), 10).unwrap();
-            let sig = sk.sign_mimc(msg.clone()).unwrap();
+            let sig = sk.sign(msg.clone()).unwrap();
 
             let compressed_sig = sig.compress();
             let decompressed_sig = decompress_signature(&compressed_sig).unwrap();
@@ -636,7 +697,7 @@ mod tests {
             assert_eq!(&sig.r_b8.y, &decompressed_sig.r_b8.y);
             assert_eq!(&sig.s, &decompressed_sig.s);
 
-            let v = verify_mimc(pk.clone(), decompressed_sig, msg);
+            let v = verify(pk.clone(), decompressed_sig, msg);
             assert_eq!(v, true);
         }
     }
@@ -646,7 +707,7 @@ mod tests {
         let sk = new_key();
         let pk = sk.public().unwrap();
 
-        let msg: Vec<u8> = ("123456".to_owned() + &1.to_string()).as_bytes().to_vec();
+        let msg = BigInt::parse_bytes(b"123456789012345678901234567890", 10).unwrap();
         let (s, e) = sk.sign_schnorr(msg.clone()).unwrap();
         println!("s {:?}", s.x.to_string());
         println!("s {:?}", s.y.to_string());