extern crate rand; #[macro_use] extern crate ff; use ff::*; #[derive(PrimeField)] #[PrimeFieldModulus = "21888242871839275222246405745257275088548364400416034343698204186575808495617"] #[PrimeFieldGenerator = "7"] pub struct Fr(FrRepr); #[macro_use] extern crate arrayref; extern crate generic_array; extern crate mimc_rs; extern crate num; extern crate num_bigint; extern crate num_traits; use rand::Rng; use blake2::{Blake2b, Digest}; use mimc_rs::Mimc7; use poseidon_rs::Poseidon; use std::cmp::min; use num_bigint::{BigInt, RandBigInt, RandomBits, Sign, ToBigInt}; use num_traits::{One, Zero}; use generic_array::GenericArray; pub mod utils; #[macro_use] extern crate lazy_static; lazy_static! { static ref D: Fr = Fr::from_str("168696").unwrap(); static ref D_big: BigInt = BigInt::parse_bytes(b"168696", 10).unwrap(); static ref A: Fr = Fr::from_str("168700").unwrap(); static ref A_big: BigInt = BigInt::parse_bytes(b"168700", 10).unwrap(); 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: Fr::from_str( "5299619240641551281634865583518297030282874472190772894086521144482721001553", ) .unwrap(), y: Fr::from_str( "16950150798460657717958625567821834550301663161624707787222815936182638968203", ) .unwrap(), z: Fr::one(), }; static ref ORDER: Fr = Fr::from_str( "21888242871839275222246405745257275088614511777268538073601725287587578984328", ) .unwrap(); // SUBORDER = ORDER >> 3 static ref SUBORDER: Fr = Fr::from_str( "i2736030358979909402780800718157159386076813972158567259200215660948447373041", ) .unwrap(); } pub struct PointAffine { pub x: Fr, pub y: Fr, } #[derive(Clone, Debug)] pub struct Point { pub x: Fr, pub y: Fr, pub z: Fr, } impl Point { pub fn affine(&self) -> PointAffine { if self.z.is_zero() { return PointAffine { 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); PointAffine { x: x.clone(), y: y.clone(), } } pub fn from_affine(p: PointAffine) -> Point { Point { x: p.x.clone(), y: p.y.clone(), z: Fr::one(), } } pub fn add(&self, q: &Point) -> Result { // 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(Point { x: x3.clone(), y: y3.clone(), z: z3.clone(), }) } pub fn mul_scalar(&self, n: &BigInt) -> Result { let mut r: Point = Point { x: Fr::zero(), y: Fr::one(), z: Fr::one(), }; let mut exp: Point = self.clone(); let (_, b) = n.to_bytes_le(); for i in 0..n.bits() { if test_bit(&b, i) { r = r.add(&exp)?; } exp = exp.add(&exp)?; } Ok(r) } pub fn compress(&self) -> [u8; 32] { let p = &self.affine(); let mut r: [u8; 32] = [0; 32]; 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 &x_big > &(&Q.clone() >> 1) { r[31] = r[31] | 0x80; } r } pub fn equals(&self, p: Point) -> bool { if self.x == p.x && self.y == p.y { return true; } false } } pub fn test_bit(b: &Vec, i: usize) -> bool { return b[i / 8] & (1 << (i % 8)) != 0; } pub fn decompress_point(bb: [u8; 32]) -> Result { // https://tools.ietf.org/html/rfc8032#section-5.2.3 let mut sign: bool = false; let mut b = bb.clone(); if b[31] & 0x80 != 0x00 { sign = true; b[31] = b[31] & 0x7F; } let y: BigInt = BigInt::from_bytes_le(Sign::Plus, &b[..]); if y >= Q.clone() { return Err("y outside the Finite Field over R".to_string()); } let one: BigInt = One::one(); // x^2 = (1 - y^2) / (a - d * y^2) (mod p) let den = utils::modinv( &utils::modulus( &(&A_big.clone() - utils::modulus(&(&D_big.clone() * (&y * &y)), &Q)), &Q, ), &Q, )?; let mut x: BigInt = utils::modulus(&((one - utils::modulus(&(&y * &y), &Q)) * den), &Q); x = utils::modsqrt(&x, &Q)?; if sign && !(&x > &(&Q.clone() >> 1)) || (!sign && (&x > &(&Q.clone() >> 1))) { x = x * -1.to_bigint().unwrap(); } x = utils::modulus(&x, &Q); let x_fr: Fr = Fr::from_str(&x.to_string()).unwrap(); let y_fr: Fr = Fr::from_str(&y.to_string()).unwrap(); Ok(Point::from_affine(PointAffine { x: x_fr, y: y_fr })) } // // #[derive(Debug, Clone)] // pub struct Signature { // r_b8: Point, // s: BigInt, // } // // impl Signature { // pub fn compress(&self) -> [u8; 64] { // let mut b: Vec = Vec::new(); // b.append(&mut self.r_b8.compress().to_vec()); // let (_, s_bytes) = self.s.to_bytes_le(); // let mut s_32bytes: [u8; 32] = [0; 32]; // let len = min(s_bytes.len(), s_32bytes.len()); // s_32bytes[..len].copy_from_slice(&s_bytes[..len]); // b.append(&mut s_32bytes.to_vec()); // let mut r: [u8; 64] = [0; 64]; // r[..].copy_from_slice(&b[..]); // r // } // } // // pub fn decompress_signature(b: &[u8; 64]) -> Result { // let r_b8_bytes: [u8; 32] = *array_ref!(b[..32], 0, 32); // let s: BigInt = BigInt::from_bytes_le(Sign::Plus, &b[32..]); // let r_b8 = decompress_point(r_b8_bytes); // match r_b8 { // Result::Err(err) => return Err(err.to_string()), // Result::Ok(res) => Ok(Signature { // r_b8: res.clone(), // s: s, // }), // } // } // pub struct PrivateKey { key: BigInt, } impl PrivateKey { pub fn public(&self) -> Result { // https://tools.ietf.org/html/rfc8032#section-5.1.5 let pk = B8.mul_scalar(&self.key)?; Ok(pk.clone()) } // pub fn sign_mimc(&self, msg: BigInt) -> Result { // // 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::::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 { // // 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::::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 poseidon = Poseidon::new(); // let hm = poseidon.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_schnorr(&self, m: Vec) -> Result<(Point, BigInt), String> { // // random r // let mut rng = rand::thread_rng(); // let k = rng.gen_biguint(1024).to_bigint().unwrap(); // // // r = k·G // let r = B8.mul_scalar(&k)?; // // // h = H(x, r, m) // let pk = &self.public()?; // let h = schnorr_hash(&pk, m, &r)?; // // // s= k+x·h // let s = k + &self.key * &h; // Ok((r, s)) // } } // pub fn schnorr_hash(pk: &Point, m: Vec, c: &Point) -> Result { // let b: &mut Vec = &mut Vec::new(); // // // other option could be to do it without compressing the points, and concatenating x|y // b.append(&mut pk.compress().to_vec()); // b.append(&mut c.compress().to_vec()); // b.append(&mut m.clone()); // // let poseidon = Poseidon::new(); // let h = poseidon.hash_bytes(b.to_vec())?; // println!("h {:?}", h.to_string()); // Ok(h) // } // // pub fn verify_schnorr(pk: Point, m: Vec, r: Point, s: BigInt) -> Result { // // 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)?; // // Ok(sg.equals(right)) // } // pub fn new_key() -> PrivateKey { // // https://tools.ietf.org/html/rfc8032#section-5.1.5 // let mut rng = rand::thread_rng(); // let sk_raw = rng.gen_biguint(1024).to_bigint().unwrap(); // // let mut hasher = Blake2b::new(); // let (_, sk_raw_bytes) = sk_raw.to_bytes_be(); // hasher.input(sk_raw_bytes); // let mut h = hasher.result(); // // h[0] = h[0] & 0xF8; // h[31] = h[31] & 0x7F; // h[31] = h[31] | 0x40; // // let sk = BigInt::from_bytes_le(Sign::Plus, &h[..]); // // PrivateKey { key: sk } // } // pub fn verify_mimc(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 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) { // 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) // } #[cfg(test)] mod tests { use super::*; extern crate rustc_hex; use rustc_hex::{FromHex, ToHex}; #[test] fn test_add_same_point() { let p: Point = Point { x: Fr::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fr::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), z: Fr::one(), }; let q: Point = Point { x: Fr::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fr::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), z: Fr::one(), }; let res = p.add(&q).unwrap().affine(); assert_eq!( res.x, Fr::from_str( "6890855772600357754907169075114257697580319025794532037257385534741338397365" ) .unwrap() ); assert_eq!( res.y, Fr::from_str( "4338620300185947561074059802482547481416142213883829469920100239455078257889" ) .unwrap() ); } #[test] fn test_add_different_points() { let p: Point = Point { x: Fr::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fr::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), z: Fr::one(), }; let q: Point = Point { x: Fr::from_str( "16540640123574156134436876038791482806971768689494387082833631921987005038935", ) .unwrap(), y: Fr::from_str( "20819045374670962167435360035096875258406992893633759881276124905556507972311", ) .unwrap(), z: Fr::one(), }; let res = p.add(&q).unwrap().affine(); assert_eq!( res.x, Fr::from_str( "7916061937171219682591368294088513039687205273691143098332585753343424131937" ) .unwrap() ); assert_eq!( res.y, Fr::from_str( "14035240266687799601661095864649209771790948434046947201833777492504781204499" ) .unwrap() ); } #[test] fn test_mul_scalar() { let p: Point = Point { x: Fr::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fr::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), z: Fr::one(), }; let res_m = p.mul_scalar(&3.to_bigint().unwrap()).unwrap().affine(); let res_a = p.add(&p).unwrap(); let res_a = res_a.add(&p).unwrap().affine(); assert_eq!(res_m.x, res_a.x); assert_eq!( res_m.x, Fr::from_str( "19372461775513343691590086534037741906533799473648040012278229434133483800898" ) .unwrap() ); assert_eq!( res_m.y, Fr::from_str( "9458658722007214007257525444427903161243386465067105737478306991484593958249" ) .unwrap() ); let n = BigInt::parse_bytes( b"14035240266687799601661095864649209771790948434046947201833777492504781204499", 10, ) .unwrap(); let res2 = p.mul_scalar(&n).unwrap().affine(); assert_eq!( res2.x, Fr::from_str( "17070357974431721403481313912716834497662307308519659060910483826664480189605" ) .unwrap() ); assert_eq!( 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_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: Fr::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fr::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), z: Fr::one(), }; let p_comp = p.compress(); assert_eq!( p_comp[..].to_hex(), "53b81ed5bffe9545b54016234682e7b2f699bd42a5e9eae27ff4051bc698ce85" ); let p2 = decompress_point(p_comp).unwrap(); assert_eq!(p.x, p2.x); assert_eq!(p.y, p2.y); } #[test] fn test_point_decompress0() { let y_bytes_raw = "b5328f8791d48f20bec6e481d91c7ada235f1facf22547901c18656b6c3e042f" .from_hex() .unwrap(); let mut y_bytes: [u8; 32] = [0; 32]; y_bytes.copy_from_slice(&y_bytes_raw); let p = decompress_point(y_bytes).unwrap(); let expected_px_raw = "b86cc8d9c97daef0afe1a4753c54fb2d8a530dc74c7eee4e72b3fdf2496d2113" .from_hex() .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_decompress1() { let y_bytes_raw = "70552d3ff548e09266ded29b33ce75139672b062b02aa66bb0d9247ffecf1d0b" .from_hex() .unwrap(); let mut y_bytes: [u8; 32] = [0; 32]; y_bytes.copy_from_slice(&y_bytes_raw); let p = decompress_point(y_bytes).unwrap(); let expected_px_raw = "30f1635ba7d56f9cb32c3ffbe6dca508a68c7f43936af11a23c785ce98cb3404" .from_hex() .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 random_bytes = rand::thread_rng().gen::<[u8; 32]>(); 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); let mut h = hasher.result(); h[0] = h[0] & 0xF8; h[31] = h[31] & 0x7F; h[31] = h[31] | 0x40; let sk = BigInt::from_bytes_le(Sign::Plus, &h[..]); let point = B8.mul_scalar(&sk).unwrap(); let cmp_point = point.compress(); let dcmp_point = decompress_point(cmp_point).unwrap().affine(); let point_affine = point.affine(); assert_eq!(&point_affine.x, &dcmp_point.x); assert_eq!(&point_affine.y, &dcmp_point.y); } } // #[test] // fn test_signature_compress_decompress() { // let sk = new_key(); // let pk = sk.public().unwrap(); // // 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 compressed_sig = sig.compress(); // let decompressed_sig = decompress_signature(&compressed_sig).unwrap(); // assert_eq!(&sig.r_b8.x, &decompressed_sig.r_b8.x); // 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); // assert_eq!(v, true); // } // } // #[test] // fn test_schnorr_signature() { // let sk = new_key(); // let pk = sk.public().unwrap(); // // let msg: Vec = ("123456".to_owned() + &1.to_string()).as_bytes().to_vec(); // let (s, e) = sk.sign_schnorr(msg.clone()).unwrap(); // println!("s {:?}", s.x.to_string()); // println!("s {:?}", s.y.to_string()); // println!("e {:?}", e.to_string()); // let verification = verify_schnorr(pk, msg, s, e).unwrap(); // assert_eq!(true, verification); // } }