// BabyJubJub elliptic curve implementation in Rust. // For LICENSE check https://github.com/arnaucube/babyjubjub-rs pub use ark_bn254::Fr as Fq; use ark_ff::{biginteger::BigInteger256 as BigInt, BigInteger}; use ark_ff::{fields::Field, PrimeField}; // use ark_ff::BigInt; // TODO use ark_std::str::FromStr; use ark_std::{One, Zero}; use core::ops::{AddAssign, MulAssign, SubAssign}; use ark_std::{rand::Rng, UniformRand}; use poseidon_ark::Poseidon; #[cfg(not(feature = "aarch64"))] #[cfg(not(feature = "wasm"))] use blake_hash::Digest; // compatible version with Blake used at circomlib #[cfg(not(feature = "wasm"))] #[cfg(feature = "aarch64")] extern crate blake; // compatible version with Blake used at circomlib #[cfg(not(feature = "aarch64"))] #[cfg(feature = "wasm")] extern crate blake2; // non-compatible version with Blake used at circomlib #[cfg(not(feature = "aarch64"))] #[cfg(feature = "wasm")] use blake2::digest::Digest; #[cfg(not(feature = "aarch64"))] #[cfg(feature = "wasm")] use blake2::Blake2b512; use generic_array::GenericArray; use ark_ff::fields::{Fp256, MontBackend, MontConfig}; #[derive(MontConfig)] #[modulus = "2736030358979909402780800718157159386076813972158567259200215660948447373041"] // suborder = ORDER >> 3 #[generator = "31"] pub struct FrConfig; pub type Fr = Fp256>; use lazy_static::lazy_static; lazy_static! { static ref D: Fq = Fq::from_str("168696").unwrap(); static ref D_BIG: BigInt = D.into_bigint(); static ref A: Fq = Fq::from_str("168700").unwrap(); static ref A_BIG: BigInt = A.into_bigint(); static ref Q: BigInt = Fq::MODULUS; static ref B8: Point = Point { x: Fq::from_str( "5299619240641551281634865583518297030282874472190772894086521144482721001553", ) .unwrap(), y: Fq::from_str( "16950150798460657717958625567821834550301663161624707787222815936182638968203", ) .unwrap(), }; static ref ORDER: Fq = Fq::from_str( "21888242871839275222246405745257275088614511777268538073601725287587578984328", ) .unwrap(); static ref POSEIDON: poseidon_ark::Poseidon = Poseidon::new(); } #[derive(Clone, Debug)] pub struct PointProjective { pub x: Fq, pub y: Fq, pub z: Fq, } impl PointProjective { pub fn affine(&self) -> Point { if self.z.is_zero() { return Point { x: Fq::zero(), y: Fq::zero(), }; } let 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, y } } #[allow(clippy::many_single_char_names)] pub fn add(&self, q: &PointProjective) -> PointProjective { // add-2008-bbjlp https://hyperelliptic.org/EFD/g1p/auto-twisted-projective.html#addition-add-2008-bbjlp let mut a = self.z; a.mul_assign(&q.z); let mut b = a; b = 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; 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; 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); PointProjective { x: x3, y: y3, z: z3, } } } #[derive(Clone, Debug)] pub struct Point { pub x: Fq, pub y: Fq, } impl Point { pub fn projective(&self) -> PointProjective { PointProjective { x: self.x, y: self.y, z: Fq::one(), } } pub fn mul_scalar(&self, n: &Fr) -> Point { let mut r: PointProjective = PointProjective { x: Fq::zero(), y: Fq::one(), z: Fq::one(), }; let mut exp: PointProjective = self.projective(); // if test_bit(&b, i.try_into().unwrap()) { let n_big = n.into_bigint(); let b = n_big.to_bits_le(); // for i in 0..(n_big.num_bits() as usize) { for bit in b.iter().take(n_big.num_bits() as usize) { if *bit { // if test_bit(&b, i.try_into().unwrap()) { r = r.add(&exp); } exp = exp.add(&exp); } r.affine() } // pub fn compress(&self) -> [u8; 32] { // let p = &self; // 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 x_big = BigInt::parse_bytes(&p.x.into_bigint().to_bytes_be(), 16).unwrap(); // // let y_big = BigInt::parse_bytes(&p.y.into_bigint().to_bytes_be(), 16).unwrap(); // let x_big = &p.x.into_bigint(); // let y_big = &p.y.into_bigint(); // // let (_, y_bytes) = y_big.to_bytes_le(); // 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] |= 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: &[u8], i: usize) -> bool { 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; // if b[31] & 0x80 != 0x00 { // sign = true; // 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 *= -(1.to_bigint().unwrap()); // } // x = utils::modulus(&x, &Q); // let x_fr: Fq = Fq::from_str(&x.to_string()).unwrap(); // let y_fr: Fq = Fq::from_str(&y.to_string()).unwrap(); // Ok(Point { x: x_fr, y: y_fr }) // } #[cfg(not(feature = "aarch64"))] #[cfg(not(feature = "wasm"))] fn blh(b: &[u8]) -> Vec { let hash = blake_hash::Blake512::digest(b); hash.to_vec() } #[cfg(not(feature = "wasm"))] #[cfg(feature = "aarch64")] fn blh(b: &[u8]) -> Vec { let mut hash = [0; 64]; blake::hash(512, b, &mut hash).unwrap(); hash.to_vec() } #[cfg(not(feature = "aarch64"))] #[cfg(feature = "wasm")] fn blh(b: &[u8]) -> Vec { // not-compatible with circomlib implementation, but using Blake2b let mut hasher = Blake2b512::new(); hasher.update(b); hasher.finalize().to_vec() } #[derive(Debug, Clone)] pub struct Signature { pub r_b8: Point, pub s: Fr, } // 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) => Err(err), // Result::Ok(res) => Ok(Signature { r_b8: res, s }), // } // } pub struct PrivateKey { pub key: [u8; 32], } impl PrivateKey { pub fn import(b: Vec) -> Result { if b.len() != 32 { return Err(String::from("imported key can not be bigger than 32 bytes")); } let mut sk: [u8; 32] = [0; 32]; sk.copy_from_slice(&b[..32]); Ok(PrivateKey { key: sk }) } pub fn scalar_key(&self) -> Fr { // not-compatible with circomlib implementation, but using Blake2b // let mut hasher = Blake2b::new(); // hasher.update(sk_raw_bytes); // let mut h = hasher.finalize(); // compatible with circomlib implementation let hash: Vec = blh(&self.key); let mut h: Vec = hash[..32].to_vec(); // prune buffer following RFC 8032 // https://tools.ietf.org/html/rfc8032#page-13 h[0] &= 0xF8; h[31] &= 0x7F; h[31] |= 0x40; // let sk = BigInt::deserialize(&h[..]); // let sk = BigInt::from_bytes_le(Sign::Plus, &h[..]); let sk = Fr::from_le_bytes_mod_order(&h[..]); // sk >> 3 sk / Fr::from(8_u8) } pub fn public(&self) -> Point { B8.mul_scalar(&self.scalar_key()) } pub fn sign(&self, msg: Fq) -> Result { // if msg > Q.clone() { // return Err("msg outside the Finite Field".to_string()); // } // let (_, sk_bytes) = self.key.to_bytes_le(); // let mut hasher = Blake2b::new(); // hasher.update(sk_bytes); // let mut h = hasher.finalize(); // h: hash(sk), s: h[32:64] let mut h: Vec = blh(&self.key); // let (_, msg_bytes) = msg.to_bytes_le(); let msg_bytes = msg.into_bigint().to_bytes_le(); let mut msg32: [u8; 32] = [0; 32]; msg32[..msg_bytes.len()].copy_from_slice(&msg_bytes[..]); // let msg_fr: Fq = Fq::from_str(&msg.to_string()).unwrap(); // TODO msg_fq // https://tools.ietf.org/html/rfc8032#section-5.1.6 let s = GenericArray::::from_mut_slice(&mut h[32..64]); let r_bytes = concatenate_arrays(s, &msg32); let r_hashed: Vec = blh(&r_bytes); let r = Fr::from_le_bytes_mod_order(&r_hashed[..]); // let mut r = BigInt::from_bytes_le(Sign::Plus, &r_hashed[..]); // r = utils::modulus(&r, &SUBORDER); let r_b8: Point = B8.mul_scalar(&r); let a = &self.public(); let hm_input = vec![r_b8.x, r_b8.y, a.x, a.y, msg]; let hm = POSEIDON.hash(hm_input)?; // let mut s = &self.scalar_key() << 3; let mut s = self.scalar_key() * Fr::from(8_u8); // let hm_b = BigInt::parse_bytes(to_hex(&hm).as_bytes(), 16).unwrap(); // let hm_b = BigInt::parse_bytes(&hm.into_bigint().to_bytes_be(), 16).unwrap(); let hm_Fr = Fr::from_le_bytes_mod_order(&hm.into_bigint().to_bytes_le()); s = hm_Fr * s; s = r + s; // s %= &SUBORDER.clone(); Ok(Signature { r_b8, s }) } // #[allow(clippy::many_single_char_names)] // pub fn sign_schnorr(&self, m: BigInt) -> 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 sk_scalar = self.scalar_key(); // let s = k + &sk_scalar * &h; // Ok((r, s)) // } } pub fn concatenate_arrays(x: &[T], y: &[T]) -> Vec { x.iter().chain(y).cloned().collect() } // // pub fn schnorr_hash(pk: &Point, msg: BigInt, c: &Point) -> Result { // if msg > Q.clone() { // return Err("msg outside the Finite Field".to_string()); // } // let msg_fr: Fq = Fq::from_str(&msg.to_string()).unwrap(); // let hm_input = vec![pk.x, pk.y, c.x, c.y, msg_fr]; // let h = POSEIDON.hash(hm_input)?; // // let h_b = BigInt::parse_bytes(to_hex(&h).as_bytes(), 16).unwrap(); // let h_b = BigInt::parse_bytes(&h.into_bigint().to_bytes_be(), 16).unwrap(); // Ok(h_b) // } // // pub fn verify_schnorr(pk: Point, m: BigInt, 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.projective().add(&pk_h.projective()); // // Ok(sg.equals(right.affine())) // } pub fn new_key(rng: &mut R) -> 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 (_, sk_raw_bytes) = sk_raw.to_bytes_be(); // PrivateKey::import(sk_raw_bytes[..32].to_vec()).unwrap() let sk_raw_bytes = BigInt::rand(rng).to_bytes_le(); PrivateKey::import(sk_raw_bytes[..32].to_vec()).unwrap() } pub fn verify(pk: Point, sig: Signature, msg: Fq) -> bool { let hm_input = vec![sig.r_b8.x, sig.r_b8.y, pk.x, pk.y, msg]; let hm = match POSEIDON.hash(hm_input) { Result::Err(_) => return false, Result::Ok(hm) => hm, }; let l = B8.mul_scalar(&sig.s); let hm_b = Fr::from_le_bytes_mod_order(&hm.into_bigint().to_bytes_le()); let r = sig .r_b8 .projective() .add(&pk.mul_scalar(&(Fr::from(8_u8) * hm_b)).projective()); l.equals(r.affine()) } #[cfg(test)] mod tests { use super::*; use ::hex; #[test] fn test_add_same_point() { let p: PointProjective = PointProjective { x: Fq::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fq::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), z: Fq::one(), }; let q: PointProjective = PointProjective { x: Fq::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fq::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), z: Fq::one(), }; let res = p.add(&q).affine(); assert_eq!( res.x, Fq::from_str( "6890855772600357754907169075114257697580319025794532037257385534741338397365" ) .unwrap() ); assert_eq!( res.y, Fq::from_str( "4338620300185947561074059802482547481416142213883829469920100239455078257889" ) .unwrap() ); } #[test] fn test_add_different_points() { let p: PointProjective = PointProjective { x: Fq::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fq::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), z: Fq::one(), }; let q: PointProjective = PointProjective { x: Fq::from_str( "16540640123574156134436876038791482806971768689494387082833631921987005038935", ) .unwrap(), y: Fq::from_str( "20819045374670962167435360035096875258406992893633759881276124905556507972311", ) .unwrap(), z: Fq::one(), }; let res = p.add(&q).affine(); assert_eq!( res.x, Fq::from_str( "7916061937171219682591368294088513039687205273691143098332585753343424131937" ) .unwrap() ); assert_eq!( res.y, Fq::from_str( "14035240266687799601661095864649209771790948434046947201833777492504781204499" ) .unwrap() ); } #[test] fn test_mul_scalar() { let p: Point = Point { x: Fq::from_str( "17777552123799933955779906779655732241715742912184938656739573121738514868268", ) .unwrap(), y: Fq::from_str( "2626589144620713026669568689430873010625803728049924121243784502389097019475", ) .unwrap(), }; let res_m = p.mul_scalar(&Fr::from(3_u32)); let res_a = p.projective().add(&p.projective()); let res_a = res_a.add(&p.projective()).affine(); assert_eq!(res_m.x, res_a.x); assert_eq!( res_m.x, Fq::from_str( "19372461775513343691590086534037741906533799473648040012278229434133483800898" ) .unwrap() ); assert_eq!( res_m.y, Fq::from_str( "9458658722007214007257525444427903161243386465067105737478306991484593958249" ) .unwrap() ); let n = Fr::from_str( "14035240266687799601661095864649209771790948434046947201833777492504781204499", ) .unwrap(); let res2 = p.mul_scalar(&n); assert_eq!( res2.x, Fq::from_str( "17070357974431721403481313912716834497662307308519659060910483826664480189605" ) .unwrap() ); assert_eq!( res2.y, Fq::from_str( "4014745322800118607127020275658861516666525056516280575712425373174125159339" ) .unwrap() ); } #[test] fn test_new_key_sign_verify_0() { let mut rng = ark_std::test_rng(); let sk = new_key(&mut rng); let pk = sk.public(); let msg = Fq::from(5_u32); let sig = sk.sign(msg.clone()).unwrap(); let v = verify(pk, sig, msg); assert_eq!(v, true); } #[test] fn test_new_key_sign_verify_1() { let mut rng = ark_std::test_rng(); let sk = new_key(&mut rng); let pk = sk.public(); let msg = Fq::from_str("123456789012345678901234567890").unwrap(); let sig = sk.sign(msg.clone()).unwrap(); let v = verify(pk, sig, msg); assert_eq!(v, true); } // // #[test] // fn test_point_compress_decompress() { // let p: Point = Point { // x: Fq::from_str( // "17777552123799933955779906779655732241715742912184938656739573121738514868268", // ) // .unwrap(), // y: Fq::from_str( // "2626589144620713026669568689430873010625803728049924121243784502389097019475", // ) // .unwrap(), // }; // let p_comp = p.compress(); // assert_eq!( // hex::encode(p_comp), // "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 = // hex::decode("b5328f8791d48f20bec6e481d91c7ada235f1facf22547901c18656b6c3e042f") // .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 = // hex::decode("b86cc8d9c97daef0afe1a4753c54fb2d8a530dc74c7eee4e72b3fdf2496d2113") // .unwrap(); // let mut e_px_bytes: [u8; 32] = [0; 32]; // e_px_bytes.copy_from_slice(&expected_px_raw); // let expected_px: Fq = // Fq::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 = // hex::decode("70552d3ff548e09266ded29b33ce75139672b062b02aa66bb0d9247ffecf1d0b") // .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 = // hex::decode("30f1635ba7d56f9cb32c3ffbe6dca508a68c7f43936af11a23c785ce98cb3404") // .unwrap(); // let mut e_px_bytes: [u8; 32] = [0; 32]; // e_px_bytes.copy_from_slice(&expected_px_raw); // let expected_px: Fq = // Fq::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 (_, sk_raw_bytes) = sk_raw.to_bytes_be(); // let mut h: Vec = blh(&sk_raw_bytes); // // 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); // let cmp_point = point.compress(); // let dcmp_point = decompress_point(cmp_point).unwrap(); // // assert_eq!(&point.x, &dcmp_point.x); // assert_eq!(&point.y, &dcmp_point.y); // } // } // // #[test] // fn test_signature_compress_decompress() { // let sk = new_key(); // let pk = sk.public(); // // 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(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(pk.clone(), decompressed_sig, msg); // assert_eq!(v, true); // } // } // // #[test] // fn test_schnorr_signature() { // let sk = new_key(); // let pk = sk.public(); // // let msg = BigInt::parse_bytes(b"123456789012345678901234567890", 10).unwrap(); // let (s, e) = sk.sign_schnorr(msg.clone()).unwrap(); // let verification = verify_schnorr(pk, msg, s, e).unwrap(); // assert_eq!(true, verification); // } #[test] fn test_circomlib_testvector() { let sk_raw_bytes = hex::decode("0001020304050607080900010203040506070809000102030405060708090001") .unwrap(); // test blake compatible with circomlib implementation let h: Vec = blh(&sk_raw_bytes); assert_eq!(hex::encode(h), "c992db23d6290c70ffcc02f7abeb00b9d00fa8b43e55d7949c28ba6be7545d3253882a61bd004a236ef1cdba01b27ba0aedfb08eefdbfb7c19657c880b43ddf1"); // test private key let sk = PrivateKey::import( hex::decode("0001020304050607080900010203040506070809000102030405060708090001") .unwrap(), ) .unwrap(); // assert_eq!( // sk.scalar_key().to_string(), // "6466070937662820620902051049739362987537906109895538826186780010858059362905" // ); // test public key let pk = sk.public(); assert_eq!( pk.x.to_string(), // "Fq(0x1d5ac1f31407018b7d413a4f52c8f74463b30e6ac2238220ad8b254de4eaa3a2)" "13277427435165878497778222415993513565335242147425444199013288855685581939618" ); assert_eq!( pk.y.to_string(), // "Fq(0x1e1de8a908826c3f9ac2e0ceee929ecd0caf3b99b3ef24523aaab796a6f733c4)" "13622229784656158136036771217484571176836296686641868549125388198837476602820" ); // test signature & verification // let msg = BigInt::from_bytes_le(Sign::Plus, &hex::decode("00010203040506070809").unwrap()); let msg = Fq::from_le_bytes_mod_order(&hex::decode("00010203040506070809").unwrap()); let sig = sk.sign(msg.clone()).unwrap(); assert_eq!( sig.r_b8.x.to_string(), // "Fq(0x192b4e51adf302c8139d356d0e08e2404b5ace440ef41fc78f5c4f2428df0765)" "11384336176656855268977457483345535180380036354188103142384839473266348197733" ); assert_eq!( sig.r_b8.y.to_string(), // "Fq(0x2202bebcf57b820863e0acc88970b6ca7d987a0d513c2ddeb42e3f5d31b4eddf)" "15383486972088797283337779941324724402501462225528836549661220478783371668959" ); assert_eq!( sig.s.to_string(), "1672775540645840396591609181675628451599263765380031905495115170613215233181" ); let v = verify(pk, sig, msg); assert_eq!(v, true); } }