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use std::io; use rand::{ Rand, Rng, OsRng }; use rand::distributions::{ Normal, Sample }; use bitpack::BitPack; use ::ntt::{ fft, flp, xmu, cmu, pwr }; use ::param::*; use ::utils::{ uniform_poly, c_oracle, greedy_sc, vecabsmax, vecscalar }; pub struct PrivateKey { pub f: [i32; N], pub g: [i32; N], pub a: [i32; N] } pub struct PublicKey { pub a: [i32; N] } pub struct Signature { pub t: [i32; N], pub z: [i32; N], pub c_idx: [usize; KAPPA] } impl PrivateKey { pub fn new<R: Rand + Rng>() -> io::Result<PrivateKey> { let mut rng = OsRng::new()?.gen::<R>(); let (mut t, mut u, mut a) = ([0; N], [0; N], [0; N]); let mut privkey = PrivateKey { f: [0; N], g: [0; N], a: [0; N] }; uniform_poly(&mut privkey.g, &mut rng); for i in 0..N { privkey.g[i] *= 2; } privkey.g[0] -= 1; xmu(&mut t, &privkey.g, &W); fft(&mut t); 'f : for _ in 0..1024 { uniform_poly(&mut privkey.f, &mut rng); xmu(&mut u, &privkey.f, &W); fft(&mut u); for i in 0..N { let x = u[i] % Q; if x == 0 { continue 'f }; u[i] = pwr(x, Q - 2, Q); } xmu(&mut a, &t, &u); fft(&mut a); xmu(&mut privkey.a, &a, &R); cmu(&mut a, &privkey.a, -1); flp(&mut a); xmu(&mut privkey.a, &a, &W); fft(&mut privkey.a); for i in 0..N { let x = privkey.a[i] % Q; privkey.a[i] = if x < 0 { x + Q } else { x }; } return Ok(privkey); } Err(io::Error::new(io::ErrorKind::Other, "Unable to generate the correct private key.")) } pub fn public(&self) -> PublicKey { let mut pubkey = PublicKey { a: [0; N] }; pubkey.a.copy_from_slice(&self.a); pubkey } pub fn signature<R: Rand + Rng>(&self, hash: &[u8]) -> io::Result<Signature> { let mut u = [0; N]; let (mut v, mut vv) = ([0; N], [0; N]); let (mut x, mut y) = ([0; N], [0; N]); let mut sign = Signature { t: [0; N], z: [0; N], c_idx: [0; KAPPA] }; let mut rng = OsRng::new()?.gen::<R>(); let mut sample = Normal::new(0.0, SIGMA); macro_rules! gauss_sample { () => { sample.sample(&mut rng) as i32 } } for _ in 0..1024 { for i in 0..N { sign.t[i] = gauss_sample!(); u[i] = gauss_sample!(); } xmu(&mut v, &sign.t, &W); fft(&mut v); xmu(&mut vv, &v, &self.a); fft(&mut vv); xmu(&mut v, &vv, &R); flp(&mut v); for i in 0..N { let mut tmp = v[i]; if tmp & 1 != 0 { tmp += Q }; tmp = (tmp + u[i]) % (2 * Q); if tmp < 0 { tmp += 2 * Q }; v[i] = tmp; sign.z[i] = ((tmp + (1 << (D - 1))) >> D) % P; } if !c_oracle(&mut sign.c_idx, hash, &sign.z) { continue }; greedy_sc(&self.f, &self.g, &sign.c_idx, &mut x, &mut y); if rng.gen() { for i in 0..N { sign.t[i] -= x[i]; u[i] -= y[i]; } } else { for i in 0..N { sign.t[i] += x[i]; u[i] += y[i]; } } let mut d = 1.0 / (SIGMA * SIGMA); d = 1.0 / ( M * (-0.5 * d * (vecscalar(&x, &x) + vecscalar(&y, &y)) as f64).exp() * (d * (vecscalar(&sign.t, &x) + vecscalar(&u, &y)) as f64).cosh() ); if rng.gen::<f64>() > d { continue }; for i in 0..N { let mut tmp = v[i] - u[i]; if tmp < 0 { tmp += 2 * Q }; if tmp >= 2 * Q { tmp -= 2 * Q }; tmp = ((tmp + (1 << (D - 1))) >> D) % P; tmp = sign.z[i] - tmp; if tmp < -P / 2 { tmp += P }; if tmp > P / 2 { tmp -= P }; sign.z[i] = tmp; } return Ok(sign); } Err(io::Error::new(io::ErrorKind::Other, "Unable to generate the correct signature.")) } pub fn export(&self) -> Result<[u8; PRIVATEKEY_LENGTH], usize> { let mut output = [0; PRIVATEKEY_LENGTH]; { let mut bitpack = BitPack::<&mut [u8]>::new(&mut output); for i in 0..N { bitpack.write((self.f[i] + (1 << (F_BITS - 1))) as u32, F_BITS)?; bitpack.write((self.g[i] + (1 << (G_BITS - 1))) as u32, G_BITS)?; bitpack.write(self.a[i] as u32, A_BITS)?; } } Ok(output) } pub fn import(input: &[u8; PRIVATEKEY_LENGTH]) -> Result<PrivateKey, usize> { let mut privkey = PrivateKey { f: [0; N], g: [0; N], a: [0; N] }; { let mut bitpack = BitPack::<&[u8]>::new(input); for i in 0..N { privkey.f[i] = bitpack.read(F_BITS)? as i32 - (1 << (F_BITS - 1)); privkey.g[i] = bitpack.read(G_BITS)? as i32 - (1 << (G_BITS - 1)); privkey.a[i] = bitpack.read(A_BITS)? as i32; } } Ok(privkey) } } impl PublicKey { pub fn verify(&self, sign: &Signature, hash: &[u8]) -> bool { if vecabsmax(&sign.t) > B_INF || (vecabsmax(&sign.z) << D) > B_INF { return false; } if vecscalar(&sign.t, &sign.t) + (vecscalar(&sign.z, &sign.z) << (2 * D)) > B_L2 { return false; } let (mut v, mut vv) = ([0; N], [0; N]); let mut my_idx = [0; KAPPA]; xmu(&mut v, &sign.t, &W); fft(&mut v); xmu(&mut vv, &v, &self.a); fft(&mut vv); xmu(&mut v, &vv, &R); flp(&mut v); for i in 0..N { if v[i] & 1 != 0 { v[i] += Q; } } for &i in sign.c_idx.iter() { v[i] = (v[i] + Q) % (2 * Q); } for i in 0..N { let tmp = (((v[i] + (1 << (D - 1))) >> D) + sign.z[i]) % P; v[i] = if tmp < 0 { tmp + P } else { tmp }; } if !c_oracle(&mut my_idx, hash, &v) { return false; } let mut d = 0; for i in 0..KAPPA { d |= my_idx[i] ^ sign.c_idx[i]; } d == 0 } pub fn export(&self) -> Result<[u8; PUBLICKEY_LENGTH], usize> { let mut output = [0; PUBLICKEY_LENGTH]; { let mut bitpack = BitPack::<&mut [u8]>::new(&mut output); for &b in &self.a[..] { bitpack.write(b as u32, A_BITS)?; } } Ok(output) } pub fn import(input: &[u8; PUBLICKEY_LENGTH]) -> Result<PublicKey, usize> { let mut pubkey = PublicKey { a: [0; N] }; { let mut bitpack = BitPack::<&[u8]>::new(input); for i in 0..N { pubkey.a[i] = bitpack.read(A_BITS)? as i32; } } Ok(pubkey) } } impl Signature { pub fn export(&self) -> Result<[u8; SIGNATURE_LENGTH], usize> { let mut output = [0; SIGNATURE_LENGTH]; { let mut bitpack = BitPack::<&mut [u8]>::new(&mut output); for i in 0..N { bitpack.write((self.t[i] + (1 << (T_BITS - 1))) as u32, T_BITS)?; bitpack.write((self.z[i] + (1 << (Z_BITS - 1))) as u32, Z_BITS)?; } for i in 0..KAPPA { bitpack.write(self.c_idx[i] as u32, CIDX_BITS)?; } } Ok(output) } pub fn import(input: &[u8]) -> Result<Signature, usize> { let mut sign = Signature { t: [0; N], z: [0; N], c_idx: [0; KAPPA] }; { let mut bitpack = BitPack::<&[u8]>::new(input); for i in 0..N { sign.t[i] = bitpack.read(T_BITS)? as i32 - (1 << (T_BITS - 1)); sign.z[i] = bitpack.read(Z_BITS)? as i32 - (1 << (Z_BITS - 1)); } for i in 0..KAPPA { sign.c_idx[i] = bitpack.read(CIDX_BITS)? as usize; } } Ok(sign) } }