1use anyhow::Result;
  2use rand::Rng;
  3use rand_distr::{Normal, Uniform};
  4use std::ops::Add;
  5
  6use arith::{Ring, Rq, TR};
  7
  8const ERR_SIGMA: f64 = 3.2;
  9
 10pub struct GLWE<const Q: u64, const N: usize, const K: usize>(TR<Rq<Q, N>, K>, Rq<Q, N>);
 11
 12#[derive(Clone, Debug)]
 13pub struct SecretKey<const Q: u64, const N: usize, const K: usize>(TR<Rq<Q, N>, K>);
 14#[derive(Clone, Debug)]
 15pub struct PublicKey<const Q: u64, const N: usize, const K: usize>(Rq<Q, N>, TR<Rq<Q, N>, K>);
 16
 17impl<const Q: u64, const N: usize, const K: usize> GLWE<Q, N, K> {
 18    pub fn new_key(mut rng: impl Rng) -> Result<(SecretKey<Q, N, K>, PublicKey<Q, N, K>)> {
 19        let Xi_key = Uniform::new(0_f64, 2_f64);
 20        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
 21
 22        let s: TR<Rq<Q, N>, K> = TR::rand(&mut rng, Xi_key);
 23        let a: TR<Rq<Q, N>, K> = TR::rand(&mut rng, Uniform::new(0_f64, Q as f64));
 24        let e = Rq::<Q, N>::rand(&mut rng, Xi_err);
 25
 26        let pk: PublicKey<Q, N, K> = PublicKey((&a * &s) + e, a);
 27        Ok((SecretKey(s), pk))
 28    }
 29
 30    // TODO delta not as input
 31    pub fn encrypt_s<const T: u64>(
 32        mut rng: impl Rng,
 33        sk: &SecretKey<Q, N, K>,
 34        m: &Rq<T, N>,
 35        delta: u64,
 36    ) -> Result<Self> {
 37        let m: Rq<Q, N> = m.remodule::<Q>();
 38
 39        let Xi_key = Uniform::new(0_f64, 2_f64);
 40        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
 41
 42        let a: TR<Rq<Q, N>, K> = TR::rand(&mut rng, Xi_key);
 43        let e = Rq::<Q, N>::rand(&mut rng, Xi_err);
 44
 45        let b: Rq<Q, N> = (&a * &sk.0) + m * delta + e;
 46        Ok(Self(a, b))
 47    }
 48    pub fn encrypt<const T: u64>(
 49        mut rng: impl Rng,
 50        pk: &PublicKey<Q, N, K>,
 51        m: &Rq<T, N>,
 52        delta: u64,
 53    ) -> Result<Self> {
 54        let m: Rq<Q, N> = m.remodule::<Q>();
 55
 56        let Xi_key = Uniform::new(0_f64, 2_f64);
 57        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
 58
 59        let u: Rq<Q, N> = Rq::rand(&mut rng, Xi_key);
 60
 61        let e0 = Rq::<Q, N>::rand(&mut rng, Xi_err);
 62        let e1 = TR::<Rq<Q, N>, K>::rand(&mut rng, Xi_err);
 63
 64        let b: Rq<Q, N> = pk.0 * u + m * delta + e0;
 65        let d: TR<Rq<Q, N>, K> = &pk.1 * &u + e1;
 66
 67        Ok(Self(d, b))
 68    }
 69    pub fn decrypt<const T: u64>(&self, sk: &SecretKey<Q, N, K>, delta: u64) -> Rq<T, N> {
 70        let (d, b): (TR<Rq<Q, N>, K>, Rq<Q, N>) = (self.0.clone(), self.1);
 71        let r: Rq<Q, N> = b - &d * &sk.0;
 72        let r_scaled: Vec<f64> = r
 73            .coeffs()
 74            .iter()
 75            .map(|e| (e.0 as f64 / delta as f64).round())
 76            .collect();
 77        let r = Rq::<Q, N>::from_vec_f64(r_scaled);
 78        r.remodule::<T>()
 79    }
 80}
 81
 82impl<const Q: u64, const N: usize, const K: usize> Add<GLWE<Q, N, K>> for GLWE<Q, N, K> {
 83    type Output = Self;
 84    fn add(self, other: Self) -> Self {
 85        let a: TR<Rq<Q, N>, K> = self.0 + other.0;
 86        let b: Rq<Q, N> = self.1 + other.1;
 87        Self(a, b)
 88    }
 89}
 90
 91impl<const Q: u64, const N: usize, const K: usize> Add<Rq<Q, N>> for GLWE<Q, N, K> {
 92    type Output = Self;
 93    fn add(self, plaintext: Rq<Q, N>) -> Self {
 94        let a: TR<Rq<Q, N>, K> = self.0;
 95        let b: Rq<Q, N> = self.1 + plaintext;
 96        Self(a, b)
 97    }
 98}
 99
100#[cfg(test)]
101mod tests {
102    use anyhow::Result;
103    use rand::distributions::Uniform;
104
105    use super::*;
106
107    #[test]
108    fn test_encrypt_decrypt() -> Result<()> {
109        const Q: u64 = 2u64.pow(16) + 1;
110        const N: usize = 128;
111        const T: u64 = 32; // plaintext modulus
112        const K: usize = 16;
113        type S = GLWE<Q, N, K>;
114
115        let delta: u64 = Q / T; // floored
116        let mut rng = rand::thread_rng();
117
118        for _ in 0..200 {
119            let (sk, pk) = S::new_key(&mut rng)?;
120
121            let msg_dist = Uniform::new(0_u64, T);
122            let m = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
123
124            let c = S::encrypt(&mut rng, &pk, &m, delta)?;
125            let m_recovered = c.decrypt(&sk, delta);
126
127            assert_eq!(m, m_recovered);
128        }
129
130        Ok(())
131    }
132
133    #[test]
134    fn test_addition() -> Result<()> {
135        const Q: u64 = 2u64.pow(16) + 1;
136        const N: usize = 128;
137        const T: u64 = 20;
138        const K: usize = 16;
139        type S = GLWE<Q, N, K>;
140
141        let delta: u64 = Q / T; // floored
142        let mut rng = rand::thread_rng();
143
144        for _ in 0..200 {
145            let (sk, pk) = S::new_key(&mut rng)?;
146
147            let msg_dist = Uniform::new(0_u64, T);
148            let m1 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
149            let m2 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
150
151            let c1 = S::encrypt(&mut rng, &pk, &m1, delta)?;
152            let c2 = S::encrypt(&mut rng, &pk, &m2, delta)?;
153
154            let c3 = c1 + c2;
155
156            let m3_recovered = c3.decrypt(&sk, delta);
157
158            assert_eq!(m1 + m2, m3_recovered);
159        }
160
161        Ok(())
162    }
163
164    #[test]
165    fn test_add_plaintext() -> Result<()> {
166        const Q: u64 = 2u64.pow(16) + 1;
167        const N: usize = 128;
168        const T: u64 = 32;
169        const K: usize = 16;
170        type S = GLWE<Q, N, K>;
171
172        let delta: u64 = Q / T; // floored
173        let mut rng = rand::thread_rng();
174
175        for _ in 0..200 {
176            let (sk, pk) = S::new_key(&mut rng)?;
177
178            let msg_dist = Uniform::new(0_u64, T);
179            let m1 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
180            let m2 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
181            let m2_scaled: Rq<Q, N> = m2.remodule::<Q>() * delta;
182
183            let c1 = S::encrypt(&mut rng, &pk, &m1, delta)?;
184
185            let c3 = c1 + m2_scaled;
186
187            let m3_recovered = c3.decrypt(&sk, delta);
188
189            assert_eq!(m1 + m2, m3_recovered);
190        }
191
192        Ok(())
193    }
194}