add BFV newkey, encrypt, decrypt, and homomorphic addition impl

bfv/src/lib.rs

@@ -0,0 +1,152 @@
+//! Implementation of BFV https://eprint.iacr.org/2012/144.pdf
+#![allow(non_snake_case)]
+#![allow(non_upper_case_globals)]
+#![allow(non_camel_case_types)]
+#![allow(clippy::upper_case_acronyms)]
+#![allow(dead_code)] // TMP
+
+use anyhow::{anyhow, Result};
+use rand::Rng;
+use rand_distr::{Normal, Uniform};
+use std::ops;
+
+use arithmetic::PR;
+
+// error deviation for the Gaussian(Normal) distribution
+// sigma=3.2 from: https://eprint.iacr.org/2022/162.pdf page 5
+const ERR_SIGMA: f64 = 3.2;
+
+#[derive(Clone, Debug)]
+pub struct SecretKey<const Q: u64, const N: usize>(PR<Q, N>);
+
+#[derive(Clone, Debug)]
+pub struct PublicKey<const Q: u64, const N: usize>(PR<Q, N>, PR<Q, N>);
+
+// RLWE ciphertext
+#[derive(Clone, Debug)]
+pub struct RLWE<const Q: u64, const N: usize>(PR<Q, N>, PR<Q, N>);
+
+impl<const Q: u64, const N: usize> RLWE<Q, N> {
+    fn add(lhs: Self, rhs: Self) -> Self {
+        RLWE::<Q, N>(lhs.0 + rhs.0, lhs.1 + rhs.1)
+    }
+    fn mul(lhs: Self, rhs: Self) -> Self {
+        todo!()
+    }
+}
+
+impl<const Q: u64, const N: usize> ops::Add<RLWE<Q, N>> for RLWE<Q, N> {
+    type Output = Self;
+    fn add(self, rhs: Self) -> Self {
+        Self::add(self, rhs)
+    }
+}
+
+pub struct BFV<const Q: u64, const N: usize, const T: u64> {}
+
+impl<const Q: u64, const N: usize, const T: u64> BFV<Q, N, T> {
+    const DELTA: u64 = Q / T;
+
+    /// generate a new key pair (privK, pubK)
+    pub fn new_key(mut rng: impl Rng) -> Result<(SecretKey<Q, N>, PublicKey<Q, N>)> {
+        // WIP: review probabilities
+
+        // let Xi_key = Uniform::new(-1_f64, 1_f64);
+        let Xi_key = Uniform::new(0_u64, 2_u64);
+        // let Xi_key = Uniform::new(0_u64, 2_u64);
+        // use rand::distributions::Bernoulli;
+        // let Xi_key = Bernoulli::new(0.5)?;
+        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
+
+        // secret key
+        let s = PR::<Q, N>::rand_u64(&mut rng, Xi_key)?;
+
+        // pk = (-a * s + e, a)
+        let a = PR::<Q, N>::rand_u64(&mut rng, Uniform::new(0_u64, Q))?;
+        let e = PR::<Q, N>::rand_f64(&mut rng, Xi_err)?;
+        let pk: PublicKey<Q, N> = PublicKey((&(-a) * &s) + e, a.clone());
+        Ok((SecretKey(s), pk))
+    }
+
+    pub fn encrypt(mut rng: impl Rng, pk: &PublicKey<Q, N>, m: &PR<T, N>) -> Result<RLWE<Q, N>> {
+        let Xi_key = Uniform::new(-1_f64, 1_f64);
+        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
+
+        let u = PR::<Q, N>::rand_f64(&mut rng, Xi_key)?;
+        let e_1 = PR::<Q, N>::rand_f64(&mut rng, Xi_err)?;
+        let e_2 = PR::<Q, N>::rand_f64(&mut rng, Xi_err)?;
+
+        // migrate m's coeffs to the bigger modulus Q (from T)
+        let m = PR::<Q, N>::from_vec_u64(m.coeffs().iter().map(|m_i| m_i.0).collect());
+        let c0 = &pk.0 * &u + e_1 + m * Self::DELTA;
+        let c1 = &pk.1 * &u + e_2;
+        Ok(RLWE::<Q, N>(c0, c1))
+    }
+
+    pub fn decrypt(sk: &SecretKey<Q, N>, c: &RLWE<Q, N>) -> PR<T, N> {
+        let cs = c.0 + c.1 * sk.0; // done in mod q
+        let r: Vec<u64> = cs
+            .coeffs()
+            .iter()
+            .map(|e| ((T as f64 * e.0 as f64) / Q as f64).round() as u64)
+            .collect();
+        PR::<T, N>::from_vec_u64(r)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use anyhow::Result;
+    use rand::distributions::Uniform;
+
+    use super::*;
+
+    #[test]
+    fn test_encrypt_decrypt() -> Result<()> {
+        const Q: u64 = 2u64.pow(16) + 1;
+        const N: usize = 32;
+        const T: u64 = 4; // plaintext modulus
+        type S = BFV<Q, N, T>;
+
+        let mut rng = rand::thread_rng();
+
+        let (sk, pk) = S::new_key(&mut rng)?;
+
+        let msg_dist = Uniform::new(0_u64, T);
+        let m = PR::<T, N>::rand_u64(&mut rng, msg_dist)?;
+
+        let c = S::encrypt(rng, &pk, &m)?;
+        let m_recovered = S::decrypt(&sk, &c);
+
+        assert_eq!(m, m_recovered);
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_addition() -> Result<()> {
+        const Q: u64 = 2u64.pow(16) + 1;
+        const N: usize = 32;
+        const T: u64 = 4; // plaintext modulus
+        type S = BFV<Q, N, T>;
+
+        let mut rng = rand::thread_rng();
+
+        let (sk, pk) = S::new_key(&mut rng)?;
+
+        let msg_dist = Uniform::new(0_u64, T);
+        let m1 = PR::<T, N>::rand_u64(&mut rng, msg_dist)?;
+        let m2 = PR::<T, N>::rand_u64(&mut rng, msg_dist)?;
+
+        let c1 = S::encrypt(&mut rng, &pk, &m1)?;
+        let c2 = S::encrypt(&mut rng, &pk, &m2)?;
+
+        let c3 = c1 + c2;
+
+        let m3_recovered = S::decrypt(&sk, &c3);
+
+        assert_eq!(m1 + m2, m3_recovered);
+
+        Ok(())
+    }
+}