add ckks encrypt & decrypt

bfv/src/lib.rs

@@ -105,7 +105,7 @@ impl BFV {
         let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
 
         // secret key
-        // let s = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;
+        // let mut s = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;
         let mut s = Rq::<Q, N>::rand_u64(&mut rng, Xi_key)?;
         // since s is going to be multiplied by other Rq elements, already
         // compute its NTT

ckks/src/lib.rs

@@ -1,10 +1,183 @@
-//! Implementation of BFV https://eprint.iacr.org/2012/144.pdf
+//! Implementation of CKKS https://eprint.iacr.org/2016/421.pdf
 #![allow(non_snake_case)]
 #![allow(non_upper_case_globals)]
 #![allow(non_camel_case_types)]
 #![allow(clippy::upper_case_acronyms)]
 #![allow(dead_code)] // TMP
 
-pub mod encoder;
+use arith::{Rq, C, R};
+
+use anyhow::Result;
+use rand::Rng;
+use rand_distr::{Normal, Uniform};
 
+pub mod encoder;
 pub use encoder::Encoder;
+
+// error deviation for the Gaussian(Normal) distribution
+// sigma=3.2 from: https://eprint.iacr.org/2016/421.pdf page 17
+const ERR_SIGMA: f64 = 3.2;
+
+#[derive(Debug)]
+pub struct PublicKey<const Q: u64, const N: usize>(Rq<Q, N>, Rq<Q, N>);
+
+pub struct SecretKey<const Q: u64, const N: usize>(Rq<Q, N>);
+
+pub struct CKKS<const Q: u64, const N: usize> {
+    encoder: Encoder<Q, N>,
+}
+
+impl<const Q: u64, const N: usize> CKKS<Q, N> {
+    pub fn new(delta: C<f64>) -> Self {
+        let encoder = Encoder::<Q, N>::new(delta);
+        Self { encoder }
+    }
+    /// generate a new key pair (privK, pubK)
+    pub fn new_key(&self, mut rng: impl Rng) -> Result<(SecretKey<Q, N>, PublicKey<Q, N>)> {
+        let Xi_key = Uniform::new(-1_f64, 1_f64);
+        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
+
+        let e = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;
+
+        let mut s = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;
+        // since s is going to be multiplied by other Rq elements, already
+        // compute its NTT
+        s.compute_evals();
+
+        let a = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;
+
+        let pk: PublicKey<Q, N> = PublicKey((&(-a) * &s) + e, a.clone());
+        Ok((SecretKey(s), pk))
+    }
+
+    // encrypts a plaintext \in R=Z_Q[X]/(X^N+1)
+    fn encrypt(
+        &self, // TODO maybe rm?
+        mut rng: impl Rng,
+        pk: &PublicKey<Q, N>,
+        m: &R<N>,
+    ) -> Result<(Rq<Q, N>, Rq<Q, N>)> {
+        let Xi_key = Uniform::new(-1_f64, 1_f64);
+        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
+
+        let e_0 = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;
+        let e_1 = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;
+
+        let v = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;
+
+        let m: Rq<Q, N> = Rq::<Q, N>::from(*m);
+
+        Ok((m + e_0 + v * pk.0.clone(), v * pk.1.clone() + e_1))
+    }
+
+    fn decrypt(
+        &self, // TODO maybe rm?
+        sk: SecretKey<Q, N>,
+        c: (Rq<Q, N>, Rq<Q, N>),
+    ) -> Result<R<N>> {
+        let m = c.0.clone() + c.1 * sk.0;
+        Ok(m.mod_centered_q())
+    }
+
+    pub fn encode_and_encrypt(
+        &self,
+        mut rng: impl Rng,
+        pk: &PublicKey<Q, N>,
+        z: &[C<f64>],
+    ) -> Result<(Rq<Q, N>, Rq<Q, N>)> {
+        let m: R<N> = self.encoder.encode(&z)?; // polynomial (encoded vec) \in R
+
+        self.encrypt(&mut rng, pk, &m)
+    }
+
+    pub fn decrypt_and_decode(
+        &self,
+        sk: SecretKey<Q, N>,
+        c: (Rq<Q, N>, Rq<Q, N>),
+    ) -> Result<Vec<C<f64>>> {
+        let d = self.decrypt(sk, c)?;
+
+        self.encoder.decode(&d)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_encrypt_decrypt() -> Result<()> {
+        const Q: u64 = 2u64.pow(16) + 1;
+        const T: u64 = 16;
+        const N: usize = 8;
+        let scale_factor_u64 = 512_u64; // delta
+        let scale_factor = C::<f64>::new(512.0, 0.0); // delta
+
+        let mut rng = rand::thread_rng();
+
+        for _ in 0..1000 {
+            let ckks = CKKS::<Q, N>::new(scale_factor);
+
+            let (sk, pk) = ckks.new_key(&mut rng)?;
+
+            let m_raw: R<N> = Rq::<Q, N>::rand_f64(&mut rng, Uniform::new(0_f64, T as f64))?.to_r();
+            let m = m_raw * scale_factor_u64;
+
+            let ct = ckks.encrypt(&mut rng, &pk, &m)?;
+            let m_decrypted = ckks.decrypt(sk, ct)?;
+
+            let m_decrypted: Vec<u64> = m_decrypted
+                .coeffs()
+                .iter()
+                .map(|e| (*e as f64 / (scale_factor_u64 as f64)).round() as u64)
+                .collect();
+            let m_decrypted = Rq::<Q, N>::from_vec_u64(m_decrypted);
+            assert_eq!(m_decrypted, Rq::<Q, N>::from(m_raw));
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_encode_encrypt_decrypt_decode() -> Result<()> {
+        const Q: u64 = 2u64.pow(16) + 1;
+        const T: u64 = 16;
+        const N: usize = 4;
+        let scale_factor = C::<f64>::new(512.0, 0.0); // delta
+
+        let mut rng = rand::thread_rng();
+
+        for _ in 0..1000 {
+            let ckks = CKKS::<Q, N>::new(scale_factor);
+            let (sk, pk) = ckks.new_key(&mut rng)?;
+
+            let z: Vec<C<f64>> = std::iter::repeat_with(|| C::<f64>::rand(&mut rng, T))
+                .take(N / 2)
+                .collect();
+            let m: R<N> = ckks.encoder.encode(&z)?;
+
+            // sanity check
+            {
+                let z_decoded = ckks.encoder.decode(&m)?;
+                let rounded_z_decoded: Vec<C<f64>> = z_decoded
+                    .iter()
+                    .map(|c| C::<f64>::new(c.re.round(), c.im.round()))
+                    .collect();
+                assert_eq!(rounded_z_decoded, z);
+            }
+
+            let ct = ckks.encrypt(&mut rng, &pk, &m)?;
+            let m_decrypted = ckks.decrypt(sk, ct)?;
+
+            let z_decrypted = ckks.encoder.decode(&m_decrypted)?;
+
+            let rounded_z_decrypted: Vec<C<f64>> = z_decrypted
+                .iter()
+                .map(|&c| C::<f64>::new(c.re.round(), c.im.round()))
+                .collect();
+            assert_eq!(rounded_z_decrypted, z);
+        }
+
+        Ok(())
+    }
+}