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

arithmetic/src/naive.rs

@@ -136,7 +136,7 @@ mod tests {
 
         let mut rng = rand::thread_rng();
         let uniform_distr = Uniform::new(0_f64, Q as f64);
-        let a = PR::<Q, N>::rand(&mut rng, uniform_distr)?;
+        let a = PR::<Q, N>::rand_f64(&mut rng, uniform_distr)?;
         // let a = PR::<Q, N>::new_from_u64(vec![36, 21, 9, 19]);
 
         // let a_padded_coeffs: [Zq<Q>; 2 * N] =
@@ -181,7 +181,7 @@ mod tests {
         let ntt = NTT::<Q, N>::new()?;
 
         let rng = rand::thread_rng();
-        let a = PR::<Q, { 2 * N }>::rand(rng, Uniform::new(0_f64, (Q - 1) as f64))?;
+        let a = PR::<Q, { 2 * N }>::rand_f64(rng, Uniform::new(0_f64, (Q - 1) as f64))?;
         let a = a.coeffs;
         dbg!(&a);
         let a_ntt = matrix_vec_product(&ntt.ntt, &a.to_vec())?;
@@ -189,6 +189,7 @@ mod tests {
         let a_intt = matrix_vec_product(&ntt.intt, &a_ntt)?;
         dbg!(&a_intt);
         assert_eq!(a_intt, a);
+        // TODO bench
 
         Ok(())
     }

arithmetic/src/ntt.rs

@@ -1,5 +1,6 @@
-//! Implementation of the NTT & iNTT, following the CT & GS algorighms, more
-//! details in https://github.com/arnaucube/math/blob/master/notes_ntt.pdf .
+//! Implementation of the NTT & iNTT, following the CT & GS algorighms, more details in
+//! https://eprint.iacr.org/2017/727.pdf, some notes at
+//! https://github.com/arnaucube/math/blob/master/notes_ntt.pdf .
 use crate::zq::Zq;
 
 #[derive(Debug)]
@@ -14,7 +15,8 @@ impl<const Q: u64, const N: usize> NTT<Q, N> {
 }
 
 impl<const Q: u64, const N: usize> NTT<Q, N> {
-    /// implements the Cooley-Tukey (CT) algorithm. Details at section 3.1 of
+    /// implements the Cooley-Tukey (CT) algorithm. Details at
+    /// https://eprint.iacr.org/2017/727.pdf, also some notes at section 3.1 of
     /// https://github.com/arnaucube/math/blob/master/notes_ntt.pdf
     pub fn ntt(a: [Zq<Q>; N]) -> [Zq<Q>; N] {
         let mut t = N / 2;
@@ -38,7 +40,8 @@ impl<const Q: u64, const N: usize> NTT<Q, N> {
         r
     }
 
-    /// implements the Gentleman-Sande (GS) algorithm. Details at section 3.2 of
+    /// implements the Cooley-Tukey (CT) algorithm. Details at
+    /// https://eprint.iacr.org/2017/727.pdf, also some notes at section 3.2 of
     /// https://github.com/arnaucube/math/blob/master/notes_ntt.pdf
     pub fn intt(a: [Zq<Q>; N]) -> [Zq<Q>; N] {
         let mut t = 1;

arithmetic/src/ring.rs

@@ -63,13 +63,20 @@ impl<const Q: u64, const N: usize> PR<Q, N> {
             evals: None,
         })
     }
-    pub fn rand(mut rng: impl Rng, dist: impl Distribution<f64>) -> Result<Self> {
+    pub fn rand_f64(mut rng: impl Rng, dist: impl Distribution<f64>) -> Result<Self> {
         let coeffs: [Zq<Q>; N] = array::from_fn(|_| Zq::from_f64(dist.sample(&mut rng)));
         Ok(Self {
             coeffs,
             evals: None,
         })
     }
+    pub fn rand_u64(mut rng: impl Rng, dist: impl Distribution<u64>) -> Result<Self> {
+        let coeffs: [Zq<Q>; N] = array::from_fn(|_| Zq::new(dist.sample(&mut rng)));
+        Ok(Self {
+            coeffs,
+            evals: None,
+        })
+    }
     // WIP. returns random v \in {0,1}. // TODO {-1, 0, 1}
     pub fn rand_bin(mut rng: impl Rng, dist: impl Distribution<bool>) -> Result<Self> {
         let coeffs: [Zq<Q>; N] = array::from_fn(|_| Zq::from_bool(dist.sample(&mut rng)));