@@ -0,0 +1,77 @@
+def run_test(a, b):
+	print("\nnew test:")
+	print(a)
+	print(b)
+	c = a*b
+	print(c)
+	print(c.list())
+
+
+
+n_iters = 100
+Q= 65537
+print(Q)
+N=4
+F = GF(Q)
+R = QuotientRing(F[x], x^N + 1, names="X")
+print(R)
+
+a = R([4,2,1,0])
+b = R([1,2,3,4])
+run_test(a,b)
+
+
+#  print("Elements of the polynomial ring:")
+#  for e in R:
+#      print(e)
+
+
+# Other:
+# ======
+#
+#  t = R.gen()
+#  a =  0 + t   + 2*t^2 + 3*t^3 + 4*t^4 + 5*t^5
+#  b =  5 + 4*t + 3*t^2 + 2*t^3 + 1*t^4 + 0*t^5
+#  print("add", a+b)
+#  print("sub", a-b)
+#  print("mul", a*b)
+#  a =  0 + t   + 2*t^2 + 3*t^3 + 4*t^4 + 5*t^5
+
+# print("ring elem mul testvectors")
+#
+#
+# def randvec(size=N):return [int(random()*(Q-1)) for t in range(size)]
+#
+# a_vecs = [None]*n_iters
+# b_vecs = [None]*n_iters
+# c_vecs = [None]*n_iters
+#
+# for i in range(n_iters):
+#     a_vec = randvec()
+#     b_vec = randvec()
+#     a_pol = R(a_vec)
+#     b_pol = R(b_vec)
+#
+#     c_pol = a_pol*b_pol
+#
+#     a_vecs[i] = a_pol.list()
+#     b_vecs[i] = b_pol.list()
+#     c_vecs[i] = c_pol.list()
+#
+# print("let a_vecs = vec!{};\n".format(a_vecs))
+# print("let b_vecs = vec!{};\n".format(b_vecs))
+# print("let c_vecs = vec!{};".format(c_vecs))
+
+
+# # cyclotomic
+# 
+# Q= 65537
+# print(Q)
+# N=4
+# F = GF(Q)
+# R = QuotientRing(F[x], x^N - 1, names="X")
+# print(R)
+# 
+# a = R([1,0,0,2])
+# b = R([0,0,0,2])
+# run_test(a, b)

@@ -31,6 +31,12 @@ Self(coeffs)
         // let coeffs: [C; N] = array::from_fn(|_| Zq::from_u64(dist.sample(&mut rng)));
         // Self(coeffs)
     }
+
+    // returns the decomposition of each polynomial coefficient
+    fn decompose(&self, beta: u32, l: u32) -> Vec<Self> {
+        unimplemented!();
+        // array::from_fn(|i| self.coeffs[i].decompose(beta, l))
+    }
 }
 
 impl<const Q: u64, const N: usize> From<crate::ringq::Rq<Q, N>> for R<N> {

@@ -47,6 +47,18 @@ coeffs,
             evals: None,
         }
     }
+
+    // returns the decomposition of each polynomial coefficient, such
+    // decomposition will be a vecotor of length N, containint N vectors of Zq
+    fn decompose(&self, beta: u32, l: u32) -> Vec<Self> {
+        let elems: Vec<Vec<Zq<Q>>> = self.coeffs.iter().map(|r| r.decompose(beta, l)).collect();
+        // transpose it
+        let r: Vec<Vec<Zq<Q>>> = (0..elems[0].len())
+            .map(|i| (0..elems.len()).map(|j| elems[j][i]).collect())
+            .collect();
+        // convert it to Rq<Q,N>
+        r.iter().map(|a_i| Self::from_vec(a_i.clone())).collect()
+    }
 }
 
 impl<const Q: u64, const N: usize> From<crate::ring::R<N>> for Rq<Q, N> {
@@ -597,6 +609,33 @@ let expected_c = Rq::new(expected_c, None);
 
         let c = mul_mut(&mut a, &mut b);
         assert_eq!(c, expected_c);
+        Ok(())
+    }
+
+    #[test]
+    fn test_rq_decompose() -> Result<()> {
+        const Q: u64 = 16;
+        const N: usize = 4;
+        let beta = 4;
+        let l = 2;
+
+        let a = Rq::<Q, N>::from_vec_u64(vec![7u64, 14, 3, 6]);
+        let d = a.decompose(beta, l);
+
+        assert_eq!(
+            d[0],
+            vec![1u64, 3, 0, 1]
+                .iter()
+                .map(|e| Zq::<Q>::from_u64(*e))
+                .collect::<Vec<_>>()
+        );
+        assert_eq!(
+            d[1],
+            vec![3u64, 2, 3, 2]
+                .iter()
+                .map(|e| Zq::<Q>::from_u64(*e))
+                .collect::<Vec<_>>()
+        );
         Ok(())
     }
 }

@@ -27,4 +27,6 @@ fn coeffs(&self) -> Vec<Self::C>;
     fn zero() -> Self;
     // note/wip/warning: dist (0,q) with f64, will output more '0=q' elements than other values
     fn rand(rng: impl Rng, dist: impl Distribution<f64>) -> Self;
+
+    fn decompose(&self, beta: u32, l: u32) -> Vec<Self>;
 }

@@ -16,6 +16,9 @@ #[derive(Clone, Debug)]
 pub struct TR<R: Ring, const K: usize>(pub Vec<R>);
 
 impl<R: Ring, const K: usize> TR<R, K> {
+    pub fn zero() -> Self {
+        Self((0..K).into_iter().map(|_| R::zero()).collect())
+    }
     pub fn rand(mut rng: impl Rng, dist: impl Distribution<f64>) -> Self {
         Self(
             (0..K)
@@ -23,6 +26,11 @@ .into_iter()
                 .map(|_| R::rand(&mut rng, &dist))
                 .collect(),
         )
+    }
+    // returns the decomposition of each polynomial element
+    pub fn decompose(&self, beta: u32, l: u32) -> Vec<Self> {
+        unimplemented!()
+        // self.0.iter().map(|r| r.decompose(beta, l)).collect() // this is Vec<Vec<Vec<R::C>>>
     }
 }
 

@@ -3,7 +3,7 @@ use rand::{distributions::Distribution, Rng};
 use std::fmt;
 use std::ops;
 
-// Z_q, integers modulus q, not necessarily prime
+/// Z_q, integers modulus q, not necessarily prime
 #[derive(Clone, Copy, PartialEq)]
 pub struct Zq<const Q: u64>(pub u64);
 
@@ -130,6 +130,28 @@ /// perform the mod switch operation from Q to Q', where Q2=Q'
     pub fn mod_switch<const Q2: u64>(&self) -> Zq<Q2> {
         Zq::<Q2>::from_u64(((self.0 as f64 * Q2 as f64) / Q as f64).round() as u64)
     }
+
+    // TODO more efficient method for when decomposing with base 2 (beta=2)
+    pub fn decompose(&self, beta: u32, l: u32) -> Vec<Self> {
+        let mut rem: u64 = self.0;
+        // next if is for cases in which beta does not divide Q (concretely
+        // beta^l!=Q). round to the nearest multiple of q/beta^l
+        if rem >= beta.pow(l) as u64 {
+            // rem = Q - 1 - (Q / beta as u64); // floor
+            return vec![Zq(beta as u64 - 1); l as usize];
+        }
+
+        let mut x: Vec<Self> = vec![];
+        for i in 1..l + 1 {
+            let den = Q / beta.pow(i) as u64;
+            let x_i = rem / den; // division between u64 already does floor
+            x.push(Self::from_u64(x_i));
+            if x_i != 0 {
+                rem = rem % den;
+            }
+        }
+        x
+    }
 }
 
 impl<const Q: u64> Zq<Q> {
@@ -243,6 +265,7 @@
 #[cfg(test)]
 mod tests {
     use super::*;
+    use rand::distributions::Uniform;
 
     #[test]
     fn exp() {
@@ -261,5 +284,63 @@ const Q: u64 = 1021;
         let a = Zq::<Q>::from_f64(101.0);
         let b = Zq::<Q>::from_f64(-1.0);
         assert_eq!(-a, a * b);
+    }
+
+    fn recompose<const Q: u64>(beta: u32, l: u32, d: Vec<Zq<Q>>) -> Zq<Q> {
+        let mut x = 0u64;
+        for i in 0..l {
+            x += d[i as usize].0 * Q / beta.pow(i + 1) as u64;
+        }
+        Zq::from_u64(x)
+    }
+
+    #[test]
+    fn test_decompose() {
+        const Q1: u64 = 16;
+        let beta: u32 = 2;
+        let l: u32 = 4;
+        let x = Zq::<Q1>::from_u64(9);
+        let d = x.decompose(beta, l);
+
+        assert_eq!(recompose::<Q1>(beta, l, d), x);
+
+        const Q: u64 = 5u64.pow(3);
+        let beta: u32 = 5;
+        let l: u32 = 3;
+
+        let dist = Uniform::new(0_u64, Q);
+        let mut rng = rand::thread_rng();
+
+        for _ in 0..1000 {
+            let x = Zq::<Q>::from_u64(dist.sample(&mut rng));
+
+            let d = x.decompose(beta, l);
+
+            assert_eq!(recompose::<Q>(beta, l, d), x);
+        }
+    }
+
+    #[test]
+    fn test_decompose_approx() {
+        const Q: u64 = 2u64.pow(4) + 1;
+        let beta: u32 = 2;
+        let l: u32 = 4;
+        let x = Zq::<Q>::from_u64(16); // in q, but bigger than beta^l
+        let d = x.decompose(beta, l);
+        assert_eq!(recompose::<Q>(beta, l, d), Zq(15));
+
+        const Q2: u64 = 5u64.pow(3) + 1;
+        let beta: u32 = 5;
+        let l: u32 = 3;
+        let x = Zq::<Q2>::from_u64(125); // in q, but bigger than beta^l
+        let d = x.decompose(beta, l);
+        assert_eq!(recompose::<Q2>(beta, l, d), Zq(124));
+
+        const Q3: u64 = 2u64.pow(16) + 1;
+        let beta: u32 = 2;
+        let l: u32 = 16;
+        let x = Zq::<Q3>::from_u64(Q3 - 1); // in q, but bigger than beta^l
+        let d = x.decompose(beta, l);
+        assert_eq!(recompose::<Q3>(beta, l, d), Zq(beta.pow(l) as u64 - 1));
     }
 }

@@ -1,20 +1,33 @@
 use anyhow::Result;
+use itertools::zip_eq;
 use rand::Rng;
 use rand_distr::{Normal, Uniform};
-use std::ops::{Add, Mul};
+use std::iter::Sum;
+use std::ops::{Add, AddAssign, Mul, Sub};
+
+use arith::{Ring, Rq, Zq, TR};
 
-use arith::{Ring, Rq, TR};
+use crate::glev::GLev;
 
 const ERR_SIGMA: f64 = 3.2;
 
+#[derive(Clone, Debug)]
 pub struct GLWE<const Q: u64, const N: usize, const K: usize>(TR<Rq<Q, N>, K>, Rq<Q, N>);
 
 #[derive(Clone, Debug)]
 pub struct SecretKey<const Q: u64, const N: usize, const K: usize>(TR<Rq<Q, N>, K>);
 #[derive(Clone, Debug)]
 pub struct PublicKey<const Q: u64, const N: usize, const K: usize>(Rq<Q, N>, TR<Rq<Q, N>, K>);
+
+// K GLevs, each KSK_i=l GLWEs
+#[derive(Clone, Debug)]
+pub struct KSK<const Q: u64, const N: usize, const K: usize>(Vec<GLev<Q, N, K>>);
 
 impl<const Q: u64, const N: usize, const K: usize> GLWE<Q, N, K> {
+    pub fn zero() -> Self {
+        Self(TR::zero(), Rq::zero())
+    }
+
     pub fn new_key(mut rng: impl Rng) -> Result<(SecretKey<Q, N, K>, PublicKey<Q, N, K>)> {
         let Xi_key = Uniform::new(0_f64, 2_f64);
         let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
@@ -27,32 +40,69 @@ let pk: PublicKey<Q, N, K> = PublicKey((&a * &s) + e, a);
         Ok((SecretKey(s), pk))
     }
 
-    // TODO delta not as input
-    pub fn encrypt_s<const T: u64>(
+    pub fn new_ksk(
+        mut rng: impl Rng,
+        beta: u32,
+        l: u32,
+        sk: &SecretKey<Q, N, K>,
+        new_sk: &SecretKey<Q, N, K>,
+    ) -> Result<KSK<Q, N, K>> {
+        let r: Vec<GLev<Q, N, K>> = (0..K)
+            .into_iter()
+            .map(|i|
+                // treat sk_i as the msg being encrypted
+                GLev::<Q, N, K>::encrypt_s(&mut rng, beta, l, &new_sk, &sk.0 .0[i]))
+            .collect::<Result<Vec<_>>>()?;
+
+        Ok(KSK(r))
+    }
+    pub fn key_switch(&self, beta: u32, l: u32, ksk: &KSK<Q, N, K>) -> Self {
+        let (a, b): (TR<Rq<Q, N>, K>, Rq<Q, N>) = (self.0.clone(), self.1);
+
+        let lhs: GLWE<Q, N, K> = GLWE(TR::zero(), b);
+
+        // K iterations, ksk.0 contains K times GLev
+        let rhs: GLWE<Q, N, K> = zip_eq(a.0, ksk.0.clone())
+            .map(|(a_i, ksk_i)| Self::dot_prod(a_i.decompose(beta, l), ksk_i))
+            .sum();
+
+        lhs - rhs
+    }
+    // note: a_decomp is of length N
+    fn dot_prod(a_decomp: Vec<Rq<Q, N>>, ksk_i: GLev<Q, N, K>) -> GLWE<Q, N, K> {
+        // l times GLWES
+        let glwes: Vec<GLWE<Q, N, K>> = ksk_i.0;
+
+        // l iterations
+        let r: GLWE<Q, N, K> = zip_eq(a_decomp, glwes)
+            .map(|(a_d_i, glwe_i)| glwe_i * a_d_i)
+            .sum();
+        r
+    }
+
+    // encrypts with the given SecretKey (instead of PublicKey)
+    pub fn encrypt_s(
         mut rng: impl Rng,
         sk: &SecretKey<Q, N, K>,
-        m: &Rq<T, N>,
+        m: &Rq<Q, N>,
+        // TODO delta not as input
         delta: u64,
     ) -> Result<Self> {
-        let m: Rq<Q, N> = m.remodule::<Q>();
-
         let Xi_key = Uniform::new(0_f64, 2_f64);
         let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
 
         let a: TR<Rq<Q, N>, K> = TR::rand(&mut rng, Xi_key);
         let e = Rq::<Q, N>::rand(&mut rng, Xi_err);
 
-        let b: Rq<Q, N> = (&a * &sk.0) + m * delta + e;
+        let b: Rq<Q, N> = (&a * &sk.0) + *m * delta + e;
         Ok(Self(a, b))
     }
-    pub fn encrypt<const T: u64>(
+    pub fn encrypt(
         mut rng: impl Rng,
         pk: &PublicKey<Q, N, K>,
-        m: &Rq<T, N>,
+        m: &Rq<Q, N>,
         delta: u64,
     ) -> Result<Self> {
-        let m: Rq<Q, N> = m.remodule::<Q>();
-
         let Xi_key = Uniform::new(0_f64, 2_f64);
         let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
 
@@ -61,23 +111,16 @@
         let e0 = Rq::<Q, N>::rand(&mut rng, Xi_err);
         let e1 = TR::<Rq<Q, N>, K>::rand(&mut rng, Xi_err);
 
-        let b: Rq<Q, N> = pk.0 * u + m * delta + e0;
+        let b: Rq<Q, N> = pk.0 * u + *m * delta + e0;
         let d: TR<Rq<Q, N>, K> = &pk.1 * &u + e1;
 
         Ok(Self(d, b))
     }
-    pub fn decrypt<const T: u64>(&self, sk: &SecretKey<Q, N, K>, delta: u64) -> Rq<T, N> {
+    pub fn decrypt<const T: u64>(&self, sk: &SecretKey<Q, N, K>, delta: u64) -> Rq<Q, N> {
         let (d, b): (TR<Rq<Q, N>, K>, Rq<Q, N>) = (self.0.clone(), self.1);
         let r: Rq<Q, N> = b - &d * &sk.0;
         let r = r.mul_div_round(T, Q);
-        // let r_scaled: Vec<f64> = r
-        //     .coeffs()
-        //     .iter()
-        //     // .map(|e| (e.0 as f64 / delta as f64).round())
-        //     .map(|e| e.mul_div_round(T, Q))
-        //     .collect();
-        // let r = Rq::<Q, N>::from_vec_f64(r_scaled);
-        r.remodule::<T>()
+        r
     }
 
     pub fn mod_switch<const P: u64>(&self) -> GLWE<P, N, K> {
@@ -104,6 +147,36 @@ let b: Rq<Q, N> = self.1 + plaintext;
         Self(a, b)
     }
 }
+impl<const Q: u64, const N: usize, const K: usize> AddAssign for GLWE<Q, N, K> {
+    fn add_assign(&mut self, rhs: Self) {
+        for i in 0..K {
+            self.0 .0[i] = self.0 .0[i] + rhs.0 .0[i];
+        }
+        self.1 = self.1 + rhs.1;
+    }
+}
+impl<const Q: u64, const N: usize, const K: usize> Sum<GLWE<Q, N, K>> for GLWE<Q, N, K> {
+    fn sum<I>(iter: I) -> Self
+    where
+        I: Iterator<Item = Self>,
+    {
+        let mut acc = GLWE::<Q, N, K>::zero();
+        for e in iter {
+            acc += e;
+        }
+        acc
+    }
+}
+
+impl<const Q: u64, const N: usize, const K: usize> Sub<GLWE<Q, N, K>> for GLWE<Q, N, K> {
+    type Output = Self;
+    fn sub(self, other: Self) -> Self {
+        let a: TR<Rq<Q, N>, K> = self.0 - other.0;
+        let b: Rq<Q, N> = self.1 - other.1;
+        Self(a, b)
+    }
+}
+
 impl<const Q: u64, const N: usize, const K: usize> Mul<Rq<Q, N>> for GLWE<Q, N, K> {
     type Output = Self;
     fn mul(self, plaintext: Rq<Q, N>) -> Self {
@@ -114,6 +187,15 @@ plaintext.compute_evals();
 
         let a: TR<Rq<Q, N>, K> = TR(self.0 .0.iter().map(|r_i| *r_i * plaintext).collect());
         let b: Rq<Q, N> = self.1 * plaintext;
+        Self(a, b)
+    }
+}
+
+impl<const Q: u64, const N: usize, const K: usize> Mul<Zq<Q>> for GLWE<Q, N, K> {
+    type Output = Self;
+    fn mul(self, e: Zq<Q>) -> Self {
+        let a: TR<Rq<Q, N>, K> = TR(self.0 .0.iter().map(|r_i| *r_i * e).collect());
+        let b: Rq<Q, N> = self.1 * e;
         Self(a, b)
     }
 }
@@ -141,11 +223,18 @@ let (sk, pk) = S::new_key(&mut rng)?;
 
             let msg_dist = Uniform::new(0_u64, T);
             let m = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
+            let m: Rq<Q, N> = m.remodule::<Q>();
 
             let c = S::encrypt(&mut rng, &pk, &m, delta)?;
-            let m_recovered = c.decrypt(&sk, delta);
+            let m_recovered = c.decrypt::<T>(&sk, delta);
+
+            assert_eq!(m.remodule::<T>(), m_recovered.remodule::<T>());
+
+            // same but using encrypt_s (with sk instead of pk))
+            let c = S::encrypt_s(&mut rng, &sk, &m, delta)?;
+            let m_recovered = c.decrypt::<T>(&sk, delta);
 
-            assert_eq!(m, m_recovered);
+            assert_eq!(m.remodule::<T>(), m_recovered.remodule::<T>());
         }
 
         Ok(())
@@ -168,15 +257,17 @@
             let msg_dist = Uniform::new(0_u64, T);
             let m1 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
             let m2 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
+            let m1: Rq<Q, N> = m1.remodule::<Q>();
+            let m2: Rq<Q, N> = m2.remodule::<Q>();
 
             let c1 = S::encrypt(&mut rng, &pk, &m1, delta)?;
             let c2 = S::encrypt(&mut rng, &pk, &m2, delta)?;
 
             let c3 = c1 + c2;
 
-            let m3_recovered = c3.decrypt(&sk, delta);
+            let m3_recovered = c3.decrypt::<T>(&sk, delta);
 
-            assert_eq!(m1 + m2, m3_recovered);
+            assert_eq!((m1 + m2).remodule::<T>(), m3_recovered.remodule::<T>());
         }
 
         Ok(())
@@ -199,15 +290,17 @@
             let msg_dist = Uniform::new(0_u64, T);
             let m1 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
             let m2 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
-            let m2_scaled: Rq<Q, N> = m2.remodule::<Q>() * delta;
+            let m1: Rq<Q, N> = m1.remodule::<Q>();
+            let m2: Rq<Q, N> = m2.remodule::<Q>();
+            let m2_scaled: Rq<Q, N> = m2 * delta;
 
             let c1 = S::encrypt(&mut rng, &pk, &m1, delta)?;
 
             let c3 = c1 + m2_scaled;
 
-            let m3_recovered = c3.decrypt(&sk, delta);
+            let m3_recovered = c3.decrypt::<T>(&sk, delta);
 
-            assert_eq!(m1 + m2, m3_recovered);
+            assert_eq!((m1 + m2).remodule::<T>(), m3_recovered.remodule::<T>());
         }
 
         Ok(())
@@ -230,12 +323,14 @@
             let msg_dist = Uniform::new(0_u64, T);
             let m1 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
             let m2 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
+            let m1: Rq<Q, N> = m1.remodule::<Q>();
             let m2: Rq<Q, N> = m2.remodule::<Q>();
             let c1 = S::encrypt(&mut rng, &pk, &m1, delta)?;
 
             let c3 = c1 * m2;
 
-            let m3_recovered: Rq<T, N> = c3.decrypt(&sk, delta);
+            let m3_recovered: Rq<Q, N> = c3.decrypt::<T>(&sk, delta);
+            let m3_recovered: Rq<T, N> = m3_recovered.remodule::<T>();
             assert_eq!((m1.to_r() * m2.to_r()).to_rq::<T>(), m3_recovered);
         }
 
@@ -265,18 +360,60 @@ let (sk, pk) = S::new_key(&mut rng)?;
 
             let msg_dist = Uniform::new(0_u64, T);
             let m = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
+            let m: Rq<Q, N> = m.remodule::<Q>();
 
             let c = S::encrypt(&mut rng, &pk, &m, delta)?;
+            // let c = S::encrypt_s(&mut rng, &sk, &m, delta)?;
 
             let c2 = c.mod_switch::<P>();
             let sk2: SecretKey<P, N, K> =
                 SecretKey(TR(sk.0 .0.iter().map(|s_i| s_i.remodule::<P>()).collect()));
             let delta2: u64 = ((P as f64 * delta as f64) / Q as f64).round() as u64;
 
-            let m_recovered = c2.decrypt(&sk2, delta2);
+            let m_recovered = c2.decrypt::<T>(&sk2, delta2);
 
-            assert_eq!(m, m_recovered);
+            assert_eq!(m.remodule::<T>(), m_recovered.remodule::<T>());
         }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_key_switch() -> Result<()> {
+        const Q: u64 = 2u64.pow(16) + 1;
+        const N: usize = 128;
+        const T: u64 = 2; // plaintext modulus
+        const K: usize = 16;
+        type S = GLWE<Q, N, K>;
+
+        let beta: u32 = 2;
+        let l: u32 = 16;
+
+        let delta: u64 = Q / T; // floored
+        let mut rng = rand::thread_rng();
+
+        let (sk, pk) = S::new_key(&mut rng)?;
+        let (sk2, _) = S::new_key(&mut rng)?;
+        // ksk to switch from sk to sk2
+        let ksk = S::new_ksk(&mut rng, beta, l, &sk, &sk2)?;
+
+        let msg_dist = Uniform::new(0_u64, T);
+        let m = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
+        let m: Rq<Q, N> = m.remodule::<Q>();
+
+        let c = S::encrypt_s(&mut rng, &sk, &m, delta)?;
+
+        let c2 = c.key_switch(beta, l, &ksk);
+
+        // decrypt with the 2nd secret key
+        let m_recovered = c2.decrypt::<T>(&sk2, delta);
+        assert_eq!(m.remodule::<T>(), m_recovered.remodule::<T>());
+
+        // do the same but now encrypting with pk
+        // let c = S::encrypt(&mut rng, &pk, &m, delta)?;
+        // let c2 = c.key_switch(beta, l, &ksk);
+        // let m_recovered = c2.decrypt::<T>(&sk2, delta);
+        // assert_eq!(m.remodule::<T>(), m_recovered.remodule::<T>());
 
         Ok(())
     }

@@ -5,4 +5,5 @@ #![allow(non_camel_case_types)]
 #![allow(clippy::upper_case_acronyms)]
 #![allow(dead_code)] // TMP
 
+pub mod glev;
 pub mod glwe;