diff --git a/arith/src/ring_torus.rs b/arith/src/ring_torus.rs
index 1a8192d..46e134c 100644
--- a/arith/src/ring_torus.rs
+++ b/arith/src/ring_torus.rs
@@ -85,14 +85,11 @@ impl<const N: usize> Ring for Tn<N> {
 impl<const N: usize> Tn<N> {
     // multiply self by X^-h
     pub fn left_rotate(&self, h: usize) -> Self {
-        dbg!(&h);
-        dbg!(&N);
         let h = h % N;
         assert!(h < N);
         let c = self.0;
         // c[h], c[h+1], c[h+2], ..., c[n-1],  -c[0], -c[1], ..., -c[h-1]
         // let r: Vec<T64> = vec![c[h..N], c[0..h].iter().map(|&c_i| -c_i).collect()].concat();
-        dbg!(&h);
         let r: Vec<T64> = c[h..N]
             .iter()
             .copied()
diff --git a/tfhe/src/tggsw.rs b/tfhe/src/tggsw.rs
index fac7c22..663cd03 100644
--- a/tfhe/src/tggsw.rs
+++ b/tfhe/src/tggsw.rs
@@ -132,3 +132,49 @@ impl<const N: usize, const K: usize> Mul<Vec<Tn<N>>> for TGLev<N, K> {
         r
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use anyhow::Result;
+    use rand::distributions::Uniform;
+
+    use super::*;
+    #[test]
+    fn test_external_product() -> Result<()> {
+        const T: u64 = 16; // plaintext modulus
+        const K: usize = 4;
+        const N: usize = 64;
+        const KN: usize = K * N;
+
+        let beta: u32 = 2;
+        let l: u32 = 64;
+
+        let mut rng = rand::thread_rng();
+        let msg_dist = Uniform::new(0_u64, T);
+
+        for _ in 0..50 {
+            let (sk, _) = TGLWE::<N, K>::new_key::<KN>(&mut rng)?;
+
+            let m1: Rq<T, N> = Rq::rand_u64(&mut rng, msg_dist)?;
+            let p1: Tn<N> = TGLev::<N, K>::encode::<T>(&m1);
+
+            let m2: Rq<T, N> = Rq::rand_u64(&mut rng, msg_dist)?;
+            let p2: Tn<N> = TGLWE::<N, K>::encode::<T>(&m2); // scaled by delta
+
+            let tgsw = TGGSW::<N, K>::encrypt_s(&mut rng, beta, l, &sk, &p1)?;
+            let tlwe = TGLWE::<N, K>::encrypt_s(&mut rng, &sk, &p2)?;
+
+            let res: TGLWE<N, K> = tgsw * tlwe;
+
+            // let p_recovered = res.decrypt(&sk, beta);
+            let p_recovered = res.decrypt(&sk);
+            // downscaled by delta^-1
+            let res_recovered = TGLWE::<N, K>::decode::<T>(&p_recovered);
+
+            // assert_eq!(m1 * m2, m_recovered);
+            assert_eq!((m1.to_r() * m2.to_r()).to_rq::<T>(), res_recovered);
+        }
+
+        Ok(())
+    }
+}
diff --git a/tfhe/src/tlwe.rs b/tfhe/src/tlwe.rs
index c087332..b905c33 100644
--- a/tfhe/src/tlwe.rs
+++ b/tfhe/src/tlwe.rs
@@ -132,21 +132,37 @@ pub fn blind_rotation<const N: usize, const K: usize, const KN: usize, const KN2
     c_j
 }
 
+pub fn bootstrapping<const N: usize, const K: usize, const KN: usize, const KN2: u64>(
+    btk: BootstrappingKey<N, K, KN>,
+    table: TGLWE<N, K>,
+    c: TLWE<KN>,
+) -> TLWE<KN> {
+    let rotated: TGLWE<N, K> = blind_rotation::<N, K, KN, KN2>(c, btk.clone(), table);
+    let c_h: TLWE<KN> = rotated.sample_extraction(0);
+    let r = c_h.key_switch(2, 64, &btk.1);
+    r
+}
+
 #[derive(Clone, Debug)]
-pub struct BootstrappingKey<const N: usize, const K: usize, const KN: usize>(pub Vec<TGGSW<N, K>>);
+pub struct BootstrappingKey<const N: usize, const K: usize, const KN: usize>(
+    pub Vec<TGGSW<N, K>>,
+    pub KSK<KN>,
+);
 impl<const N: usize, const K: usize, const KN: usize> BootstrappingKey<N, K, KN> {
     pub fn from_sk(mut rng: impl Rng, sk: &tglwe::SecretKey<N, K>) -> Result<Self> {
         let (beta, l) = (2u32, 64u32); // TMP
                                        //
         let s: TR<Tn<N>, K> = sk.0 .0.clone();
+        let (sk2, _) = TLWE::<KN>::new_key(&mut rng)?; // TLWE<KN> compatible with TGLWE<N,K>
 
         // each btk_j = TGGSW_sk(s_i)
         let btk: Vec<TGGSW<N, K>> = s
             .iter()
             .map(|s_i| TGGSW::<N, K>::encrypt_s(&mut rng, beta, l, sk, s_i))
             .collect::<Result<Vec<_>>>()?;
+        let ksk = TLWE::<KN>::new_ksk(&mut rng, beta, l, &sk.to_tlwe(), &sk2)?;
 
-        Ok(Self(btk))
+        Ok(Self(btk, ksk))
     }
 }
 
@@ -399,4 +415,45 @@ mod tests {
 
         Ok(())
     }
+
+    #[test]
+    fn test_bootstrapping() -> Result<()> {
+        const T: u64 = 128; // plaintext modulus
+        const K: usize = 1;
+        const N: usize = 1024;
+        const KN: usize = K * N;
+        let mut rng = rand::thread_rng();
+
+        let start = Instant::now();
+        let table: TGLWE<N, K> = compute_lookup_table::<T, K, N>();
+        println!("table took: {:?}", start.elapsed());
+
+        let (sk, _) = TGLWE::<N, K>::new_key::<KN>(&mut rng)?;
+        let sk_tlwe: SecretKey<KN> = sk.to_tlwe::<KN>();
+
+        let start = Instant::now();
+        let btk = BootstrappingKey::<N, K, KN>::from_sk(&mut rng, &sk)?;
+        println!("btk took: {:?}", start.elapsed());
+
+        let msg_dist = Uniform::new(0_u64, T);
+        let m = Rq::<T, 1>::rand_u64(&mut rng, msg_dist)?;
+        // let m = Rq::<T, 1>::from_vec(vec![Zq(5)]);
+        dbg!(&m);
+        let p = TLWE::<K>::encode::<T>(&m); // plaintext
+
+        let c = TLWE::<KN>::encrypt_s(&mut rng, &sk_tlwe, &p)?;
+
+        let start = Instant::now();
+        // the ugly const generics are temporary
+        let bootstrapped: TLWE<KN> =
+            bootstrapping::<N, K, KN, { K as u64 * N as u64 }>(btk, table, c);
+        println!("bootstrapping took: {:?}", start.elapsed());
+
+        let p_recovered: T64 = bootstrapped.decrypt(&sk_tlwe);
+        let m_recovered = TLWE::<KN>::decode::<T>(&p_recovered);
+        dbg!(&m_recovered);
+        assert_eq!(m_recovered, m);
+
+        Ok(())
+    }
 }