diff --git a/tfhe/src/lib.rs b/tfhe/src/lib.rs
index 604bf17..784d84e 100644
--- a/tfhe/src/lib.rs
+++ b/tfhe/src/lib.rs
@@ -5,5 +5,6 @@
 #![allow(clippy::upper_case_acronyms)]
 #![allow(dead_code)] // TMP
 
+pub mod tgsw;
 pub mod tlev;
 pub mod tlwe;
diff --git a/tfhe/src/tgsw.rs b/tfhe/src/tgsw.rs
new file mode 100644
index 0000000..28c7593
--- /dev/null
+++ b/tfhe/src/tgsw.rs
@@ -0,0 +1,74 @@
+use anyhow::Result;
+use itertools::zip_eq;
+use rand::Rng;
+use std::array;
+use std::ops::{Add, Mul};
+
+use arith::{Ring, Rq, Tn, T64, TR};
+
+use crate::tlev::TLev;
+use crate::tlwe::{PublicKey, SecretKey, TLWE};
+use gfhe::glwe::GLWE;
+
+/// vector of length K+1 = [K], [1]
+#[derive(Clone, Debug)]
+pub struct TGSW<const K: usize>(pub(crate) Vec<TLev<K>>, TLev<K>);
+
+impl<const K: usize> TGSW<K> {
+    pub fn encrypt_s(
+        mut rng: impl Rng,
+        beta: u32,
+        l: u32,
+        sk: &SecretKey<K>,
+        m: &T64,
+    ) -> Result<Self> {
+        let a: Vec<TLev<K>> = (0..K)
+            .map(|i| TLev::encrypt_s(&mut rng, beta, l, sk, &(-sk.0 .0[i] * *m)))
+            .collect::<Result<Vec<_>>>()?;
+        let b: TLev<K> = TLev::encrypt_s(&mut rng, beta, l, sk, m)?;
+        Ok(Self(a, b))
+    }
+
+    pub fn decrypt(&self, sk: &SecretKey<K>, beta: u32) -> T64 {
+        self.1.decrypt(sk, beta)
+    }
+    pub fn from_tlwe(_tlwe: TLWE<K>) -> Self {
+        todo!()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use anyhow::Result;
+    use rand::distributions::Uniform;
+
+    use super::*;
+
+    #[test]
+    fn test_encrypt_decrypt() -> Result<()> {
+        const T: u64 = 2; // plaintext modulus
+        const K: usize = 16;
+        type S = TGSW<K>;
+
+        let beta: u32 = 2;
+        let l: u32 = 16;
+
+        let mut rng = rand::thread_rng();
+        let msg_dist = Uniform::new(0_u64, T);
+
+        for _ in 0..50 {
+            let (sk, _) = TLWE::<K>::new_key(&mut rng)?;
+
+            let m: Rq<T, 1> = Rq::rand_u64(&mut rng, msg_dist)?;
+            let p: T64 = TLev::<K>::encode::<T>(&m); // plaintext
+
+            let c = S::encrypt_s(&mut rng, beta, l, &sk, &p)?;
+            let p_recovered = c.decrypt(&sk, beta);
+            let m_recovered = TLev::<K>::decode::<T>(&p_recovered);
+
+            assert_eq!(m, m_recovered);
+        }
+
+        Ok(())
+    }
+}
diff --git a/tfhe/src/tlev.rs b/tfhe/src/tlev.rs
index de7a2ab..8209330 100644
--- a/tfhe/src/tlev.rs
+++ b/tfhe/src/tlev.rs
@@ -1,4 +1,5 @@
 use anyhow::Result;
+use itertools::zip_eq;
 use rand::Rng;
 use std::array;
 use std::ops::{Add, Mul};
@@ -11,11 +12,11 @@ use crate::tlwe::{PublicKey, SecretKey, TLWE};
 pub struct TLev<const K: usize>(pub(crate) Vec<TLWE<K>>);
 
 impl<const K: usize> TLev<K> {
-    pub fn encode<const T: u64>(m: &Rq<T, 1>) -> Tn<1> {
+    pub fn encode<const T: u64>(m: &Rq<T, 1>) -> T64 {
         let coeffs = m.coeffs();
-        Tn(array::from_fn(|i| T64(coeffs[i].0)))
+        T64(coeffs[0].0) // N=1, so take the only coeff
     }
-    pub fn decode<const T: u64>(p: &Tn<1>) -> Rq<T, 1> {
+    pub fn decode<const T: u64>(p: &T64) -> Rq<T, 1> {
         Rq::<T, 1>::from_vec_u64(p.coeffs().iter().map(|c| c.0).collect())
     }
     pub fn encrypt(
@@ -23,7 +24,7 @@ impl<const K: usize> TLev<K> {
         beta: u32,
         l: u32,
         pk: &PublicKey<K>,
-        m: &Tn<1>,
+        m: &T64,
     ) -> Result<Self> {
         let tlev: Vec<TLWE<K>> = (1..l + 1)
             .map(|i| {
@@ -35,25 +36,33 @@ impl<const K: usize> TLev<K> {
     }
     pub fn encrypt_s(
         mut rng: impl Rng,
-        beta: u32,
+        _beta: u32, // TODO rm, and make beta=2 always
         l: u32,
         sk: &SecretKey<K>,
-        m: &Tn<1>,
+        m: &T64,
     ) -> Result<Self> {
-        let tlev: Vec<TLWE<K>> = (1..l + 1)
+        let tlev: Vec<TLWE<K>> = (1..l as u64 + 1)
             .map(|i| {
-                TLWE::<K>::encrypt_s(&mut rng, sk, &(*m * (u64::MAX / beta.pow(i as u32) as u64)))
+                let aux = if i < 64 {
+                    *m * (u64::MAX / (1u64 << i))
+                } else {
+                    // 1<<64 would overflow, and anyways we're dividing u64::MAX
+                    // by it, which would be equal to 1
+                    *m
+                };
+                TLWE::<K>::encrypt_s(&mut rng, sk, &aux)
             })
             .collect::<Result<Vec<_>>>()?;
 
         Ok(Self(tlev))
     }
 
-    pub fn decrypt(&self, sk: &SecretKey<K>, beta: u32) -> Tn<1> {
+    pub fn decrypt(&self, sk: &SecretKey<K>, beta: u32) -> T64 {
         let pt = self.0[0].decrypt(sk);
         pt.mul_div_round(beta as u64, u64::MAX)
     }
 }
+// TODO review u64::MAX, since is -1 of the value we actually want
 
 #[cfg(test)]
 mod tests {
@@ -78,7 +87,7 @@ mod tests {
             let (sk, pk) = TLWE::<K>::new_key(&mut rng)?;
 
             let m: Rq<T, 1> = Rq::rand_u64(&mut rng, msg_dist)?;
-            let p: Tn<1> = S::encode::<T>(&m); // plaintext
+            let p: T64 = S::encode::<T>(&m); // plaintext
 
             let c = S::encrypt(&mut rng, beta, l, &pk, &p)?;
             let p_recovered = c.decrypt(&sk, beta);
diff --git a/tfhe/src/tlwe.rs b/tfhe/src/tlwe.rs
index 6ab4809..edd2e51 100644
--- a/tfhe/src/tlwe.rs
+++ b/tfhe/src/tlwe.rs
@@ -10,47 +10,50 @@ use std::ops::{Add, AddAssign, Mul, Sub};
 use arith::{Ring, Rq, Tn, T64, TR};
 use gfhe::{glwe, GLWE};
 
-const ERR_SIGMA: f64 = 3.2;
+// #[derive(Clone, Debug)]
+// pub struct SecretKey<const K: usize>(glwe::SecretKey<T64, K>);
+pub type SecretKey<const K: usize> = glwe::SecretKey<T64, K>;
 
-#[derive(Clone, Debug)]
-pub struct SecretKey<const K: usize>(glwe::SecretKey<Tn<1>, K>);
-#[derive(Clone, Debug)]
-pub struct PublicKey<const K: usize>(glwe::PublicKey<Tn<1>, K>);
+// #[derive(Clone, Debug)]
+// pub struct PublicKey<const K: usize>(glwe::PublicKey<T64, K>);
+pub type PublicKey<const K: usize> = glwe::PublicKey<T64, K>;
 
 #[derive(Clone, Debug)]
-pub struct TLWE<const K: usize>(pub GLWE<Tn<1>, K>);
+pub struct TLWE<const K: usize>(pub GLWE<T64, K>);
 
 impl<const K: usize> TLWE<K> {
     pub fn zero() -> Self {
-        Self(GLWE::<Tn<1>, K>::zero())
+        Self(GLWE::<T64, K>::zero())
     }
 
     pub fn new_key(rng: impl Rng) -> Result<(SecretKey<K>, PublicKey<K>)> {
         let (sk, pk) = GLWE::new_key(rng)?;
-        Ok((SecretKey(sk), PublicKey(pk)))
+        // Ok((SecretKey(sk), PublicKey(pk)))
+        Ok((sk, pk))
     }
 
-    pub fn encode<const P: u64>(m: &Rq<P, 1>) -> Tn<1> {
+    pub fn encode<const P: u64>(m: &Rq<P, 1>) -> T64 {
         let delta = u64::MAX / P; // floored
         let coeffs = m.coeffs();
-        Tn(array::from_fn(|i| T64(coeffs[i].0 * delta)))
+        // Tn(array::from_fn(|i| T64(coeffs[i].0 * delta)))
+        T64(coeffs[0].0 * delta)
     }
-    pub fn decode<const P: u64>(p: &Tn<1>) -> Rq<P, 1> {
+    pub fn decode<const P: u64>(p: &T64) -> Rq<P, 1> {
         let p = p.mul_div_round(P, u64::MAX);
         Rq::<P, 1>::from_vec_u64(p.coeffs().iter().map(|c| c.0).collect())
     }
 
     // encrypts with the given SecretKey (instead of PublicKey)
-    pub fn encrypt_s(rng: impl Rng, sk: &SecretKey<K>, p: &Tn<1>) -> Result<Self> {
-        let glwe = GLWE::encrypt_s(rng, &sk.0, p)?;
+    pub fn encrypt_s(rng: impl Rng, sk: &SecretKey<K>, p: &T64) -> Result<Self> {
+        let glwe = GLWE::encrypt_s(rng, &sk, p)?;
         Ok(Self(glwe))
     }
-    pub fn encrypt(rng: impl Rng, pk: &PublicKey<K>, p: &Tn<1>) -> Result<Self> {
-        let glwe = GLWE::encrypt(rng, &pk.0, p)?;
+    pub fn encrypt(rng: impl Rng, pk: &PublicKey<K>, p: &T64) -> Result<Self> {
+        let glwe = GLWE::encrypt(rng, &pk, p)?;
         Ok(Self(glwe))
     }
-    pub fn decrypt(&self, sk: &SecretKey<K>) -> Tn<1> {
-        self.0.decrypt(&sk.0)
+    pub fn decrypt(&self, sk: &SecretKey<K>) -> T64 {
+        self.0.decrypt(&sk)
     }
 }
 
@@ -86,29 +89,29 @@ impl<const K: usize> Sub<TLWE<K>> for TLWE<K> {
 }
 
 // plaintext addition
-impl<const K: usize> Add<Tn<1>> for TLWE<K> {
+impl<const K: usize> Add<T64> for TLWE<K> {
     type Output = Self;
-    fn add(self, plaintext: Tn<1>) -> Self {
-        let a: TR<Tn<1>, K> = self.0 .0;
-        let b: Tn<1> = self.0 .1 + plaintext;
+    fn add(self, plaintext: T64) -> Self {
+        let a: TR<T64, K> = self.0 .0;
+        let b: T64 = self.0 .1 + plaintext;
         Self(GLWE(a, b))
     }
 }
 // plaintext substraction
-impl<const K: usize> Sub<Tn<1>> for TLWE<K> {
+impl<const K: usize> Sub<T64> for TLWE<K> {
     type Output = Self;
-    fn sub(self, plaintext: Tn<1>) -> Self {
-        let a: TR<Tn<1>, K> = self.0 .0;
-        let b: Tn<1> = self.0 .1 - plaintext;
+    fn sub(self, plaintext: T64) -> Self {
+        let a: TR<T64, K> = self.0 .0;
+        let b: T64 = self.0 .1 - plaintext;
         Self(GLWE(a, b))
     }
 }
 // plaintext multiplication
-impl<const K: usize> Mul<Tn<1>> for TLWE<K> {
+impl<const K: usize> Mul<T64> for TLWE<K> {
     type Output = Self;
-    fn mul(self, plaintext: Tn<1>) -> Self {
-        let a: TR<Tn<1>, K> = TR(self.0 .0 .0.iter().map(|r_i| *r_i * plaintext).collect());
-        let b: Tn<1> = self.0 .1 * plaintext;
+    fn mul(self, plaintext: T64) -> Self {
+        let a: TR<T64, K> = TR(self.0 .0 .0.iter().map(|r_i| *r_i * plaintext).collect());
+        let b: T64 = self.0 .1 * plaintext;
         Self(GLWE(a, b))
     }
 }
@@ -134,7 +137,7 @@ mod tests {
 
             let m = Rq::<T, 1>::rand_u64(&mut rng, msg_dist)?;
             dbg!(&m);
-            let p: Tn<1> = S::encode::<T>(&m);
+            let p: T64 = S::encode::<T>(&m);
             dbg!(&p);
 
             let c = S::encrypt(&mut rng, &pk, &p)?;
@@ -168,8 +171,8 @@ mod tests {
 
             let m1 = Rq::<T, 1>::rand_u64(&mut rng, msg_dist)?;
             let m2 = Rq::<T, 1>::rand_u64(&mut rng, msg_dist)?;
-            let p1: Tn<1> = S::encode::<T>(&m1); // plaintext
-            let p2: Tn<1> = S::encode::<T>(&m2); // plaintext
+            let p1: T64 = S::encode::<T>(&m1); // plaintext
+            let p2: T64 = S::encode::<T>(&m2); // plaintext
 
             let c1 = S::encrypt(&mut rng, &pk, &p1)?;
             let c2 = S::encrypt(&mut rng, &pk, &p2)?;
@@ -199,8 +202,8 @@ mod tests {
 
             let m1 = Rq::<T, 1>::rand_u64(&mut rng, msg_dist)?;
             let m2 = Rq::<T, 1>::rand_u64(&mut rng, msg_dist)?;
-            let p1: Tn<1> = S::encode::<T>(&m1); // plaintext
-            let p2: Tn<1> = S::encode::<T>(&m2); // plaintext
+            let p1: T64 = S::encode::<T>(&m1); // plaintext
+            let p2: T64 = S::encode::<T>(&m2); // plaintext
 
             let c1 = S::encrypt(&mut rng, &pk, &p1)?;
 
@@ -209,7 +212,7 @@ mod tests {
             let p3_recovered = c3.decrypt(&sk);
             let m3_recovered = S::decode::<T>(&p3_recovered);
 
-            assert_eq!((m1 + m2).remodule::<T>(), m3_recovered);
+            assert_eq!(m1 + m2, m3_recovered);
         }
 
         Ok(())
@@ -229,15 +232,16 @@ mod tests {
 
             let m1 = Rq::<T, 1>::rand_u64(&mut rng, msg_dist)?;
             let m2 = Rq::<T, 1>::rand_u64(&mut rng, msg_dist)?;
-            let p1: Tn<1> = S::encode::<T>(&m1);
+            let p1: T64 = S::encode::<T>(&m1);
             // don't scale up p2, set it directly from m2
-            let p2: Tn<1> = Tn(array::from_fn(|i| T64(m2.coeffs()[i].0)));
+            // let p2: T64 = Tn(array::from_fn(|i| T64(m2.coeffs()[i].0)));
+            let p2: T64 = T64(m2.coeffs()[0].0);
 
             let c1 = S::encrypt(&mut rng, &pk, &p1)?;
 
             let c3 = c1 * p2;
 
-            let p3_recovered: Tn<1> = c3.decrypt(&sk);
+            let p3_recovered: T64 = c3.decrypt(&sk);
             let m3_recovered = S::decode::<T>(&p3_recovered);
             assert_eq!((m1.to_r() * m2.to_r()).to_rq::<T>(), m3_recovered);
         }