diff --git a/README.md b/README.md
index a58d409..7cea5d4 100644
--- a/README.md
+++ b/README.md
@@ -16,7 +16,7 @@ Implementations from scratch done while studying some FHE papers; do not use in
 
 This example shows usage of TFHE, but the idea is that the same interface would
 work for using CKKS & BFV, the only thing to be changed would be the parameters
-and the line `type S = TWLE<K>` to use `CKKS<Q, N>` or `BFV<Q, N, T>`.
+and the usage of `TLWE` by `CKKS` or `BFV`.
 
 ```rust
 let param = Param {
@@ -31,7 +31,7 @@ let msg_dist = Uniform::new(0_u64, param.t);
 
 let (sk, pk) = TLWE::new_key(&mut rng, &param)?;
 
-// get two random msgs in Z_t
+// get three random msgs in Rt
 let m1 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
 let m2 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
 let m3 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
@@ -39,8 +39,9 @@ let m3 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
 // encode the msgs into the plaintext space
 let p1 = TLWE::encode(&param, &m1); // plaintext
 let p2 = TLWE::encode(&param, &m2); // plaintext
-let c3_const: T64 = T64(m3.coeffs()[0].v); // encode it as constant
+let c3_const = TLWE::new_const(&param, &m3); // as constant/public value
 
+// encrypt p1 and m2
 let c1 = TLWE::encrypt(&mut rng, &param, &pk, &p1)?;
 let c2 = TLWE::encrypt(&mut rng, &param, &pk, &p2)?;
 
diff --git a/tfhe/src/tglwe.rs b/tfhe/src/tglwe.rs
index 6328a2c..ae4c97b 100644
--- a/tfhe/src/tglwe.rs
+++ b/tfhe/src/tglwe.rs
@@ -61,6 +61,16 @@ impl TGLWE {
         let pt = pt.mul_div_round(p, u64::MAX);
         Rq::from_vec_u64(&param.pt(), pt.coeffs().iter().map(|c| c.0).collect())
     }
+    /// encodes the given message as a TGLWE constant/public value, for using it
+    /// in ct-pt-multiplication.
+    pub fn new_const(param: &Param, m: &Rq) -> Tn {
+        debug_assert_eq!(param.t, m.param.q);
+        // don't scale up m, set the Tn element directly from m's coefficients
+        Tn {
+            param: param.ring,
+            coeffs: m.coeffs().iter().map(|c_i| T64(c_i.v)).collect(),
+        }
+    }
 
     /// encrypts with the given SecretKey (instead of PublicKey)
     pub fn encrypt_s(rng: impl Rng, param: &Param, sk: &SecretKey, p: &Tn) -> Result<Self> {
@@ -310,11 +320,7 @@ mod tests {
             let m1 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
             let m2 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
             let p1: Tn = TGLWE::encode(&param, &m1);
-            // don't scale up p2, set it directly from m2
-            let p2: Tn = Tn {
-                param: param.ring,
-                coeffs: m2.coeffs().iter().map(|c_i| T64(c_i.v)).collect(),
-            };
+            let p2: Tn = TGLWE::new_const(&param, &m2); // as constant/public value
 
             let c1 = TGLWE::encrypt(&mut rng, &param, &pk, &p1)?;
 
diff --git a/tfhe/src/tlwe.rs b/tfhe/src/tlwe.rs
index 6a4f92f..dac81ac 100644
--- a/tfhe/src/tlwe.rs
+++ b/tfhe/src/tlwe.rs
@@ -61,6 +61,12 @@ impl TLWE {
         let p = p.mul_div_round(param.t, u64::MAX);
         Rq::from_vec_u64(&param.pt(), p.coeffs().iter().map(|c| c.0).collect())
     }
+    /// encodes the given message as a TLWE constant/public value, for using it
+    /// in ct-pt-multiplication.
+    pub fn new_const(param: &Param, m: &Rq) -> T64 {
+        debug_assert_eq!(param.t, m.param.q);
+        T64(m.coeffs()[0].v)
+    }
 
     // encrypts with the given SecretKey (instead of PublicKey)
     pub fn encrypt_s(rng: impl Rng, param: &Param, sk: &SecretKey, p: &T64) -> Result<Self> {
@@ -400,8 +406,7 @@ mod tests {
             let m1 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
             let m2 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
             let p1: T64 = TLWE::encode(&param, &m1);
-            // don't scale up p2, set it directly from m2
-            let p2: T64 = T64(m2.coeffs()[0].v);
+            let p2: T64 = TLWE::new_const(&param, &m2); // as constant/public value
 
             let c1 = TLWE::encrypt(&mut rng, &param, &pk, &p1)?;