diff --git a/tfhe/src/core_crypto/backward_compatibility/commons/dispersion.rs b/tfhe/src/core_crypto/backward_compatibility/commons/dispersion.rs
index 6982f8dee1..b4fd37a9f0 100644
--- a/tfhe/src/core_crypto/backward_compatibility/commons/dispersion.rs
+++ b/tfhe/src/core_crypto/backward_compatibility/commons/dispersion.rs
@@ -1,7 +1,12 @@
-use crate::core_crypto::commons::dispersion::StandardDev;
+use crate::core_crypto::commons::dispersion::{StandardDev, Variance};
 use tfhe_versionable::VersionsDispatch;
 
 #[derive(VersionsDispatch)]
 pub enum StandardDevVersions {
     V0(StandardDev),
 }
+
+#[derive(VersionsDispatch)]
+pub enum VarianceVersions {
+    V0(Variance),
+}
diff --git a/tfhe/src/core_crypto/commons/ciphertext_modulus.rs b/tfhe/src/core_crypto/commons/ciphertext_modulus.rs
index beeaeb3406..e398a1a38f 100644
--- a/tfhe/src/core_crypto/commons/ciphertext_modulus.rs
+++ b/tfhe/src/core_crypto/commons/ciphertext_modulus.rs
@@ -345,6 +345,13 @@ impl<Scalar: UnsignedInteger> CiphertextModulus<Scalar> {
             }
         }
     }
+
+    pub fn raw_modulus_float(&self) -> f64 {
+        match self.inner {
+            CiphertextModulusInner::Native => 2_f64.powi(Scalar::BITS as i32),
+            CiphertextModulusInner::Custom(non_zero) => non_zero.get() as f64,
+        }
+    }
 }
 
 impl<Scalar: UnsignedInteger> std::fmt::Display for CiphertextModulus<Scalar> {
diff --git a/tfhe/src/core_crypto/commons/dispersion.rs b/tfhe/src/core_crypto/commons/dispersion.rs
index 0a101e07d9..d2c9157d14 100644
--- a/tfhe/src/core_crypto/commons/dispersion.rs
+++ b/tfhe/src/core_crypto/commons/dispersion.rs
@@ -16,7 +16,9 @@
 use serde::{Deserialize, Serialize};
 use tfhe_versionable::Versionize;
 
-use crate::core_crypto::backward_compatibility::commons::dispersion::StandardDevVersions;
+use crate::core_crypto::backward_compatibility::commons::dispersion::{
+    StandardDevVersions, VarianceVersions,
+};
 
 /// A trait for types representing distribution parameters, for a given unsigned integer type.
 //  Warning:
@@ -32,17 +34,13 @@ pub trait DispersionParameter: Copy {
     /// $\log\_2(\sigma)=p$
     fn get_log_standard_dev(&self) -> LogStandardDev;
     /// For a `Uint` type representing $\mathbb{Z}/2^q\mathbb{Z}$, we return $2^{q-p}$.
-    fn get_modular_standard_dev(&self, log2_modulus: u32) -> ModularStandardDev;
+    fn get_modular_standard_dev(&self, modulus: f64) -> ModularStandardDev;
 
     /// For a `Uint` type representing $\mathbb{Z}/2^q\mathbb{Z}$, we return $2^{2(q-p)}$.
-    fn get_modular_variance(&self, log2_modulus: u32) -> ModularVariance;
+    fn get_modular_variance(&self, modulus: f64) -> ModularVariance;
 
     /// For a `Uint` type representing $\mathbb{Z}/2^q\mathbb{Z}$, we return $q-p$.
-    fn get_modular_log_standard_dev(&self, log2_modulus: u32) -> ModularLogStandardDev;
-}
-
-fn log2_modulus_to_modulus(log2_modulus: u32) -> f64 {
-    2.0f64.powi(log2_modulus as i32)
+    fn get_modular_log_standard_dev(&self, modulus: f64) -> ModularLogStandardDev;
 }
 
 /// A distribution parameter that uses the base-2 logarithm of the standard deviation as
@@ -57,12 +55,15 @@ fn log2_modulus_to_modulus(log2_modulus: u32) -> f64 {
 /// assert_eq!(params.get_log_standard_dev().0, -25.);
 /// assert_eq!(params.get_variance().0, 2_f64.powf(-25.).powi(2));
 /// assert_eq!(
-///     params.get_modular_standard_dev(32).value,
+///     params.get_modular_standard_dev(2_f64.powi(32)).value,
 ///     2_f64.powf(32. - 25.)
 /// );
-/// assert_eq!(params.get_modular_log_standard_dev(32).value, 32. - 25.);
 /// assert_eq!(
-///     params.get_modular_variance(32).value,
+///     params.get_modular_log_standard_dev(2_f64.powi(32)).value,
+///     32. - 25.
+/// );
+/// assert_eq!(
+///     params.get_modular_variance(2_f64.powi(32)).value,
 ///     2_f64.powf(32. - 25.).powi(2)
 /// );
 ///
@@ -98,22 +99,24 @@ impl DispersionParameter for LogStandardDev {
     fn get_log_standard_dev(&self) -> Self {
         Self(self.0)
     }
-    fn get_modular_standard_dev(&self, log2_modulus: u32) -> ModularStandardDev {
+    fn get_modular_standard_dev(&self, modulus: f64) -> ModularStandardDev {
         ModularStandardDev {
-            value: f64::powf(2., log2_modulus as f64 + self.0),
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: 2_f64.powf(self.0) * modulus,
+            modulus,
         }
     }
-    fn get_modular_variance(&self, log2_modulus: u32) -> ModularVariance {
+    fn get_modular_variance(&self, modulus: f64) -> ModularVariance {
+        let std_dev = 2_f64.powf(self.0) * modulus;
+
         ModularVariance {
-            value: f64::powf(2., (log2_modulus as f64 + self.0) * 2.),
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: std_dev * std_dev,
+            modulus,
         }
     }
-    fn get_modular_log_standard_dev(&self, log2_modulus: u32) -> ModularLogStandardDev {
+    fn get_modular_log_standard_dev(&self, modulus: f64) -> ModularLogStandardDev {
         ModularLogStandardDev {
-            value: log2_modulus as f64 + self.0,
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: modulus.log2() + self.0,
+            modulus,
         }
     }
 }
@@ -129,12 +132,15 @@ impl DispersionParameter for LogStandardDev {
 /// assert_eq!(params.get_log_standard_dev().0, -25.);
 /// assert_eq!(params.get_variance().0, 2_f64.powf(-25.).powi(2));
 /// assert_eq!(
-///     params.get_modular_standard_dev(32).value,
+///     params.get_modular_standard_dev(2_f64.powi(32)).value,
 ///     2_f64.powf(32. - 25.)
 /// );
-/// assert_eq!(params.get_modular_log_standard_dev(32).value, 32. - 25.);
 /// assert_eq!(
-///     params.get_modular_variance(32).value,
+///     params.get_modular_log_standard_dev(2_f64.powi(32)).value,
+///     32. - 25.
+/// );
+/// assert_eq!(
+///     params.get_modular_variance(2_f64.powi(32)).value,
 ///     2_f64.powf(32. - 25.).powi(2)
 /// );
 /// ```
@@ -168,22 +174,24 @@ impl DispersionParameter for StandardDev {
     fn get_log_standard_dev(&self) -> LogStandardDev {
         LogStandardDev(self.0.log2())
     }
-    fn get_modular_standard_dev(&self, log2_modulus: u32) -> ModularStandardDev {
+    fn get_modular_standard_dev(&self, modulus: f64) -> ModularStandardDev {
         ModularStandardDev {
-            value: 2_f64.powf(log2_modulus as f64 + self.0.log2()),
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: self.0 * modulus,
+            modulus,
         }
     }
-    fn get_modular_variance(&self, log2_modulus: u32) -> ModularVariance {
+    fn get_modular_variance(&self, modulus: f64) -> ModularVariance {
+        let std_dev = self.0 * modulus;
+
         ModularVariance {
-            value: 2_f64.powf(2. * (log2_modulus as f64 + self.0.log2())),
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: std_dev * std_dev,
+            modulus,
         }
     }
-    fn get_modular_log_standard_dev(&self, log2_modulus: u32) -> ModularLogStandardDev {
+    fn get_modular_log_standard_dev(&self, modulus: f64) -> ModularLogStandardDev {
         ModularLogStandardDev {
-            value: log2_modulus as f64 + self.0.log2(),
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: modulus.log2() + self.0.log2(),
+            modulus,
         }
     }
 }
@@ -199,16 +207,20 @@ impl DispersionParameter for StandardDev {
 /// assert_eq!(params.get_log_standard_dev().0, -25.);
 /// assert_eq!(params.get_variance().0, 2_f64.powf(-25.).powi(2));
 /// assert_eq!(
-///     params.get_modular_standard_dev(32).value,
+///     params.get_modular_standard_dev(2_f64.powi(32)).value,
 ///     2_f64.powf(32. - 25.)
 /// );
-/// assert_eq!(params.get_modular_log_standard_dev(32).value, 32. - 25.);
 /// assert_eq!(
-///     params.get_modular_variance(32).value,
+///     params.get_modular_log_standard_dev(2_f64.powi(32)).value,
+///     32. - 25.
+/// );
+/// assert_eq!(
+///     params.get_modular_variance(2_f64.powi(32)).value,
 ///     2_f64.powf(32. - 25.).powi(2)
 /// );
 /// ```
-#[derive(Debug, Copy, Clone, PartialEq, PartialOrd)]
+#[derive(Debug, Copy, Clone, PartialEq, PartialOrd, Serialize, Deserialize, Versionize)]
+#[versionize(VarianceVersions)]
 pub struct Variance(pub f64);
 
 #[derive(Debug, Copy, Clone, PartialEq, PartialOrd)]
@@ -222,8 +234,8 @@ impl Variance {
         Self(var)
     }
 
-    pub fn from_modular_variance(var: f64, log2_modulus: u32) -> Self {
-        Self(var / 2_f64.powf(log2_modulus as f64 * 2.))
+    pub fn from_modular_variance(var: f64, modulus: f64) -> Self {
+        Self(var / (modulus * modulus))
     }
 }
 
@@ -237,22 +249,22 @@ impl DispersionParameter for Variance {
     fn get_log_standard_dev(&self) -> LogStandardDev {
         LogStandardDev(self.0.sqrt().log2())
     }
-    fn get_modular_standard_dev(&self, log2_modulus: u32) -> ModularStandardDev {
+    fn get_modular_standard_dev(&self, modulus: f64) -> ModularStandardDev {
         ModularStandardDev {
-            value: 2_f64.powf(log2_modulus as f64 + self.0.sqrt().log2()),
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: self.0.sqrt() * modulus,
+            modulus,
         }
     }
-    fn get_modular_variance(&self, log2_modulus: u32) -> ModularVariance {
+    fn get_modular_variance(&self, modulus: f64) -> ModularVariance {
         ModularVariance {
-            value: 2_f64.powf(2. * (log2_modulus as f64 + self.0.sqrt().log2())),
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: self.0 * modulus * modulus,
+            modulus,
         }
     }
-    fn get_modular_log_standard_dev(&self, log2_modulus: u32) -> ModularLogStandardDev {
+    fn get_modular_log_standard_dev(&self, modulus: f64) -> ModularLogStandardDev {
         ModularLogStandardDev {
-            value: log2_modulus as f64 + self.0.sqrt().log2(),
-            modulus: log2_modulus_to_modulus(log2_modulus),
+            value: modulus.log2() + self.0.sqrt().log2(),
+            modulus,
         }
     }
 }