diff --git a/poulpy-schemes/src/tfhe/bdd_arithmetic/bdd_1w_to_1w.rs b/poulpy-schemes/src/tfhe/bdd_arithmetic/bdd_1w_to_1w.rs
new file mode 100644
index 0000000..7fc4ded
--- /dev/null
+++ b/poulpy-schemes/src/tfhe/bdd_arithmetic/bdd_1w_to_1w.rs
@@ -0,0 +1,157 @@
+use poulpy_core::{
+    GLWECopy, GLWEPacking, ScratchTakeCore,
+    layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWEAutomorphismKeyHelper, GetGaloisElement},
+};
+use poulpy_hal::{
+    api::ModuleLogN,
+    layouts::{Backend, DataMut, DataRef, Module, Scratch},
+};
+
+use crate::tfhe::bdd_arithmetic::{ExecuteBDDCircuit, FheUint, FheUintPrepared, GetBitCircuitInfo, UnsignedInteger, circuits};
+
+impl<BE: Backend> ExecuteBDDCircuit1WTo1W<BE> for Module<BE> where Self: Sized + ExecuteBDDCircuit<BE> + GLWEPacking<BE> + GLWECopy
+{}
+
+pub trait ExecuteBDDCircuit1WTo1W<BE: Backend>
+where
+    Self: Sized + ModuleLogN + ExecuteBDDCircuit<BE> + GLWEPacking<BE> + GLWECopy,
+{
+    fn execute_bdd_circuit_1w_to_1w<R, C, A, K, H, T>(
+        &self,
+        out: &mut FheUint<R, T>,
+        circuit: &C,
+        a: &FheUintPrepared<A, T, BE>,
+        key: &H,
+        scratch: &mut Scratch<BE>,
+    ) where
+        T: UnsignedInteger,
+        C: GetBitCircuitInfo,
+        R: DataMut,
+        A: DataRef,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+        H: GLWEAutomorphismKeyHelper<K, BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        self.execute_bdd_circuit_1w_to_1w_multi_thread(1, out, circuit, a, key, scratch);
+    }
+
+    #[allow(clippy::too_many_arguments)]
+    /// Operations Z x Z -> Z
+    fn execute_bdd_circuit_1w_to_1w_multi_thread<R, C, A, K, H, T>(
+        &self,
+        threads: usize,
+        out: &mut FheUint<R, T>,
+        circuit: &C,
+        a: &FheUintPrepared<A, T, BE>,
+        key: &H,
+        scratch: &mut Scratch<BE>,
+    ) where
+        T: UnsignedInteger,
+        C: GetBitCircuitInfo,
+        R: DataMut,
+        A: DataRef,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+        H: GLWEAutomorphismKeyHelper<K, BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let (mut out_bits, scratch_1) = scratch.take_glwe_slice(T::BITS as usize, out);
+
+        // Evaluates out[i] = circuit[i](a, b)
+        self.execute_bdd_circuit_multi_thread(threads, &mut out_bits, a, circuit, scratch_1);
+
+        // Repacks the bits
+        out.pack(self, out_bits, key, scratch_1);
+    }
+}
+
+#[macro_export]
+macro_rules! define_bdd_1w_to_1w_trait {
+    ($(#[$meta:meta])* $vis:vis $trait_name:ident, $method_name:ident) => {
+        paste::paste! {
+            $(#[$meta])*
+            $vis trait $trait_name<T: UnsignedInteger, BE: Backend> {
+
+                /// Single-threaded version
+                fn $method_name<A, M, K, H>(
+                    &mut self,
+                    module: &M,
+                    a: &FheUintPrepared<A, T, BE>,
+                    key: &H,
+                    scratch: &mut Scratch<BE>,
+                ) where
+                    M: ExecuteBDDCircuit1WTo1W<BE>,
+                    A: DataRef,
+                    K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+                    H: GLWEAutomorphismKeyHelper<K, BE>,
+                    Scratch<BE>: ScratchTakeCore<BE>;
+
+                /// Multithreaded version – same vis, method_name + "_multi_thread"
+                fn [<$method_name _multi_thread>]<A, M, K, H>(
+                    &mut self,
+                    threads: usize,
+                    module: &M,
+                    a: &FheUintPrepared<A, T, BE>,
+                    key: &H,
+                    scratch: &mut Scratch<BE>,
+                ) where
+                    M: ExecuteBDDCircuit1WTo1W<BE>,
+                    A: DataRef,
+                    K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+                    H: GLWEAutomorphismKeyHelper<K, BE>,
+                    Scratch<BE>: ScratchTakeCore<BE>;
+            }
+        }
+    };
+}
+
+#[macro_export]
+macro_rules! impl_bdd_1w_to_1w_trait {
+    ($trait_name:ident, $method_name:ident, $ty:ty, $circuit_ty:ty, $output_circuits:path) => {
+        paste::paste! {
+            impl<D: DataMut, BE: Backend> $trait_name<$ty, BE> for FheUint<D, $ty> {
+
+                fn $method_name<A, M, K, H>(
+                    &mut self,
+                    module: &M,
+                    a: &FheUintPrepared<A, $ty, BE>,
+                    key: &H,
+                    scratch: &mut Scratch<BE>,
+                ) where
+                    M: ExecuteBDDCircuit1WTo1W<BE>,
+                    A: DataRef,
+                    K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+                    H: GLWEAutomorphismKeyHelper<K, BE>,
+                    Scratch<BE>: ScratchTakeCore<BE>,
+                {
+                    module.execute_bdd_circuit_1w_to_1w(self, &$output_circuits, a, key, scratch)
+                }
+
+                fn [<$method_name _multi_thread>]<A, M, K, H>(
+                    &mut self,
+                    threads: usize,
+                    module: &M,
+                    a: &FheUintPrepared<A, $ty, BE>,
+                    key: &H,
+                    scratch: &mut Scratch<BE>,
+                ) where
+                    M: ExecuteBDDCircuit1WTo1W<BE>,
+                    A: DataRef,
+                    K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+                    H: GLWEAutomorphismKeyHelper<K, BE>,
+                    Scratch<BE>: ScratchTakeCore<BE>,
+                {
+                    module.execute_bdd_circuit_1w_to_1w_multi_thread(threads, self, &$output_circuits, a, key, scratch)
+                }
+            }
+        }
+    };
+}
+define_bdd_1w_to_1w_trait!(pub Identity, identity);
+
+impl_bdd_1w_to_1w_trait!(
+    Identity,
+    identity,
+    u32,
+    circuits::u32::identity_codgen::AnyBitCircuit,
+    circuits::u32::identity_codgen::OUTPUT_CIRCUITS
+);
diff --git a/poulpy-schemes/src/tfhe/bdd_arithmetic/bdd_2w_to_1w.rs b/poulpy-schemes/src/tfhe/bdd_arithmetic/bdd_2w_to_1w.rs
index f167657..59a745c 100644
--- a/poulpy-schemes/src/tfhe/bdd_arithmetic/bdd_2w_to_1w.rs
+++ b/poulpy-schemes/src/tfhe/bdd_arithmetic/bdd_2w_to_1w.rs
@@ -209,7 +209,6 @@ macro_rules! impl_bdd_2w_to_1w_trait {
         }
     };
 }
-
 define_bdd_2w_to_1w_trait!(pub Add, add);
 define_bdd_2w_to_1w_trait!(pub Sub, sub);
 define_bdd_2w_to_1w_trait!(pub Sll, sll);
diff --git a/poulpy-schemes/src/tfhe/bdd_arithmetic/ciphertexts/fhe_uint_prepared.rs b/poulpy-schemes/src/tfhe/bdd_arithmetic/ciphertexts/fhe_uint_prepared.rs
index 2f26b06..bc4f74c 100644
--- a/poulpy-schemes/src/tfhe/bdd_arithmetic/ciphertexts/fhe_uint_prepared.rs
+++ b/poulpy-schemes/src/tfhe/bdd_arithmetic/ciphertexts/fhe_uint_prepared.rs
@@ -20,7 +20,9 @@ use poulpy_hal::{
     source::Source,
 };
 
-use crate::tfhe::bdd_arithmetic::{BDDKey, BDDKeyHelper, BDDKeyInfos, BDDKeyPrepared, BDDKeyPreparedFactory, FheUint, ToBits};
+use crate::tfhe::bdd_arithmetic::{
+    BDDKey, BDDKeyHelper, BDDKeyInfos, BDDKeyPrepared, BDDKeyPreparedFactory, BitSize, FheUint, ToBits,
+};
 use crate::tfhe::bdd_arithmetic::{Cmux, FromBits, ScratchTakeBDD, UnsignedInteger};
 use crate::tfhe::blind_rotation::BlindRotationAlgo;
 use crate::tfhe::circuit_bootstrapping::{CircuitBootstrappingKeyInfos, CirtuitBootstrappingExecute};
@@ -55,6 +57,12 @@ impl<D: DataMut, T: UnsignedInteger, BE: Backend> GetGGSWBitMut<T, BE> for FheUi
     }
 }
 
+impl<D: Data, T: UnsignedInteger, BE: Backend> BitSize for FheUintPrepared<D, T, BE> {
+    fn bit_size(&self) -> usize {
+        T::BITS as usize
+    }
+}
+
 pub trait FheUintPreparedFactory<T: UnsignedInteger, BE: Backend>
 where
     Self: Sized + GGSWPreparedFactory<BE>,
diff --git a/poulpy-schemes/src/tfhe/bdd_arithmetic/circuits/u32/identity_codgen.rs b/poulpy-schemes/src/tfhe/bdd_arithmetic/circuits/u32/identity_codgen.rs
new file mode 100644
index 0000000..caae248
--- /dev/null
+++ b/poulpy-schemes/src/tfhe/bdd_arithmetic/circuits/u32/identity_codgen.rs
@@ -0,0 +1,111 @@
+use crate::tfhe::bdd_arithmetic::{BitCircuit, BitCircuitFamily, BitCircuitInfo, Circuit, Node};
+pub(crate) enum AnyBitCircuit {
+    B0(BitCircuit<2>),
+    B1(BitCircuit<2>),
+    B2(BitCircuit<2>),
+    B3(BitCircuit<2>),
+    B4(BitCircuit<2>),
+    B5(BitCircuit<2>),
+    B6(BitCircuit<2>),
+    B7(BitCircuit<2>),
+    B8(BitCircuit<2>),
+    B9(BitCircuit<2>),
+    B10(BitCircuit<2>),
+    B11(BitCircuit<2>),
+    B12(BitCircuit<2>),
+    B13(BitCircuit<2>),
+    B14(BitCircuit<2>),
+    B15(BitCircuit<2>),
+    B16(BitCircuit<2>),
+    B17(BitCircuit<2>),
+    B18(BitCircuit<2>),
+    B19(BitCircuit<2>),
+    B20(BitCircuit<2>),
+    B21(BitCircuit<2>),
+    B22(BitCircuit<2>),
+    B23(BitCircuit<2>),
+    B24(BitCircuit<2>),
+    B25(BitCircuit<2>),
+    B26(BitCircuit<2>),
+    B27(BitCircuit<2>),
+    B28(BitCircuit<2>),
+    B29(BitCircuit<2>),
+    B30(BitCircuit<2>),
+    B31(BitCircuit<2>),
+}
+impl BitCircuitFamily for AnyBitCircuit {
+    const INPUT_BITS: usize = 32usize;
+    const OUTPUT_BITS: usize = 32usize;
+}
+impl BitCircuitInfo for AnyBitCircuit {
+    fn info(&self) -> (&[Node], usize) {
+        match self {
+            AnyBitCircuit::B0(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B1(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B2(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B3(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B4(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B5(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B6(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B7(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B8(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B9(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B10(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B11(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B12(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B13(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B14(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B15(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B16(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B17(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B18(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B19(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B20(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B21(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B22(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B23(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B24(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B25(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B26(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B27(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B28(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B29(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B30(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+            AnyBitCircuit::B31(bit_circuit) => (bit_circuit.nodes.as_ref(), bit_circuit.max_inter_state),
+        }
+    }
+}
+pub(crate) static OUTPUT_CIRCUITS: Circuit<AnyBitCircuit, 32usize> = Circuit([
+    AnyBitCircuit::B0(BitCircuit::new([Node::Cmux(0, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B1(BitCircuit::new([Node::Cmux(1, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B2(BitCircuit::new([Node::Cmux(2, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B3(BitCircuit::new([Node::Cmux(3, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B4(BitCircuit::new([Node::Cmux(4, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B5(BitCircuit::new([Node::Cmux(5, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B6(BitCircuit::new([Node::Cmux(6, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B7(BitCircuit::new([Node::Cmux(7, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B8(BitCircuit::new([Node::Cmux(8, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B9(BitCircuit::new([Node::Cmux(9, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B10(BitCircuit::new([Node::Cmux(10, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B11(BitCircuit::new([Node::Cmux(11, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B12(BitCircuit::new([Node::Cmux(12, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B13(BitCircuit::new([Node::Cmux(13, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B14(BitCircuit::new([Node::Cmux(14, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B15(BitCircuit::new([Node::Cmux(15, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B16(BitCircuit::new([Node::Cmux(16, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B17(BitCircuit::new([Node::Cmux(17, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B18(BitCircuit::new([Node::Cmux(18, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B19(BitCircuit::new([Node::Cmux(19, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B20(BitCircuit::new([Node::Cmux(20, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B21(BitCircuit::new([Node::Cmux(21, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B22(BitCircuit::new([Node::Cmux(22, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B23(BitCircuit::new([Node::Cmux(23, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B24(BitCircuit::new([Node::Cmux(24, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B25(BitCircuit::new([Node::Cmux(25, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B26(BitCircuit::new([Node::Cmux(26, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B27(BitCircuit::new([Node::Cmux(27, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B28(BitCircuit::new([Node::Cmux(28, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B29(BitCircuit::new([Node::Cmux(29, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B30(BitCircuit::new([Node::Cmux(30, 1, 0), Node::None], 2)),
+    AnyBitCircuit::B31(BitCircuit::new([Node::Cmux(31, 1, 0), Node::None], 2)),
+]);
diff --git a/poulpy-schemes/src/tfhe/bdd_arithmetic/circuits/u32/mod.rs b/poulpy-schemes/src/tfhe/bdd_arithmetic/circuits/u32/mod.rs
index 72deb2a..bcc1e35 100644
--- a/poulpy-schemes/src/tfhe/bdd_arithmetic/circuits/u32/mod.rs
+++ b/poulpy-schemes/src/tfhe/bdd_arithmetic/circuits/u32/mod.rs
@@ -1,5 +1,6 @@
 pub(crate) mod add_codegen;
 pub(crate) mod and_codegen;
+pub(crate) mod identity_codgen;
 pub(crate) mod or_codegen;
 pub(crate) mod sll_codegen;
 pub(crate) mod slt_codegen;
diff --git a/poulpy-schemes/src/tfhe/bdd_arithmetic/mod.rs b/poulpy-schemes/src/tfhe/bdd_arithmetic/mod.rs
index 7ef1921..d8cc783 100644
--- a/poulpy-schemes/src/tfhe/bdd_arithmetic/mod.rs
+++ b/poulpy-schemes/src/tfhe/bdd_arithmetic/mod.rs
@@ -1,3 +1,4 @@
+mod bdd_1w_to_1w;
 mod bdd_2w_to_1w;
 mod blind_retrieval;
 mod blind_rotation;
@@ -7,6 +8,7 @@ mod circuits;
 mod eval;
 mod key;
 
+pub use bdd_1w_to_1w::*;
 pub use bdd_2w_to_1w::*;
 pub use blind_retrieval::*;
 pub use blind_rotation::*;