@@ -25,4 +25,12 @@ paste = "1.0.15"
 
 [[bench]]
 name = "circuit_bootstrapping"
+harness = false
+
+[[bench]]
+name = "bdd_prepare"
+harness = false
+
+[[bench]]
+name = "bdd_arithmetic"
 harness = false

@@ -9,7 +9,7 @@
 ## Available Schemes
 
 - **BIN FHE**:
-  - **bdd_arithmetic**: high level API for u32 arithmetic (u8 to u256 planned) using binary decision circuits. Also provides API for blind retrieval, blind rotation (using encpypted integers) and blind selection.
+  - **bdd_arithmetic**: high level API for u32 arithmetic (u8 to u256 planned) using binary decision circuits. Also provides API for blind retrieval, blind rotation (using encrypted integers) and blind selection.
   - **blind_rotation**: API for blind rotation (LWE(m) -> GLWE(X^m))
   - **circuit_bootstrapping**: API for circuit bootstrapping (LWE(m) -> GGSW(m) or GGSW(X^m)).
 - **CKKS**: planned

@@ -0,0 +1,454 @@
+use std::hint::black_box;
+
+use criterion::{BenchmarkId, Criterion, criterion_group, criterion_main};
+use poulpy_core::{
+    GGSWNoise, GLWEDecrypt, GLWEEncryptSk, GLWEExternalProduct, LWEEncryptSk, ScratchTakeCore,
+    layouts::{
+        Base2K, Degree, Dnum, Dsize, GGLWEToGGSWKeyLayout, GGSWLayout, GGSWPreparedFactory, GLWEAutomorphismKeyLayout,
+        GLWELayout, GLWESecret, GLWESecretPrepared, GLWESecretPreparedFactory, GLWESwitchingKeyLayout, GLWEToLWEKeyLayout,
+        LWESecret, Rank, TorusPrecision,
+    },
+};
+
+#[cfg(all(feature = "enable-avx", target_arch = "x86_64"))]
+pub use poulpy_cpu_avx::FFT64Avx as BackendImpl;
+
+#[cfg(not(all(feature = "enable-avx", target_arch = "x86_64")))]
+pub use poulpy_cpu_ref::FFT64Ref as BackendImpl;
+
+use poulpy_hal::{
+    api::{ModuleN, ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxRotateInplace},
+    layouts::{Backend, Module, Scratch, ScratchOwned},
+    source::Source,
+};
+use poulpy_schemes::bin_fhe::{
+    bdd_arithmetic::{
+        Add, And, BDDKey, BDDKeyEncryptSk, BDDKeyLayout, BDDKeyPrepared, BDDKeyPreparedFactory, ExecuteBDDCircuit2WTo1W, FheUint,
+        FheUintPrepare, FheUintPrepared, Or, Sll, Slt, Sltu, Sra, Srl, Sub, Xor,
+    },
+    blind_rotation::{
+        BlindRotationAlgo, BlindRotationKey, BlindRotationKeyFactory, BlindRotationKeyInfos, BlindRotationKeyLayout, CGGI,
+    },
+    circuit_bootstrapping::{
+        CircuitBootstrappingKey, CircuitBootstrappingKeyEncryptSk, CircuitBootstrappingKeyLayout,
+        CircuitBootstrappingKeyPrepared, CircuitBootstrappingKeyPreparedFactory, CirtuitBootstrappingExecute,
+    },
+};
+
+// Common setup data structure
+struct BenchmarkSetup<BE: Backend, BRA: BlindRotationAlgo> {
+    module: Module<BE>,
+    scratch: ScratchOwned<BE>,
+    a_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE>,
+    b_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE>,
+    bdd_key_prepared: BDDKeyPrepared<Vec<u8>, BRA, BE>,
+    glwe_layout: GLWELayout,
+}
+
+struct Params {
+    name: String,
+    block_size: usize,
+    glwe_layout: GLWELayout,
+    ggsw_layout: GGSWLayout,
+    bdd_layout: BDDKeyLayout,
+}
+
+fn setup_benchmark<BE: Backend, BRA: BlindRotationAlgo>(params: &Params) -> BenchmarkSetup<BE, BRA>
+where
+    Module<BE>: ModuleNew<BE>
+        + ModuleN
+        + GLWESecretPreparedFactory<BE>
+        + GLWEExternalProduct<BE>
+        + GLWEDecrypt<BE>
+        + LWEEncryptSk<BE>
+        + CircuitBootstrappingKeyEncryptSk<BRA, BE>
+        + CircuitBootstrappingKeyPreparedFactory<BRA, BE>
+        + CirtuitBootstrappingExecute<BRA, BE>
+        + GGSWPreparedFactory<BE>
+        + GGSWNoise<BE>
+        + GLWEEncryptSk<BE>
+        + VecZnxRotateInplace<BE>
+        + BDDKeyEncryptSk<BRA, BE>
+        + BDDKeyPreparedFactory<BRA, BE>
+        + FheUintPrepare<BRA, BE>
+        + ExecuteBDDCircuit2WTo1W<BE>,
+    BlindRotationKey<Vec<u8>, BRA>: BlindRotationKeyFactory<BRA>,
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    // Scratch space (16MB)
+    let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(1 << 24);
+
+    let n_glwe: poulpy_core::layouts::Degree = params.bdd_layout.cbt_layout.brk_layout.n_glwe();
+    let n_lwe: poulpy_core::layouts::Degree = params.bdd_layout.cbt_layout.brk_layout.n_lwe();
+    let rank: poulpy_core::layouts::Rank = params.bdd_layout.cbt_layout.brk_layout.rank;
+
+    let module: Module<BE> = Module::<BE>::new(n_glwe.as_u32() as u64);
+
+    let mut source_xs: Source = Source::new([1u8; 32]);
+    let mut source_xa: Source = Source::new([1u8; 32]);
+    let mut source_xe: Source = Source::new([1u8; 32]);
+
+    let mut sk_lwe: LWESecret<Vec<u8>> = LWESecret::alloc(n_lwe);
+    sk_lwe.fill_binary_block(params.block_size, &mut source_xs);
+
+    let mut sk_glwe: GLWESecret<Vec<u8>> = GLWESecret::alloc(n_glwe, rank);
+    sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
+
+    // Circuit bootstrapping evaluation key
+    let mut cbt_key: CircuitBootstrappingKey<Vec<u8>, BRA> =
+        CircuitBootstrappingKey::alloc_from_infos(&params.bdd_layout.cbt_layout);
+    cbt_key.encrypt_sk(
+        &module,
+        &sk_lwe,
+        &sk_glwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+
+    let mut cbt_key_prepared: CircuitBootstrappingKeyPrepared<Vec<u8>, BRA, BE> =
+        CircuitBootstrappingKeyPrepared::alloc_from_infos(&module, &params.bdd_layout.cbt_layout);
+    cbt_key_prepared.prepare(&module, &cbt_key, scratch.borrow());
+
+    let mut sk_glwe_prepared = GLWESecretPrepared::alloc_from_infos(&module, &params.glwe_layout);
+    sk_glwe_prepared.prepare(&module, &sk_glwe);
+
+    let mut bdd_key: BDDKey<Vec<u8>, BRA> = BDDKey::alloc_from_infos(&params.bdd_layout);
+    bdd_key.encrypt_sk(
+        &module,
+        &sk_lwe,
+        &sk_glwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+
+    let input_a = 255_u32;
+    let input_b = 30_u32;
+
+    let mut a_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&params.glwe_layout);
+    a_enc.encrypt_sk(
+        &module,
+        input_a,
+        &sk_glwe_prepared,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+
+    let mut b_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&params.glwe_layout);
+    b_enc.encrypt_sk(
+        &module,
+        input_b,
+        &sk_glwe_prepared,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+
+    //////// Homomorphic computation starts here ////////
+
+    // Preparing the BDD Key
+    // The BDD key must be prepared once before any operation is performed
+    let mut bdd_key_prepared: BDDKeyPrepared<Vec<u8>, BRA, BE> = BDDKeyPrepared::alloc_from_infos(&module, &params.bdd_layout);
+    bdd_key_prepared.prepare(&module, &bdd_key, scratch.borrow());
+
+    // Input Preparation
+    // Before each operation, the inputs to that operation must be prepared
+    // Preparation extracts each bit of the integer into a seperate GLWE ciphertext and bootstraps it into a GGSW ciphertext
+    let mut a_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> = FheUintPrepared::alloc_from_infos(&module, &params.ggsw_layout);
+    a_enc_prepared.prepare(&module, &a_enc, &bdd_key_prepared, scratch.borrow());
+
+    let mut b_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> = FheUintPrepared::alloc_from_infos(&module, &params.ggsw_layout);
+    b_enc_prepared.prepare(&module, &b_enc, &bdd_key_prepared, scratch.borrow());
+
+    BenchmarkSetup {
+        module,
+        scratch,
+        a_enc_prepared,
+        b_enc_prepared,
+        bdd_key_prepared,
+        glwe_layout: params.glwe_layout.clone(),
+    }
+}
+
+fn create_runner<BE: Backend, BRA: BlindRotationAlgo, F>(setup: BenchmarkSetup<BE, BRA>, operation: F) -> impl FnMut()
+where
+    Module<BE>: ExecuteBDDCircuit2WTo1W<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+    ScratchOwned<BE>: ScratchOwnedBorrow<BE>,
+    F: Fn(
+        &mut FheUint<Vec<u8>, u32>,
+        &Module<BE>,
+        &FheUintPrepared<Vec<u8>, u32, BE>,
+        &FheUintPrepared<Vec<u8>, u32, BE>,
+        &BDDKeyPrepared<Vec<u8>, BRA, BE>,
+        &mut Scratch<BE>,
+    ),
+{
+    let BenchmarkSetup {
+        module,
+        mut scratch,
+        a_enc_prepared,
+        b_enc_prepared,
+        bdd_key_prepared,
+        glwe_layout,
+    } = setup;
+
+    let mut c_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+
+    move || {
+        operation(
+            &mut c_enc,
+            &module,
+            &a_enc_prepared,
+            &b_enc_prepared,
+            &bdd_key_prepared,
+            scratch.borrow(),
+        );
+        black_box(());
+    }
+}
+
+fn bench_operation<BE: Backend, BRA: BlindRotationAlgo, F>(
+    group: &mut criterion::BenchmarkGroup<'_, criterion::measurement::WallTime>,
+    params: &Params,
+    operation_name: &str,
+    operation: F,
+) where
+    Module<BE>: ModuleNew<BE>
+        + ModuleN
+        + GLWESecretPreparedFactory<BE>
+        + GLWEExternalProduct<BE>
+        + GLWEDecrypt<BE>
+        + LWEEncryptSk<BE>
+        + CircuitBootstrappingKeyEncryptSk<BRA, BE>
+        + CircuitBootstrappingKeyPreparedFactory<BRA, BE>
+        + CirtuitBootstrappingExecute<BRA, BE>
+        + GGSWPreparedFactory<BE>
+        + GGSWNoise<BE>
+        + GLWEEncryptSk<BE>
+        + VecZnxRotateInplace<BE>
+        + BDDKeyEncryptSk<BRA, BE>
+        + BDDKeyPreparedFactory<BRA, BE>
+        + FheUintPrepare<BRA, BE>
+        + ExecuteBDDCircuit2WTo1W<BE>,
+    BlindRotationKey<Vec<u8>, BRA>: BlindRotationKeyFactory<BRA>,
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+    F: Fn(
+            &mut FheUint<Vec<u8>, u32>,
+            &Module<BE>,
+            &FheUintPrepared<Vec<u8>, u32, BE>,
+            &FheUintPrepared<Vec<u8>, u32, BE>,
+            &BDDKeyPrepared<Vec<u8>, BRA, BE>,
+            &mut Scratch<BE>,
+        ) + 'static,
+{
+    let setup = setup_benchmark::<BE, BRA>(params);
+    let mut runner = create_runner(setup, operation);
+    let id = BenchmarkId::from_parameter(format!("{}_{}", params.name, operation_name));
+    group.bench_with_input(id, &(), |b, _| b.iter(&mut runner));
+}
+
+pub fn benc_bdd_arithmetic<BE: Backend, BRA: BlindRotationAlgo>(c: &mut Criterion, label: &str)
+where
+    Module<BE>: ModuleNew<BE>
+        + ModuleN
+        + GLWESecretPreparedFactory<BE>
+        + GLWEExternalProduct<BE>
+        + GLWEDecrypt<BE>
+        + LWEEncryptSk<BE>
+        + CircuitBootstrappingKeyEncryptSk<BRA, BE>
+        + CircuitBootstrappingKeyPreparedFactory<BRA, BE>
+        + CirtuitBootstrappingExecute<BRA, BE>
+        + GGSWPreparedFactory<BE>
+        + GGSWNoise<BE>
+        + GLWEEncryptSk<BE>
+        + VecZnxRotateInplace<BE>
+        + BDDKeyEncryptSk<BRA, BE>
+        + BDDKeyPreparedFactory<BRA, BE>
+        + FheUintPrepare<BRA, BE>
+        + ExecuteBDDCircuit2WTo1W<BE>,
+    BlindRotationKey<Vec<u8>, BRA>: BlindRotationKeyFactory<BRA>, // TODO find a way to remove this bound or move it to CBT KEY
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    let group_name: String = format!("bdd_arithmetic::{label}");
+
+    let mut group = c.benchmark_group(group_name);
+
+    const N_GLWE: u32 = 1024;
+    const N_LWE: u32 = 679;
+    const BINARY_BLOCK_SIZE: u32 = 7;
+    const BASE2K: u32 = 15;
+    const RANK: u32 = 2;
+
+    let params: Params = Params {
+        name: String::from(format!("n_glwe={N_GLWE}")),
+        block_size: BINARY_BLOCK_SIZE as usize,
+        glwe_layout: GLWELayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(2 * BASE2K),
+            rank: Rank(RANK),
+        },
+        ggsw_layout: GGSWLayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(3 * BASE2K),
+            rank: Rank(RANK),
+            dnum: Dnum(3),
+            dsize: Dsize(1),
+        },
+        bdd_layout: BDDKeyLayout {
+            cbt_layout: CircuitBootstrappingKeyLayout {
+                brk_layout: BlindRotationKeyLayout {
+                    n_glwe: Degree(N_GLWE),
+                    n_lwe: Degree(N_LWE),
+                    base2k: Base2K(BASE2K),
+                    k: TorusPrecision(4 * BASE2K),
+                    dnum: Dnum(4),
+                    rank: Rank(RANK),
+                },
+                atk_layout: GLWEAutomorphismKeyLayout {
+                    n: Degree(N_GLWE),
+                    base2k: Base2K(BASE2K),
+                    k: TorusPrecision(4 * BASE2K),
+                    dnum: Dnum(4),
+                    dsize: Dsize(1),
+                    rank: Rank(RANK),
+                },
+                tsk_layout: GGLWEToGGSWKeyLayout {
+                    n: Degree(N_GLWE),
+                    base2k: Base2K(BASE2K),
+                    k: TorusPrecision(4 * BASE2K),
+                    dnum: Dnum(4),
+                    dsize: Dsize(1),
+                    rank: Rank(RANK),
+                },
+            },
+            ks_glwe_layout: Some(GLWESwitchingKeyLayout {
+                n: Degree(N_GLWE),
+                base2k: Base2K(BASE2K),
+                k: TorusPrecision(4 * BASE2K),
+                dnum: Dnum(4),
+                dsize: Dsize(1),
+                rank_in: Rank(RANK),
+                rank_out: Rank(1),
+            }),
+            ks_lwe_layout: GLWEToLWEKeyLayout {
+                n: Degree(N_GLWE),
+                base2k: Base2K(BASE2K),
+                k: TorusPrecision(4 * BASE2K),
+                rank_in: Rank(1),
+                dnum: Dnum(4),
+            },
+        },
+    };
+
+    // Benchmark each operation
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "add",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.add(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "sub",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.sub(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "sll",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.sll(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "sra",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.sra(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "srl",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.srl(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "slt",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.slt(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "sltu",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.sltu(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "or",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.or(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "and",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.and(module, a, b, key, scratch);
+        },
+    );
+
+    bench_operation::<BE, BRA, _>(
+        &mut group,
+        &params,
+        "xor",
+        |c_enc, module, a, b, key, scratch| {
+            c_enc.xor(module, a, b, key, scratch);
+        },
+    );
+
+    group.finish();
+}
+
+fn bench_bdd_arithmetic_fft64(c: &mut Criterion) {
+    #[cfg(all(feature = "enable-avx", target_arch = "x86_64"))]
+    let label = "fft64_avx";
+    #[cfg(not(all(feature = "enable-avx", target_arch = "x86_64")))]
+    let label = "fft64_ref";
+    benc_bdd_arithmetic::<BackendImpl, CGGI>(c, label);
+}
+
+criterion_group!(benches, bench_bdd_arithmetic_fft64);
+criterion_main!(benches);

@@ -0,0 +1,238 @@
+use std::hint::black_box;
+
+use criterion::{BenchmarkId, Criterion, criterion_group, criterion_main};
+use poulpy_core::{
+    GGSWNoise, GLWEDecrypt, GLWEEncryptSk, GLWEExternalProduct, LWEEncryptSk, ScratchTakeCore,
+    layouts::{
+        Base2K, Degree, Dnum, Dsize, GGLWEToGGSWKeyLayout, GGSWLayout, GGSWPreparedFactory, GLWEAutomorphismKeyLayout,
+        GLWELayout, GLWESecret, GLWESecretPrepared, GLWESecretPreparedFactory, GLWESwitchingKeyLayout, GLWEToLWEKeyLayout,
+        LWESecret, Rank, TorusPrecision,
+    },
+};
+
+#[cfg(all(feature = "enable-avx", target_arch = "x86_64"))]
+pub use poulpy_cpu_avx::FFT64Avx as BackendImpl;
+
+#[cfg(not(all(feature = "enable-avx", target_arch = "x86_64")))]
+pub use poulpy_cpu_ref::FFT64Ref as BackendImpl;
+
+use poulpy_hal::{
+    api::{ModuleN, ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxRotateInplace},
+    layouts::{Backend, Module, Scratch, ScratchOwned},
+    source::Source,
+};
+use poulpy_schemes::bin_fhe::{
+    bdd_arithmetic::{
+        BDDKey, BDDKeyEncryptSk, BDDKeyLayout, BDDKeyPrepared, BDDKeyPreparedFactory, ExecuteBDDCircuit2WTo1W, FheUint,
+        FheUintPrepare, FheUintPrepared,
+    },
+    blind_rotation::{
+        BlindRotationAlgo, BlindRotationKey, BlindRotationKeyFactory, BlindRotationKeyInfos, BlindRotationKeyLayout, CGGI,
+    },
+    circuit_bootstrapping::{
+        CircuitBootstrappingKeyEncryptSk, CircuitBootstrappingKeyLayout, CircuitBootstrappingKeyPreparedFactory,
+        CirtuitBootstrappingExecute,
+    },
+};
+
+pub fn benc_bdd_prepare<BE: Backend, BRA: BlindRotationAlgo>(c: &mut Criterion, label: &str)
+where
+    Module<BE>: ModuleNew<BE>
+        + ModuleN
+        + GLWESecretPreparedFactory<BE>
+        + GLWEExternalProduct<BE>
+        + GLWEDecrypt<BE>
+        + LWEEncryptSk<BE>
+        + CircuitBootstrappingKeyEncryptSk<BRA, BE>
+        + CircuitBootstrappingKeyPreparedFactory<BRA, BE>
+        + CirtuitBootstrappingExecute<BRA, BE>
+        + GGSWPreparedFactory<BE>
+        + GGSWNoise<BE>
+        + GLWEEncryptSk<BE>
+        + VecZnxRotateInplace<BE>
+        + BDDKeyEncryptSk<BRA, BE>
+        + BDDKeyPreparedFactory<BRA, BE>
+        + FheUintPrepare<BRA, BE>
+        + ExecuteBDDCircuit2WTo1W<BE>,
+    BlindRotationKey<Vec<u8>, BRA>: BlindRotationKeyFactory<BRA>, // TODO find a way to remove this bound or move it to CBT KEY
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    let group_name: String = format!("bdd_arithmetic::{label}");
+
+    let mut group = c.benchmark_group(group_name);
+
+    struct Params {
+        name: String,
+        block_size: usize,
+        glwe_layout: GLWELayout,
+        ggsw_layout: GGSWLayout,
+        bdd_layout: BDDKeyLayout,
+    }
+
+    fn runner<BE: Backend, BRA: BlindRotationAlgo>(params: &Params) -> impl FnMut()
+    where
+        Module<BE>: ModuleNew<BE>
+            + ModuleN
+            + GLWESecretPreparedFactory<BE>
+            + GLWEExternalProduct<BE>
+            + GLWEDecrypt<BE>
+            + LWEEncryptSk<BE>
+            + CircuitBootstrappingKeyEncryptSk<BRA, BE>
+            + CircuitBootstrappingKeyPreparedFactory<BRA, BE>
+            + CirtuitBootstrappingExecute<BRA, BE>
+            + GGSWPreparedFactory<BE>
+            + GGSWNoise<BE>
+            + GLWEEncryptSk<BE>
+            + VecZnxRotateInplace<BE>
+            + BDDKeyEncryptSk<BRA, BE>
+            + BDDKeyPreparedFactory<BRA, BE>
+            + FheUintPrepare<BRA, BE>
+            + ExecuteBDDCircuit2WTo1W<BE>,
+        BlindRotationKey<Vec<u8>, BRA>: BlindRotationKeyFactory<BRA>, /* TODO find a way to remove this bound or move it to CBT KEY */
+        ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        // Scratch space (4MB)
+        let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(1 << 25);
+
+        let n_glwe: poulpy_core::layouts::Degree = params.bdd_layout.cbt_layout.brk_layout.n_glwe();
+        let n_lwe: poulpy_core::layouts::Degree = params.bdd_layout.cbt_layout.brk_layout.n_lwe();
+        let rank: poulpy_core::layouts::Rank = params.bdd_layout.cbt_layout.brk_layout.rank;
+
+        let module: Module<BE> = Module::<BE>::new(n_glwe.as_u32() as u64);
+
+        let mut source_xs: Source = Source::new([1u8; 32]);
+        let mut source_xa: Source = Source::new([1u8; 32]);
+        let mut source_xe: Source = Source::new([1u8; 32]);
+
+        let mut sk_lwe: LWESecret<Vec<u8>> = LWESecret::alloc(n_lwe);
+        sk_lwe.fill_binary_block(params.block_size, &mut source_xs);
+
+        let mut sk_glwe: GLWESecret<Vec<u8>> = GLWESecret::alloc(n_glwe, rank);
+        sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
+
+        let mut sk_glwe_prepared = GLWESecretPrepared::alloc_from_infos(&module, &params.glwe_layout);
+        sk_glwe_prepared.prepare(&module, &sk_glwe);
+
+        let mut bdd_key: BDDKey<Vec<u8>, BRA> = BDDKey::alloc_from_infos(&params.bdd_layout);
+        bdd_key.encrypt_sk(
+            &module,
+            &sk_lwe,
+            &sk_glwe,
+            &mut source_xa,
+            &mut source_xe,
+            scratch.borrow(),
+        );
+
+        let input_a = 255_u32;
+
+        let mut a_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&params.glwe_layout);
+        a_enc.encrypt_sk(
+            &module,
+            input_a,
+            &sk_glwe_prepared,
+            &mut source_xa,
+            &mut source_xe,
+            scratch.borrow(),
+        );
+
+        let mut bdd_key_prepared: BDDKeyPrepared<Vec<u8>, BRA, BE> =
+            BDDKeyPrepared::alloc_from_infos(&module, &params.bdd_layout);
+        bdd_key_prepared.prepare(&module, &bdd_key, scratch.borrow());
+
+        let mut a_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> =
+            FheUintPrepared::alloc_from_infos(&module, &params.ggsw_layout);
+
+        move || {
+            a_enc_prepared.prepare(&module, &a_enc, &bdd_key_prepared, scratch.borrow());
+            black_box(());
+        }
+    }
+
+    const N_GLWE: u32 = 1024;
+    const N_LWE: u32 = 679;
+    const BINARY_BLOCK_SIZE: u32 = 7;
+    const BASE2K: u32 = 15;
+    const RANK: u32 = 2;
+
+    let params: Params = Params {
+        name: String::from(format!("n_glwe={N_GLWE}")),
+        block_size: BINARY_BLOCK_SIZE as usize,
+        glwe_layout: GLWELayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(2 * BASE2K),
+            rank: Rank(RANK),
+        },
+        ggsw_layout: GGSWLayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(3 * BASE2K),
+            rank: Rank(RANK),
+            dnum: Dnum(3),
+            dsize: Dsize(1),
+        },
+        bdd_layout: BDDKeyLayout {
+            cbt_layout: CircuitBootstrappingKeyLayout {
+                brk_layout: BlindRotationKeyLayout {
+                    n_glwe: Degree(N_GLWE),
+                    n_lwe: Degree(N_LWE),
+                    base2k: Base2K(BASE2K),
+                    k: TorusPrecision(4 * BASE2K),
+                    dnum: Dnum(4),
+                    rank: Rank(RANK),
+                },
+                atk_layout: GLWEAutomorphismKeyLayout {
+                    n: Degree(N_GLWE),
+                    base2k: Base2K(BASE2K),
+                    k: TorusPrecision(4 * BASE2K),
+                    dnum: Dnum(4),
+                    dsize: Dsize(1),
+                    rank: Rank(RANK),
+                },
+                tsk_layout: GGLWEToGGSWKeyLayout {
+                    n: Degree(N_GLWE),
+                    base2k: Base2K(BASE2K),
+                    k: TorusPrecision(4 * BASE2K),
+                    dnum: Dnum(4),
+                    dsize: Dsize(1),
+                    rank: Rank(RANK),
+                },
+            },
+            ks_glwe_layout: Some(GLWESwitchingKeyLayout {
+                n: Degree(N_GLWE),
+                base2k: Base2K(BASE2K),
+                k: TorusPrecision(4 * BASE2K),
+                dnum: Dnum(4),
+                dsize: Dsize(1),
+                rank_in: Rank(RANK),
+                rank_out: Rank(1),
+            }),
+            ks_lwe_layout: GLWEToLWEKeyLayout {
+                n: Degree(N_GLWE),
+                base2k: Base2K(BASE2K),
+                k: TorusPrecision(4 * BASE2K),
+                rank_in: Rank(1),
+                dnum: Dnum(4),
+            },
+        },
+    };
+
+    let id: BenchmarkId = BenchmarkId::from_parameter(params.name.clone());
+    let mut runner = runner::<BE, BRA>(&params);
+    group.bench_with_input(id, &(), |b, _| b.iter(&mut runner));
+
+    group.finish();
+}
+
+fn bench_bdd_prepare_fft64(c: &mut Criterion) {
+    #[cfg(all(feature = "enable-avx", target_arch = "x86_64"))]
+    let label = "fft64_avx";
+    #[cfg(not(all(feature = "enable-avx", target_arch = "x86_64")))]
+    let label = "fft64_ref";
+    benc_bdd_prepare::<BackendImpl, CGGI>(c, label);
+}
+
+criterion_group!(benches, bench_bdd_prepare_fft64);
+criterion_main!(benches);

@@ -85,9 +85,9 @@ {
         // Scratch space (4MB)
         let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(1 << 22);
 
-        let n_glwe: poulpy_core::layouts::Degree = params.cbt_infos.layout_brk.n_glwe();
-        let n_lwe: poulpy_core::layouts::Degree = params.cbt_infos.layout_brk.n_lwe();
-        let rank: poulpy_core::layouts::Rank = params.cbt_infos.layout_brk.rank;
+        let n_glwe: poulpy_core::layouts::Degree = params.cbt_infos.brk_layout.n_glwe();
+        let n_lwe: poulpy_core::layouts::Degree = params.cbt_infos.brk_layout.n_lwe();
+        let rank: poulpy_core::layouts::Rank = params.cbt_infos.brk_layout.rank;
 
         let module: Module<BE> = Module::<BE>::new(n_glwe.as_u32() as u64);
 
@@ -97,7 +97,6 @@ let mut source_xe: Source = Source::new([1u8; 32]);
 
         let mut sk_lwe: LWESecret<Vec<u8>> = LWESecret::alloc(n_lwe);
         sk_lwe.fill_binary_block(params.block_size, &mut source_xs);
-        sk_lwe.fill_zero();
 
         let mut sk_glwe: GLWESecret<Vec<u8>> = GLWESecret::alloc(n_glwe, rank);
         sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
@@ -151,7 +150,7 @@ dsize: 1_u32.into(),
             rank: 2_u32.into(),
         },
         cbt_infos: CircuitBootstrappingKeyLayout {
-            layout_brk: BlindRotationKeyLayout {
+            brk_layout: BlindRotationKeyLayout {
                 n_glwe: 1024_u32.into(),
                 n_lwe: 574_u32.into(),
                 base2k: 13_u32.into(),
@@ -159,7 +158,7 @@ k: 52_u32.into(),
                 dnum: 3_u32.into(),
                 rank: 2_u32.into(),
             },
-            layout_atk: GLWEAutomorphismKeyLayout {
+            atk_layout: GLWEAutomorphismKeyLayout {
                 n: 1024_u32.into(),
                 base2k: 13_u32.into(),
                 k: 52_u32.into(),
@@ -167,7 +166,7 @@ dnum: 3_u32.into(),
                 dsize: Dsize(1),
                 rank: 2_u32.into(),
             },
-            layout_tsk: GGLWEToGGSWKeyLayout {
+            tsk_layout: GGLWEToGGSWKeyLayout {
                 n: 1024_u32.into(),
                 base2k: 13_u32.into(),
                 k: 52_u32.into(),

@@ -0,0 +1,332 @@
+use std::collections::HashMap;
+
+use poulpy_core::{
+    GLWEDecrypt, GLWEEncryptSk, GLWEExternalProduct, LWEEncryptSk, ScratchTakeCore,
+    layouts::{
+        Base2K, Degree, Dnum, Dsize, GGLWEToGGSWKeyLayout, GGSWLayout, GGSWPreparedFactory, GLWEAutomorphismKeyLayout,
+        GLWELayout, GLWESecret, GLWESecretPrepared, GLWESecretPreparedFactory, GLWESwitchingKeyLayout, GLWEToLWEKeyLayout,
+        LWESecret, Rank, TorusPrecision,
+    },
+};
+use poulpy_hal::{
+    api::{ModuleN, ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxRotateInplace},
+    layouts::{Backend, Module, Scratch, ScratchOwned},
+    source::Source,
+};
+use poulpy_schemes::bin_fhe::{
+    bdd_arithmetic::{
+        Add, BDDKey, BDDKeyEncryptSk, BDDKeyLayout, BDDKeyPrepared, BDDKeyPreparedFactory, ExecuteBDDCircuit2WTo1W, FheUint,
+        FheUintPrepare, FheUintPrepared, GLWEBlindSelection, Xor,
+    },
+    blind_rotation::{BlindRotationAlgo, BlindRotationKey, BlindRotationKeyFactory, BlindRotationKeyLayout, CGGI},
+    circuit_bootstrapping::CircuitBootstrappingKeyLayout,
+};
+use rand::Rng;
+
+#[cfg(all(feature = "enable-avx", target_arch = "x86_64"))]
+use poulpy_cpu_avx::FFT64Avx;
+#[cfg(not(all(feature = "enable-avx", target_arch = "x86_64")))]
+use poulpy_cpu_ref::FFT64Ref;
+
+// This example demonstrates and end-to-end example usage of the BDD arithmetic API
+// It includes all steps including:
+//
+// - Parameter Selection
+// - Key Generation
+// - Input Encryption
+//
+// - Key preparation
+// - Input Preparation
+// - Operation Execution
+//
+// - Result Decryption
+//
+
+fn example_bdd_arithmetic<BE: Backend, BRA: BlindRotationAlgo>()
+where
+    Module<BE>: ModuleNew<BE>
+        + ModuleN
+        + GLWESecretPreparedFactory<BE>
+        + GLWEExternalProduct<BE>
+        + GLWEDecrypt<BE>
+        + LWEEncryptSk<BE>
+        + GGSWPreparedFactory<BE>
+        + GLWEEncryptSk<BE>
+        + VecZnxRotateInplace<BE>
+        + BDDKeyEncryptSk<BRA, BE>
+        + BDDKeyPreparedFactory<BRA, BE>
+        + FheUintPrepare<BRA, BE>
+        + ExecuteBDDCircuit2WTo1W<BE>
+        + GLWEBlindSelection<u32, BE>,
+    BlindRotationKey<Vec<u8>, BRA>: BlindRotationKeyFactory<BRA>, // TODO find a way to remove this bound or move it to CBT KEY
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    ////////// Parameter Selection
+    const N_GLWE: u32 = 1024;
+    const N_LWE: u32 = 567;
+    const BINARY_BLOCK_SIZE: u32 = 7;
+    const BASE2K: u32 = 17;
+    const RANK: u32 = 1;
+
+    // GLWE layout, used to generate GLWE Ciphertexts, keys, switching keys, etc
+    let glwe_layout = GLWELayout {
+        n: Degree(N_GLWE),
+        base2k: Base2K(BASE2K),
+        k: TorusPrecision(2 * BASE2K),
+        rank: Rank(RANK),
+    };
+
+    // Used to generate GGSW Ciphertexts
+    let ggsw_layout = GGSWLayout {
+        n: Degree(N_GLWE),
+        base2k: Base2K(BASE2K),
+        k: TorusPrecision(3 * BASE2K),
+        rank: Rank(RANK),
+        dnum: Dnum(3),
+        dsize: Dsize(1),
+    };
+
+    // Used to generate BDD Keys, for the arithmetic operations
+    let bdd_layout = BDDKeyLayout {
+        cbt_layout: CircuitBootstrappingKeyLayout {
+            brk_layout: BlindRotationKeyLayout {
+                n_glwe: Degree(N_GLWE),
+                n_lwe: Degree(N_LWE),
+                base2k: Base2K(BASE2K),
+                k: TorusPrecision(4 * BASE2K),
+                dnum: Dnum(4),
+                rank: Rank(RANK),
+            },
+            atk_layout: GLWEAutomorphismKeyLayout {
+                n: Degree(N_GLWE),
+                base2k: Base2K(BASE2K),
+                k: TorusPrecision(4 * BASE2K),
+                dnum: Dnum(4),
+                dsize: Dsize(1),
+                rank: Rank(RANK),
+            },
+            tsk_layout: GGLWEToGGSWKeyLayout {
+                n: Degree(N_GLWE),
+                base2k: Base2K(BASE2K),
+                k: TorusPrecision(4 * BASE2K),
+                dnum: Dnum(4),
+                dsize: Dsize(1),
+                rank: Rank(RANK),
+            },
+        },
+        ks_glwe_layout: Some(GLWESwitchingKeyLayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(4 * BASE2K),
+            dnum: Dnum(4),
+            dsize: Dsize(1),
+            rank_in: Rank(RANK),
+            rank_out: Rank(1),
+        }),
+        ks_lwe_layout: GLWEToLWEKeyLayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(4 * BASE2K),
+            rank_in: Rank(1),
+            dnum: Dnum(4),
+        },
+    };
+
+    let module = Module::<BE>::new(N_GLWE as u64);
+
+    // Secret key sampling source
+    let mut source_xs: Source = Source::new([1u8; 32]);
+
+    // Public randomness sampling source
+    let mut source_xa: Source = Source::new([1u8; 32]);
+
+    // Noise sampling source
+    let mut source_xe: Source = Source::new([1u8; 32]);
+
+    // Scratch space (4MB)
+    let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(1 << 22);
+
+    ////////// Key Generation and Preparation
+    // Generating the GLWE and LWE key
+    let mut sk_glwe = GLWESecret::alloc_from_infos(&glwe_layout);
+    sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
+
+    let mut sk_lwe = LWESecret::alloc(bdd_layout.cbt_layout.brk_layout.n_lwe);
+    sk_lwe.fill_binary_block(BINARY_BLOCK_SIZE as usize, &mut source_xs);
+
+    // Preparing the private keys
+    let mut sk_glwe_prepared = GLWESecretPrepared::alloc_from_infos(&module, &glwe_layout);
+    sk_glwe_prepared.prepare(&module, &sk_glwe);
+
+    // Creating the public BDD Key
+    // This key is required to prepare all Fhe Integers for operations,
+    // and for performing the operations themselves
+    let mut bdd_key: BDDKey<Vec<u8>, BRA> = BDDKey::alloc_from_infos(&bdd_layout);
+    bdd_key.encrypt_sk(
+        &module,
+        &sk_lwe,
+        &sk_glwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+
+    ////////// Input Encryption
+    // Encrypting the inputs
+    let input_a = 255_u32;
+    let input_b = 30_u32;
+
+    let mut a_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+    a_enc.encrypt_sk(
+        &module,
+        input_a,
+        &sk_glwe_prepared,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+
+    let mut b_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+    b_enc.encrypt_sk(
+        &module,
+        input_b,
+        &sk_glwe_prepared,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+
+    //////// Homomorphic computation starts here ////////
+
+    // Preparing the BDD Key
+    // The BDD key must be prepared once before any operation is performed
+    let mut bdd_key_prepared: BDDKeyPrepared<Vec<u8>, BRA, BE> = BDDKeyPrepared::alloc_from_infos(&module, &bdd_layout);
+    bdd_key_prepared.prepare(&module, &bdd_key, scratch.borrow());
+
+    // Input Preparation
+    // Before each operation, the inputs to that operation must be prepared
+    // Preparation extracts each bit of the integer into a seperate GLWE ciphertext and bootstraps it into a GGSW ciphertext
+    let mut a_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> = FheUintPrepared::alloc_from_infos(&module, &ggsw_layout);
+    a_enc_prepared.prepare(&module, &a_enc, &bdd_key_prepared, scratch.borrow());
+
+    let mut b_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> = FheUintPrepared::alloc_from_infos(&module, &ggsw_layout);
+    b_enc_prepared.prepare(&module, &b_enc, &bdd_key_prepared, scratch.borrow());
+
+    // Allocating the intermediate ciphertext c_enc
+    let mut c_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+
+    // Performing the operation
+    c_enc.add(
+        &module,
+        &a_enc_prepared,
+        &b_enc_prepared,
+        &bdd_key_prepared,
+        scratch.borrow(),
+    );
+
+    // Preparing the intermediate result ciphertext, c_enc, for the next operation
+    let mut c_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> = FheUintPrepared::alloc_from_infos(&module, &ggsw_layout);
+    c_enc_prepared.prepare(&module, &c_enc, &bdd_key_prepared, scratch.borrow());
+
+    // Creating the output ciphertext d_enc
+    let mut selected_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+    selected_enc.xor(
+        &module,
+        &c_enc_prepared,
+        &a_enc_prepared,
+        &bdd_key_prepared,
+        scratch.borrow(),
+    );
+
+    //////// Homomorphic computation ends here ////////
+
+    // Decrypting the result
+    let d_dec = selected_enc.decrypt(&module, &sk_glwe_prepared, scratch.borrow());
+
+    // d = (a + b) ^ a
+    let d_correct = (input_a.wrapping_add(input_b)) ^ input_a;
+    println!("Result: {} == {}", d_dec, d_correct);
+
+    // List of available operations are:
+    // - add: addition
+    // - sub: subtraction
+    // - sll: left shift logical
+    // - sra: right shift arithmetic
+    // - srl: right shift logical
+    // - slt: less than
+    // - sltu: less than unsigned
+    // - and: bitwise and
+    // - or: bitwise or
+    // - xor: bitwise xor
+
+    ///////////////////////////// GLWE Blind Selection
+    // This example demonstrates the use of the GLWE Blind Selection operation
+    // It can choose between any number of encrypted fheuint inputs
+    // using an encrypted fheuint selector
+
+    let log_2_number_of_inputs: usize = 5;
+    let number_of_inputs: usize = 1 << log_2_number_of_inputs;
+    let inputs_a_vec: Vec<u32> = (0..number_of_inputs)
+        .map(|_| rand::rng().random_range(0..u32::MAX - 1))
+        .collect();
+    let input_selector: u32 = rand::rng().random_range(0..number_of_inputs as u32);
+
+    let mut inputs_a_enc_vec: Vec<FheUint<Vec<u8>, u32>> = Vec::new();
+    for input in &inputs_a_vec {
+        let mut next_input: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+        next_input.encrypt_sk(
+            &module,
+            *input,
+            &sk_glwe_prepared,
+            &mut source_xa,
+            &mut source_xe,
+            scratch.borrow(),
+        );
+        inputs_a_enc_vec.push(next_input);
+    }
+
+    let mut inputs_a_enc_vec_map: HashMap<usize, &mut FheUint<Vec<u8>, u32>> = HashMap::new();
+    for (i, input) in inputs_a_enc_vec.iter_mut().enumerate() {
+        inputs_a_enc_vec_map.insert(i, input);
+    }
+
+    let mut input_selector_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+    input_selector_enc.encrypt_sk(
+        &module,
+        input_selector,
+        &sk_glwe_prepared,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+    let mut input_selector_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> =
+        FheUintPrepared::alloc_from_infos(&module, &ggsw_layout);
+    input_selector_enc_prepared.prepare(
+        &module,
+        &input_selector_enc,
+        &bdd_key_prepared,
+        scratch.borrow(),
+    );
+
+    module.glwe_blind_selection(
+        &mut selected_enc,
+        inputs_a_enc_vec_map,
+        &input_selector_enc_prepared,
+        0,
+        log_2_number_of_inputs,
+        scratch.borrow(),
+    );
+
+    let selected_dec = selected_enc.decrypt(&module, &sk_glwe_prepared, scratch.borrow());
+    let selected_correct = inputs_a_vec[input_selector as usize];
+    println!("Result: {} == {}", selected_dec, selected_correct);
+}
+
+fn main() {
+    #[cfg(all(feature = "enable-avx", target_arch = "x86_64"))]
+    example_bdd_arithmetic::<FFT64Avx, CGGI>();
+
+    #[cfg(not(all(feature = "enable-avx", target_arch = "x86_64")))]
+    example_bdd_arithmetic::<FFT64Ref, CGGI>();
+}

@@ -77,8 +77,8 @@
     // GGLWE tensor key modulus
     let k_tsk: usize = (rows_tsk + 1) * base2k;
 
-    let cbt_infos: CircuitBootstrappingKeyLayout = CircuitBootstrappingKeyLayout {
-        layout_brk: BlindRotationKeyLayout {
+    let cbt_layout: CircuitBootstrappingKeyLayout = CircuitBootstrappingKeyLayout {
+        brk_layout: BlindRotationKeyLayout {
             n_glwe: n_glwe.into(),
             n_lwe: n_lwe.into(),
             base2k: base2k.into(),
@@ -86,7 +86,7 @@ k: k_brk.into(),
             dnum: rows_brk.into(),
             rank: rank.into(),
         },
-        layout_atk: GLWEAutomorphismKeyLayout {
+        atk_layout: GLWEAutomorphismKeyLayout {
             n: n_glwe.into(),
             base2k: base2k.into(),
             k: k_trace.into(),
@@ -94,7 +94,7 @@ dnum: rows_trace.into(),
             dsize: 1_u32.into(),
             rank: rank.into(),
         },
-        layout_tsk: GGLWEToGGSWKeyLayout {
+        tsk_layout: GGLWEToGGSWKeyLayout {
             n: n_glwe.into(),
             base2k: base2k.into(),
             k: k_tsk.into(),
@@ -134,12 +134,12 @@
     // LWE secret
     let mut sk_lwe: LWESecret<Vec<u8>> = LWESecret::alloc(n_lwe.into());
     sk_lwe.fill_binary_block(block_size, &mut source_xs);
-    sk_lwe.fill_zero();
+    // sk_lwe.fill_zero(); // for testing
 
     // GLWE secret
     let mut sk_glwe: GLWESecret<Vec<u8>> = GLWESecret::alloc(n_glwe.into(), rank.into());
     sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
-    // sk_glwe.fill_zero();
+    // sk_glwe.fill_zero(); // for testing
 
     // GLWE secret prepared (opaque backend dependant write only struct)
     let mut sk_glwe_prepared: GLWESecretPrepared<Vec<u8>, BackendImpl> = GLWESecretPrepared::alloc(&module, rank.into());
@@ -151,7 +151,7 @@
     // LWE plaintext
     let mut pt_lwe: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(base2k.into(), k_lwe_pt.into());
 
-    // LWE plaintext(data * 2^{- (k_lwe_pt - 1)})
+    // LWE plaintext(data * 2^{- (k_lwe_pt + 1)})
     pt_lwe.encode_i64(data, (k_lwe_pt + 1).into()); // +1 for padding bit
 
     // Normalize plaintext to nicely print coefficients
@@ -174,7 +174,7 @@
     let now: Instant = Instant::now();
 
     // Circuit bootstrapping evaluation key
-    let mut cbt_key: CircuitBootstrappingKey<Vec<u8>, CGGI> = CircuitBootstrappingKey::alloc_from_infos(&cbt_infos);
+    let mut cbt_key: CircuitBootstrappingKey<Vec<u8>, CGGI> = CircuitBootstrappingKey::alloc_from_infos(&cbt_layout);
 
     cbt_key.encrypt_sk(
         &module,
@@ -192,7 +192,7 @@ let mut res: GGSW<Vec<u8>> = GGSW::alloc_from_infos(&ggsw_infos);
 
     // Circuit bootstrapping key prepared (opaque backend dependant write only struct)
     let mut cbt_prepared: CircuitBootstrappingKeyPrepared<Vec<u8>, CGGI, BackendImpl> =
-        CircuitBootstrappingKeyPrepared::alloc_from_infos(&module, &cbt_infos);
+        CircuitBootstrappingKeyPrepared::alloc_from_infos(&module, &cbt_layout);
     cbt_prepared.prepare(&module, &cbt_key, scratch.borrow());
 
     // Apply circuit bootstrapping: LWE(data * 2^{- (k_lwe_pt + 2)}) -> GGSW(data)

@@ -0,0 +1,259 @@
+use std::collections::HashMap;
+
+use poulpy_core::{
+    GLWECopy, GLWEDecrypt, GLWEEncryptSk, GLWEExternalProduct, LWEEncryptSk, ScratchTakeCore,
+    layouts::{
+        Base2K, Degree, Dnum, Dsize, GGLWEToGGSWKeyLayout, GGSWLayout, GGSWPreparedFactory, GLWEAutomorphismKeyLayout,
+        GLWELayout, GLWESecret, GLWESecretPrepared, GLWESecretPreparedFactory, GLWESwitchingKeyLayout, GLWEToLWEKeyLayout,
+        GLWEToMut, GLWEToRef, LWESecret, Rank, TorusPrecision,
+    },
+};
+use poulpy_hal::{
+    api::{ModuleN, ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxRotateInplace},
+    layouts::{Backend, Module, Scratch, ScratchOwned},
+    source::Source,
+};
+use poulpy_schemes::bin_fhe::{
+    bdd_arithmetic::{
+        BDDKey, BDDKeyEncryptSk, BDDKeyLayout, BDDKeyPrepared, BDDKeyPreparedFactory, ExecuteBDDCircuit2WTo1W, FheUint,
+        FheUintPrepare, FheUintPrepared, GLWEBlindSelection, Sltu,
+    },
+    blind_rotation::{BlindRotationAlgo, BlindRotationKey, BlindRotationKeyFactory, BlindRotationKeyLayout, CGGI},
+    circuit_bootstrapping::CircuitBootstrappingKeyLayout,
+};
+use rand::Rng;
+
+#[cfg(all(feature = "enable-avx", target_arch = "x86_64"))]
+use poulpy_cpu_avx::FFT64Avx;
+#[cfg(not(all(feature = "enable-avx", target_arch = "x86_64")))]
+use poulpy_cpu_ref::FFT64Ref;
+
+// This example demonstrates and end-to-end example usage of the BDD arithmetic API
+// to compute the maximum of an array of integers.
+
+fn example_max_array<BE: Backend, BRA: BlindRotationAlgo>()
+where
+    Module<BE>: ModuleNew<BE>
+        + ModuleN
+        + GLWESecretPreparedFactory<BE>
+        + GLWEExternalProduct<BE>
+        + GLWEDecrypt<BE>
+        + LWEEncryptSk<BE>
+        + GGSWPreparedFactory<BE>
+        + GLWEEncryptSk<BE>
+        + VecZnxRotateInplace<BE>
+        + BDDKeyEncryptSk<BRA, BE>
+        + BDDKeyPreparedFactory<BRA, BE>
+        + FheUintPrepare<BRA, BE>
+        + ExecuteBDDCircuit2WTo1W<BE>
+        + GLWEBlindSelection<u32, BE>,
+    BlindRotationKey<Vec<u8>, BRA>: BlindRotationKeyFactory<BRA>, // TODO find a way to remove this bound or move it to CBT KEY
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    ////////// Parameter Selection
+    const N_GLWE: u32 = 1024;
+    const N_LWE: u32 = 567;
+    const BINARY_BLOCK_SIZE: u32 = 7;
+    const BASE2K: u32 = 17;
+    const RANK: u32 = 1;
+
+    // GLWE layout, used to generate GLWE Ciphertexts, keys, switching keys, etc
+    let glwe_layout = GLWELayout {
+        n: Degree(N_GLWE),
+        base2k: Base2K(BASE2K),
+        k: TorusPrecision(2 * BASE2K),
+        rank: Rank(RANK),
+    };
+
+    // Used to generate GGSW Ciphertexts
+    let ggsw_layout = GGSWLayout {
+        n: Degree(N_GLWE),
+        base2k: Base2K(BASE2K),
+        k: TorusPrecision(3 * BASE2K),
+        rank: Rank(RANK),
+        dnum: Dnum(3),
+        dsize: Dsize(1),
+    };
+
+    // Used to generate CBT Keys
+    let cbt_layout = CircuitBootstrappingKeyLayout {
+        brk_layout: BlindRotationKeyLayout {
+            n_glwe: Degree(N_GLWE),
+            n_lwe: Degree(N_LWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(4 * BASE2K),
+            dnum: Dnum(4),
+            rank: Rank(RANK),
+        },
+        atk_layout: GLWEAutomorphismKeyLayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(4 * BASE2K),
+            dnum: Dnum(4),
+            dsize: Dsize(1),
+            rank: Rank(RANK),
+        },
+        tsk_layout: GGLWEToGGSWKeyLayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(4 * BASE2K),
+            dnum: Dnum(4),
+            dsize: Dsize(1),
+            rank: Rank(RANK),
+        },
+    };
+
+    // Used to generate BDD Keys, for the arithmetic operations
+    let bdd_layout = BDDKeyLayout {
+        cbt_layout: cbt_layout,
+        ks_glwe_layout: Some(GLWESwitchingKeyLayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(4 * BASE2K),
+            dnum: Dnum(4),
+            dsize: Dsize(1),
+            rank_in: Rank(RANK),
+            rank_out: Rank(1),
+        }),
+        ks_lwe_layout: GLWEToLWEKeyLayout {
+            n: Degree(N_GLWE),
+            base2k: Base2K(BASE2K),
+            k: TorusPrecision(4 * BASE2K),
+            rank_in: Rank(RANK),
+            dnum: Dnum(4),
+        },
+    };
+
+    let module = Module::<BE>::new(N_GLWE as u64);
+
+    // Secret key sampling source
+    let mut source_xs: Source = Source::new([1u8; 32]);
+
+    // Public randomness sampling source
+    let mut source_xa: Source = Source::new([1u8; 32]);
+
+    // Noise sampling source
+    let mut source_xe: Source = Source::new([1u8; 32]);
+
+    // Scratch space (4MB)
+    let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(1 << 22);
+
+    ////////// Key Generation and Preparation
+    // Generating the GLWE and LWE key
+    let mut sk_glwe = GLWESecret::alloc_from_infos(&glwe_layout);
+    sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
+
+    let mut sk_lwe = LWESecret::alloc(Degree(N_LWE));
+    sk_lwe.fill_binary_block(BINARY_BLOCK_SIZE as usize, &mut source_xs);
+
+    // Preparing the private keys
+    let mut sk_glwe_prepared = GLWESecretPrepared::alloc_from_infos(&module, &glwe_layout);
+    sk_glwe_prepared.prepare(&module, &sk_glwe);
+
+    // Creating the public BDD Key
+    // This key is required to prepare all Fhe Integers for operations,
+    // and for performing the operations themselves
+    let mut bdd_key: BDDKey<Vec<u8>, BRA> = BDDKey::alloc_from_infos(&bdd_layout);
+    bdd_key.encrypt_sk(
+        &module,
+        &sk_lwe,
+        &sk_glwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+
+    ////////// Input Encryption
+    // Encrypting the inputs
+    let mut rng = rand::rng();
+    let inputs: Vec<u32> = (0..3).map(|_| rng.random_range(0..u32::MAX - 1)).collect();
+
+    let mut inputs_enc: Vec<FheUint<Vec<u8>, u32>> = Vec::new();
+    for input in &inputs {
+        let mut next_input = FheUint::alloc_from_infos(&glwe_layout);
+        next_input.encrypt_sk(
+            &module,
+            *input,
+            &sk_glwe_prepared,
+            &mut source_xa,
+            &mut source_xe,
+            scratch.borrow(),
+        );
+        inputs_enc.push(next_input);
+    }
+
+    //////// Homomorphic computation starts here ////////
+
+    // Preparing the BDD Key
+    // The BDD key must be prepared once before any operation is performed
+    let mut bdd_key_prepared: BDDKeyPrepared<Vec<u8>, BRA, BE> = BDDKeyPrepared::alloc_from_infos(&module, &bdd_layout);
+    bdd_key_prepared.prepare(&module, &bdd_key, scratch.borrow());
+
+    let mut max_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+    max_enc.encrypt_sk(
+        &module,
+        0,
+        &sk_glwe_prepared,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
+    // Copy of max_enc for the HashMap
+    let mut max_enc_copy: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+
+    // Allocating the intermediate ciphertext c_enc
+    let mut compare_enc: FheUint<Vec<u8>, u32> = FheUint::alloc_from_infos(&glwe_layout);
+    let mut compare_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> = FheUintPrepared::alloc_from_infos(&module, &ggsw_layout);
+
+    for input_i in inputs_enc.iter_mut() {
+        let mut max_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> = FheUintPrepared::alloc_from_infos(&module, &ggsw_layout);
+        max_enc_prepared.prepare(&module, &max_enc, &bdd_key_prepared, scratch.borrow());
+
+        let mut input_i_enc_prepared: FheUintPrepared<Vec<u8>, u32, BE> =
+            FheUintPrepared::alloc_from_infos(&module, &ggsw_layout);
+        input_i_enc_prepared.prepare(&module, &input_i, &bdd_key_prepared, scratch.borrow());
+
+        // b = (input_i < max)
+        compare_enc.sltu(
+            &module,
+            &input_i_enc_prepared,
+            &max_enc_prepared,
+            &bdd_key_prepared,
+            scratch.borrow(),
+        );
+
+        compare_enc_prepared.prepare(&module, &compare_enc, &bdd_key_prepared, scratch.borrow());
+
+        module.glwe_copy(&mut max_enc_copy.to_mut(), &max_enc.to_ref());
+
+        let cts = HashMap::from([(0, input_i), (1, &mut max_enc_copy)]);
+
+        <Module<BE> as GLWEBlindSelection<u32, BE>>::glwe_blind_selection(
+            &module,
+            &mut max_enc,
+            cts,
+            &compare_enc_prepared,
+            0,
+            1,
+            scratch.borrow(),
+        );
+    }
+
+    //////// Homomorphic computation ends here ////////
+
+    // Decrypting the result
+    let result_dec = max_enc.decrypt(&module, &sk_glwe_prepared, scratch.borrow());
+
+    // result = max of inputs
+    let result_correct = inputs.iter().max().unwrap();
+    println!("Result: {} == {}", result_dec, result_correct);
+}
+
+fn main() {
+    #[cfg(all(feature = "enable-avx", target_arch = "x86_64"))]
+    example_max_array::<FFT64Avx, CGGI>();
+
+    #[cfg(not(all(feature = "enable-avx", target_arch = "x86_64")))]
+    example_max_array::<FFT64Ref, CGGI>();
+}

@@ -188,15 +188,35 @@ }
         }
     };
 }
+
+// a + b
 define_bdd_2w_to_1w_trait!(pub Add, add);
+
+// a - b
 define_bdd_2w_to_1w_trait!(pub Sub, sub);
+
+// a << b
 define_bdd_2w_to_1w_trait!(pub Sll, sll);
+
+// a >> b arithmetic
 define_bdd_2w_to_1w_trait!(pub Sra, sra);
+
+// a >> b logical
 define_bdd_2w_to_1w_trait!(pub Srl, srl);
+
+// signed a < signed b
 define_bdd_2w_to_1w_trait!(pub Slt, slt);
+
+// unsigned a < unsigned b
 define_bdd_2w_to_1w_trait!(pub Sltu, sltu);
+
+// a or b
 define_bdd_2w_to_1w_trait!(pub Or, or);
+
+// a and b
 define_bdd_2w_to_1w_trait!(pub And, and);
+
+// a xor b
 define_bdd_2w_to_1w_trait!(pub Xor, xor);
 
 impl_bdd_2w_to_1w_trait!(

@@ -8,9 +8,9 @@ use poulpy_hal::layouts::{Backend, Module, Scratch, ZnxZero};
 
 use crate::bin_fhe::bdd_arithmetic::{Cmux, GetGGSWBit, UnsignedInteger};
 
-impl<T: UnsignedInteger, BE: Backend> GLWEBlinSelection<T, BE> for Module<BE> where Self: GLWECopy + Cmux<BE> + GLWEDecrypt<BE> {}
+impl<T: UnsignedInteger, BE: Backend> GLWEBlindSelection<T, BE> for Module<BE> where Self: GLWECopy + Cmux<BE> + GLWEDecrypt<BE> {}
 
-pub trait GLWEBlinSelection<T: UnsignedInteger, BE: Backend>
+pub trait GLWEBlindSelection<T: UnsignedInteger, BE: Backend>
 where
     Self: GLWECopy + Cmux<BE> + GLWEDecrypt<BE>,
 {

@@ -87,7 +87,7 @@ pub fn encrypt_sk<S, M, BE: Backend>(
         &mut self,
         module: &M,
         data: T,
-        sk: &S,
+        sk_glwe: &S,
         source_xa: &mut Source,
         source_xe: &mut Source,
         scratch: &mut Scratch<BE>,
@@ -100,7 +100,7 @@ #[cfg(debug_assertions)]
         {
             assert!(module.n().is_multiple_of(T::BITS as usize));
             assert_eq!(self.n(), module.n() as u32);
-            assert_eq!(sk.n(), module.n() as u32);
+            assert_eq!(sk_glwe.n(), module.n() as u32);
         }
 
         let mut data_bits: Vec<i64> = vec![0i64; module.n()];
@@ -122,7 +122,7 @@ let (mut pt, scratch_1) = scratch.take_glwe_plaintext(&pt_infos);
 
         pt.encode_vec_i64(&data_bits, TorusPrecision(2));
         self.bits
-            .encrypt_sk(module, &pt, sk, source_xa, source_xe, scratch_1);
+            .encrypt_sk(module, &pt, sk_glwe, source_xa, source_xe, scratch_1);
     }
 }
 
@@ -150,7 +150,7 @@ pt.encode_vec_i64(&data_bits, TorusPrecision(2));
         self.bits.noise(module, &pt, sk, scratch_1)
     }
 
-    pub fn decrypt<S, M, BE: Backend>(&self, module: &M, sk: &S, scratch: &mut Scratch<BE>) -> T
+    pub fn decrypt<S, M, BE: Backend>(&self, module: &M, sk_glwe: &S, scratch: &mut Scratch<BE>) -> T
     where
         S: GLWESecretPreparedToRef<BE> + GLWEInfos,
         M: ModuleLogN + GLWEDecrypt<BE>,
@@ -160,7 +160,7 @@ #[cfg(debug_assertions)]
         {
             assert!(module.n().is_multiple_of(T::BITS as usize));
             assert_eq!(self.n(), module.n() as u32);
-            assert_eq!(sk.n(), module.n() as u32);
+            assert_eq!(sk_glwe.n(), module.n() as u32);
         }
 
         let pt_infos = GLWEPlaintextLayout {
@@ -171,7 +171,7 @@ };
 
         let (mut pt, scratch_1) = scratch.take_glwe_plaintext(&pt_infos);
 
-        self.bits.decrypt(module, &mut pt, sk, scratch_1);
+        self.bits.decrypt(module, &mut pt, sk_glwe, scratch_1);
 
         let mut data_bits: Vec<i64> = vec![0i64; module.n()];
         pt.decode_vec_i64(&mut data_bits, TorusPrecision(2));

@@ -34,22 +34,22 @@ }
 
 #[derive(Debug, Clone, Copy)]
 pub struct BDDKeyLayout {
-    pub cbt: CircuitBootstrappingKeyLayout,
-    pub ks_glwe: Option<GLWESwitchingKeyLayout>,
-    pub ks_lwe: GLWEToLWEKeyLayout,
+    pub cbt_layout: CircuitBootstrappingKeyLayout,
+    pub ks_glwe_layout: Option<GLWESwitchingKeyLayout>,
+    pub ks_lwe_layout: GLWEToLWEKeyLayout,
 }
 
 impl BDDKeyInfos for BDDKeyLayout {
     fn cbt_infos(&self) -> CircuitBootstrappingKeyLayout {
-        self.cbt
+        self.cbt_layout
     }
 
     fn ks_glwe_infos(&self) -> Option<GLWESwitchingKeyLayout> {
-        self.ks_glwe
+        self.ks_glwe_layout
     }
 
     fn ks_lwe_infos(&self) -> GLWEToLWEKeyLayout {
-        self.ks_lwe
+        self.ks_lwe_layout
     }
 }
 
@@ -176,9 +176,9 @@
 impl<D: DataRef, BRA: BlindRotationAlgo, BE: Backend> BDDKeyInfos for BDDKeyPrepared<D, BRA, BE> {
     fn cbt_infos(&self) -> CircuitBootstrappingKeyLayout {
         CircuitBootstrappingKeyLayout {
-            layout_brk: self.cbt.brk_infos(),
-            layout_atk: self.cbt.atk_infos(),
-            layout_tsk: self.cbt.tsk_infos(),
+            brk_layout: self.cbt.brk_infos(),
+            atk_layout: self.cbt.atk_infos(),
+            tsk_layout: self.cbt.tsk_infos(),
         }
     }
     fn ks_glwe_infos(&self) -> Option<GLWESwitchingKeyLayout> {

@@ -16,7 +16,7 @@ use rand::RngCore;
 
 use crate::bin_fhe::{
     bdd_arithmetic::{
-        FheUintPrepared, GLWEBlinSelection,
+        FheUintPrepared, GLWEBlindSelection,
         tests::test_suite::{TEST_FHEUINT_BASE2K, TEST_RANK, TestContext},
     },
     blind_rotation::BlindRotationAlgo,
@@ -28,7 +28,7 @@ Module<BE>: ModuleNew<BE>
         + GLWESecretPreparedFactory<BE>
         + GGSWPreparedFactory<BE>
         + GGSWEncryptSk<BE>
-        + GLWEBlinSelection<u32, BE>
+        + GLWEBlindSelection<u32, BE>
         + GLWEDecrypt<BE>
         + GLWEEncryptSk<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,

@@ -165,8 +165,8 @@ dsize: Dsize(1),
 };
 
 pub(crate) static TEST_BDD_KEY_LAYOUT: BDDKeyLayout = BDDKeyLayout {
-    cbt: CircuitBootstrappingKeyLayout {
-        layout_brk: BlindRotationKeyLayout {
+    cbt_layout: CircuitBootstrappingKeyLayout {
+        brk_layout: BlindRotationKeyLayout {
             n_glwe: Degree(TEST_N_GLWE),
             n_lwe: Degree(TEST_N_LWE),
             base2k: Base2K(TEST_BRK_BASE2K),
@@ -174,7 +174,7 @@ k: TorusPrecision(52),
             dnum: Dnum(4),
             rank: Rank(TEST_RANK),
         },
-        layout_atk: GLWEAutomorphismKeyLayout {
+        atk_layout: GLWEAutomorphismKeyLayout {
             n: Degree(TEST_N_GLWE),
             base2k: Base2K(TEST_ATK_BASE2K),
             k: TorusPrecision(52),
@@ -182,7 +182,7 @@ rank: Rank(TEST_RANK),
             dnum: Dnum(4),
             dsize: Dsize(1),
         },
-        layout_tsk: GGLWEToGGSWKeyLayout {
+        tsk_layout: GGLWEToGGSWKeyLayout {
             n: Degree(TEST_N_GLWE),
             base2k: Base2K(TEST_TSK_BASE2K),
             k: TorusPrecision(52),
@@ -191,7 +191,7 @@ dnum: Dnum(4),
             dsize: Dsize(1),
         },
     },
-    ks_glwe: Some(GLWESwitchingKeyLayout {
+    ks_glwe_layout: Some(GLWESwitchingKeyLayout {
         n: Degree(TEST_N_GLWE),
         base2k: Base2K(TEST_LWE_BASE2K),
         k: TorusPrecision(20),
@@ -200,7 +200,7 @@ rank_out: Rank(1),
         dnum: Dnum(3),
         dsize: Dsize(1),
     }),
-    ks_lwe: GLWEToLWEKeyLayout {
+    ks_lwe_layout: GLWEToLWEKeyLayout {
         n: Degree(TEST_N_GLWE),
         base2k: Base2K(TEST_LWE_BASE2K),
         k: TorusPrecision(16),

@@ -27,9 +27,9 @@ }
 
 #[derive(Debug, Clone, Copy)]
 pub struct CircuitBootstrappingKeyLayout {
-    pub layout_brk: BlindRotationKeyLayout,
-    pub layout_atk: GLWEAutomorphismKeyLayout,
-    pub layout_tsk: GGLWEToGGSWKeyLayout,
+    pub brk_layout: BlindRotationKeyLayout,
+    pub atk_layout: GLWEAutomorphismKeyLayout,
+    pub tsk_layout: GGLWEToGGSWKeyLayout,
 }
 
 impl CircuitBootstrappingKeyInfos for CircuitBootstrappingKeyLayout {
@@ -38,15 +38,15 @@ unimplemented!("unimplemented for CircuitBootstrappingKeyLayout")
     }
 
     fn atk_infos(&self) -> GLWEAutomorphismKeyLayout {
-        self.layout_atk
+        self.atk_layout
     }
 
     fn brk_infos(&self) -> BlindRotationKeyLayout {
-        self.layout_brk
+        self.brk_layout
     }
 
     fn tsk_infos(&self) -> GGLWEToGGSWKeyLayout {
-        self.layout_tsk
+        self.tsk_layout
     }
 }
 

@@ -78,7 +78,7 @@ base2k: base2k_lwe.into(),
     };
 
     let cbt_infos: CircuitBootstrappingKeyLayout = CircuitBootstrappingKeyLayout {
-        layout_brk: BlindRotationKeyLayout {
+        brk_layout: BlindRotationKeyLayout {
             n_glwe: n_glwe.into(),
             n_lwe: n_lwe.into(),
             base2k: base2k_brk.into(),
@@ -86,7 +86,7 @@ k: k_brk.into(),
             dnum: rows_brk.into(),
             rank: rank.into(),
         },
-        layout_atk: GLWEAutomorphismKeyLayout {
+        atk_layout: GLWEAutomorphismKeyLayout {
             n: n_glwe.into(),
             base2k: base2k_atk.into(),
             k: k_atk.into(),
@@ -94,7 +94,7 @@ dnum: rows_atk.into(),
             rank: rank.into(),
             dsize: Dsize(1),
         },
-        layout_tsk: GGLWEToGGSWKeyLayout {
+        tsk_layout: GGLWEToGGSWKeyLayout {
             n: n_glwe.into(),
             base2k: base2k_tsk.into(),
             k: k_tsk.into(),
@@ -285,7 +285,7 @@ base2k: base2k_lwe.into(),
     };
 
     let cbt_infos: CircuitBootstrappingKeyLayout = CircuitBootstrappingKeyLayout {
-        layout_brk: BlindRotationKeyLayout {
+        brk_layout: BlindRotationKeyLayout {
             n_glwe: n_glwe.into(),
             n_lwe: n_lwe.into(),
             base2k: base2k_brk.into(),
@@ -293,7 +293,7 @@ k: k_brk.into(),
             dnum: rows_brk.into(),
             rank: rank.into(),
         },
-        layout_atk: GLWEAutomorphismKeyLayout {
+        atk_layout: GLWEAutomorphismKeyLayout {
             n: n_glwe.into(),
             base2k: base2k_atk.into(),
             k: k_atk.into(),
@@ -301,7 +301,7 @@ dnum: rows_atk.into(),
             rank: rank.into(),
             dsize: Dsize(1),
         },
-        layout_tsk: GGLWEToGGSWKeyLayout {
+        tsk_layout: GGLWEToGGSWKeyLayout {
             n: n_glwe.into(),
             base2k: base2k_tsk.into(),
             k: k_tsk.into(),