@@ -12,7 +12,7 @@ use itertools::izip;
 
 use crate::{
     GLWECiphertext, GLWECiphertextToMut, GLWEExternalProductFamily, GLWEOps, Infos, LWECiphertext, LWECiphertextToRef,
-    TakeGLWECt,
+    LookUpTableRotationDirection, TakeGLWECt,
     blind_rotation::{key::BlindRotationKeyCGGIExec, lut::LookUpTable},
     dist::Distribution,
 };
@@ -158,7 +158,7 @@
     let two_n: usize = 2 * n_glwe;
     let two_n_ext: usize = 2 * lut.domain_size();
 
-    negate_and_mod_switch_2n(two_n_ext, &mut lwe_2n, &lwe_ref);
+    mod_switch_2n(two_n_ext, &mut lwe_2n, &lwe_ref, lut.rotation_direction());
 
     let a: &[i64] = &lwe_2n[1..];
     let b_pos: usize = ((lwe_2n[0] + two_n_ext as i64) & (two_n_ext - 1) as i64) as usize;
@@ -284,7 +284,12 @@ let rows: usize = brk.rows();
 
     let cols: usize = out_mut.rank() + 1;
 
-    negate_and_mod_switch_2n(2 * lut.domain_size(), &mut lwe_2n, &lwe_ref);
+    mod_switch_2n(
+        2 * lut.domain_size(),
+        &mut lwe_2n,
+        &lwe_ref,
+        lut.rotation_direction(),
+    );
 
     let a: &[i64] = &lwe_2n[1..];
     let b: i64 = lwe_2n[0];
@@ -398,7 +403,12 @@ let mut out_mut: GLWECiphertext<&mut [u8]> = res.to_mut();
     let lwe_ref: LWECiphertext<&[u8]> = lwe.to_ref();
     let basek: usize = brk.basek();
 
-    negate_and_mod_switch_2n(2 * lut.domain_size(), &mut lwe_2n, &lwe_ref);
+    mod_switch_2n(
+        2 * lut.domain_size(),
+        &mut lwe_2n,
+        &lwe_ref,
+        lut.rotation_direction(),
+    );
 
     let a: &[i64] = &lwe_2n[1..];
     let b: i64 = lwe_2n[0];
@@ -429,13 +439,19 @@ // on top of each others, thus ~ 2^{63-basek} additions are supported before overflow.
     out_mut.normalize_inplace(module, scratch1);
 }
 
-pub(crate) fn negate_and_mod_switch_2n(n: usize, res: &mut [i64], lwe: &LWECiphertext<&[u8]>) {
+pub(crate) fn mod_switch_2n(n: usize, res: &mut [i64], lwe: &LWECiphertext<&[u8]>, rot_dir: LookUpTableRotationDirection) {
     let basek: usize = lwe.basek();
 
     let log2n: usize = usize::BITS as usize - (n - 1).leading_zeros() as usize + 1;
 
     res.copy_from_slice(&lwe.data.at(0, 0));
-    res.iter_mut().for_each(|x| *x = -*x);
+
+    match rot_dir {
+        LookUpTableRotationDirection::Left => {
+            res.iter_mut().for_each(|x| *x = -*x);
+        }
+        LookUpTableRotationDirection::Right => {}
+    }
 
     if basek > log2n {
         let diff: usize = basek - log2n;

@@ -7,10 +7,18 @@ layouts::{Backend, Module, ScratchOwned, VecZnx},
     oep::{ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl},
 };
 
+#[derive(Debug, Clone, Copy)]
+pub enum LookUpTableRotationDirection {
+    Left,
+    Right,
+}
+
 pub struct LookUpTable {
     pub(crate) data: Vec<VecZnx<Vec<u8>>>,
+    pub(crate) rot_dir: LookUpTableRotationDirection,
     pub(crate) basek: usize,
     pub(crate) k: usize,
+    pub(crate) drift: usize,
 }
 
 impl LookUpTable {
@@ -28,7 +36,13 @@ let mut data: Vec<VecZnx<Vec<u8>>> = Vec::with_capacity(extension_factor);
         (0..extension_factor).for_each(|_| {
             data.push(VecZnx::alloc(n, 1, size));
         });
-        Self { data, basek, k }
+        Self {
+            data,
+            basek,
+            k,
+            drift: 0,
+            rot_dir: LookUpTableRotationDirection::Left,
+        }
     }
 
     pub fn log_extension_factor(&self) -> usize {
@@ -43,6 +57,18 @@ pub fn domain_size(&self) -> usize {
         self.data.len() * self.data[0].n()
     }
 
+    pub fn rotation_direction(&self) -> LookUpTableRotationDirection {
+        self.rot_dir
+    }
+
+    // By default X^{-dec(lwe)} is computed during the blind rotation.
+    // Setting [reverse_rotation] to true will reverse the sign of
+    // rotation of the LUT by instead evaluating X^{dec(lwe)} during
+    // the blind rotation.
+    pub fn set_rotation_direction(&mut self, rot_dir: LookUpTableRotationDirection) {
+        self.rot_dir = rot_dir
+    }
+
     pub fn set<B: Backend>(&mut self, module: &Module<B>, f: &Vec<i64>, k: usize)
     where
         Module<B>: VecZnxRotateInplace + VecZnxNormalizeInplace<B> + VecZnxNormalizeTmpBytes + VecZnxSwithcDegree + VecZnxCopy,
@@ -53,15 +79,23 @@
         let basek: usize = self.basek;
 
         // Get the number minimum limb to store the message modulus
-        let limbs: usize = k.div_ceil(1 << basek);
+        let limbs: usize = k.div_ceil(basek);
 
         #[cfg(debug_assertions)]
         {
+            assert!(f.len() <= module.n());
+            assert!(
+                (max_bit_size(f) + (k % basek) as u32) < i64::BITS,
+                "overflow: max(|f|) << (k%basek) > i64::BITS"
+            );
             assert!(limbs <= self.data[0].size());
         }
 
         // Scaling factor
-        let scale: i64 = 1 << (k % basek) as i64;
+        let mut scale = 1;
+        if k % basek != 0 {
+            scale <<= basek - (k % basek);
+        }
 
         // #elements in lookup table
         let f_len: usize = f.len();
@@ -76,16 +110,18 @@ let mut lut_full: VecZnx<Vec<u8>> = VecZnx::alloc(domain_size, 1, size);
 
         let lut_at: &mut [i64] = lut_full.at_mut(0, limbs - 1);
 
+        let step: usize = domain_size.div_round(f_len);
+
         f.iter().enumerate().for_each(|(i, fi)| {
-            let start: usize = (i * domain_size).div_round(f_len);
-            let end: usize = ((i + 1) * domain_size).div_round(f_len);
+            let start: usize = i * step;
+            let end: usize = start + step;
             lut_at[start..end].fill(fi * scale);
         });
 
+        let drift: usize = step >> 1;
+
         // Rotates half the step to the left
-        let half_step: usize = domain_size.div_round(f_len << 1);
-
-        module.vec_znx_rotate_inplace(-(half_step as i64), &mut lut_full, 0);
+        module.vec_znx_rotate_inplace(-(drift as i64), &mut lut_full, 0);
 
         let n_large: usize = lut_full.n();
 
@@ -106,6 +142,8 @@ });
         } else {
             module.vec_znx_copy(&mut self.data[0], 0, &lut_full, 0);
         }
+
+        self.drift = drift
     }
 
     #[allow(dead_code)]
@@ -144,3 +182,16 @@ fn div_round(self, rhs: Self) -> Self {
         (self + rhs / 2) / rhs
     }
 }
+
+fn max_bit_size(vec: &[i64]) -> u32 {
+    vec.iter()
+        .map(|&v| {
+            if v == 0 {
+                0
+            } else {
+                v.unsigned_abs().ilog2() + 1
+            }
+        })
+        .max()
+        .unwrap_or(0)
+}

@@ -0,0 +1,130 @@
+use backend::{Encoding, FFT64, Module, ScratchOwned, ZnxView};
+use sampling::source::Source;
+
+use crate::{
+    FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, LWECiphertext, LWESecret,
+    blind_rotation::{
+        cggi::{cggi_blind_rotate, cggi_blind_rotate_scratch_space, mod_switch_2n},
+        key::BlindRotationKeyCGGI,
+        lut::LookUpTable,
+    },
+    lwe::{LWEPlaintext, ciphertext::LWECiphertextToRef},
+};
+
+#[test]
+fn standard() {
+    blind_rotatio_test(224, 1, 1);
+}
+
+#[test]
+fn block_binary() {
+    blind_rotatio_test(224, 7, 1);
+}
+
+#[test]
+fn block_binary_extended() {
+    blind_rotatio_test(224, 7, 2);
+}
+
+fn blind_rotatio_test(n_lwe: usize, block_size: usize, extension_factor: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(512);
+    let basek: usize = 19;
+
+    let k_lwe: usize = 24;
+    let k_brk: usize = 3 * basek;
+    let rows_brk: usize = 2; // Ensures first limb is noise-free.
+    let k_lut: usize = 1 * basek;
+    let k_res: usize = 2 * basek;
+    let rank: usize = 1;
+
+    let message_modulus: usize = 1 << 4;
+
+    let mut source_xs: Source = Source::new([2u8; 32]);
+    let mut source_xe: Source = Source::new([2u8; 32]);
+    let mut source_xa: Source = Source::new([1u8; 32]);
+
+    let mut sk_glwe: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_glwe_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_glwe);
+
+    let mut sk_lwe: LWESecret<Vec<u8>> = LWESecret::alloc(n_lwe);
+    sk_lwe.fill_binary_block(block_size, &mut source_xs);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(BlindRotationKeyCGGI::generate_from_sk_scratch_space(
+        &module, basek, k_brk, rank,
+    ));
+
+    let mut scratch_br: ScratchOwned = ScratchOwned::new(cggi_blind_rotate_scratch_space(
+        &module,
+        block_size,
+        extension_factor,
+        basek,
+        k_res,
+        k_brk,
+        rows_brk,
+        rank,
+    ));
+
+    let mut brk: BlindRotationKeyCGGI<Vec<u8>, FFT64> =
+        BlindRotationKeyCGGI::allocate(&module, n_lwe, basek, k_brk, rows_brk, rank);
+
+    brk.generate_from_sk(
+        &module,
+        &sk_glwe_dft,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        3.2,
+        scratch.borrow(),
+    );
+
+    let mut lwe: LWECiphertext<Vec<u8>> = LWECiphertext::alloc(n_lwe, basek, k_lwe);
+
+    let mut pt_lwe: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(basek, k_lwe);
+
+    let x: i64 = 2;
+    let bits: usize = 8;
+
+    pt_lwe.data.encode_coeff_i64(0, basek, bits, 0, x, bits);
+
+    lwe.encrypt_sk(&pt_lwe, &sk_lwe, &mut source_xa, &mut source_xe, 3.2);
+
+    let mut f: Vec<i64> = vec![0i64; message_modulus];
+    f.iter_mut()
+        .enumerate()
+        .for_each(|(i, x)| *x = 2 * (i as i64) + 1);
+
+    let mut lut: LookUpTable = LookUpTable::alloc(&module, basek, k_lut, extension_factor);
+    lut.set(&module, &f, message_modulus);
+
+    let mut res: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_res, rank);
+
+    cggi_blind_rotate(&module, &mut res, &lwe, &lut, &brk, scratch_br.borrow());
+
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_res);
+
+    res.decrypt(&module, &mut pt_have, &sk_glwe_dft, scratch.borrow());
+
+    let mut lwe_2n: Vec<i64> = vec![0i64; lwe.n() + 1]; // TODO: from scratch space
+
+    mod_switch_2n(
+        2 * lut.domain_size(),
+        &mut lwe_2n,
+        &lwe.to_ref(),
+        lut.rotation_direction(),
+    );
+
+    let pt_want: i64 = (lwe_2n[0]
+        + lwe_2n[1..]
+            .iter()
+            .zip(sk_lwe.data.at(0, 0))
+            .map(|(x, y)| x * y)
+            .sum::<i64>())
+        & (2 * lut.domain_size() - 1) as i64;
+
+    lut.rotate(pt_want);
+
+    // First limb should be exactly equal (test are parameterized such that the noise does not reach
+    // the first limb)
+    assert_eq!(pt_have.data.at(0, 0), lut.data[0].at(0, 0));
+}

@@ -14,8 +14,7 @@
 use crate::{
     BlindRotationKeyCGGI, BlindRotationKeyCGGIExec, BlindRotationKeyCGGIExecLayoutFamily, CCGIBlindRotationFamily,
     GLWECiphertext, GLWEDecryptFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, GLWESecretFamily, Infos, LWECiphertext,
-    LWECiphertextToRef, LWEPlaintext, LWESecret, LookUpTable, cggi_blind_rotate, cggi_blind_rotate_scratch_space,
-    negate_and_mod_switch_2n,
+    LWECiphertextToRef, LWEPlaintext, LWESecret, LookUpTable, cggi_blind_rotate, cggi_blind_rotate_scratch_space, mod_switch_2n,
 };
 
 pub(crate) trait CGGITestModuleFamily<B: Backend> = CCGIBlindRotationFamily<B>
@@ -133,7 +132,12 @@ res.decrypt(module, &mut pt_have, &sk_glwe_dft, scratch.borrow());
 
     let mut lwe_2n: Vec<i64> = vec![0i64; lwe.n() + 1]; // TODO: from scratch space
 
-    negate_and_mod_switch_2n(2 * lut.domain_size(), &mut lwe_2n, &lwe.to_ref());
+    mod_switch_2n(
+        2 * lut.domain_size(),
+        &mut lwe_2n,
+        &lwe.to_ref(),
+        lut.rotation_direction(),
+    );
 
     let pt_want: i64 = (lwe_2n[0]
         + lwe_2n[1..]

@@ -1,7 +1,9 @@
 use std::vec;
 
 use backend::hal::{
-    api::{VecZnxCopy, VecZnxNormalizeInplace, VecZnxNormalizeTmpBytes, VecZnxRotateInplace, VecZnxSwithcDegree, ZnxView},
+    api::{
+        VecZnxCopy, VecZnxDecodeVeci64, VecZnxNormalizeInplace, VecZnxNormalizeTmpBytes, VecZnxRotateInplace, VecZnxSwithcDegree,
+    },
     layouts::{Backend, Module},
     oep::{ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl},
 };
@@ -10,7 +12,12 @@ use crate::{DivRound, LookUpTable};
 
 pub(crate) fn test_lut_standard<B: Backend>(module: &Module<B>)
 where
-    Module<B>: VecZnxRotateInplace + VecZnxNormalizeInplace<B> + VecZnxNormalizeTmpBytes + VecZnxSwithcDegree + VecZnxCopy,
+    Module<B>: VecZnxRotateInplace
+        + VecZnxNormalizeInplace<B>
+        + VecZnxNormalizeTmpBytes
+        + VecZnxSwithcDegree
+        + VecZnxCopy
+        + VecZnxDecodeVeci64,
     B: ScratchOwnedAllocImpl<B> + ScratchOwnedBorrowImpl<B>,
 {
     let n: usize = module.n();
@@ -34,20 +41,24 @@ lut.rotate(module, half_step);
 
     let step: usize = lut.domain_size().div_round(message_modulus);
 
+    let mut lut_dec: Vec<i64> = vec![0i64; module.n()];
+    module.decode_vec_i64(basek, &lut.data[0], 0, log_scale, &mut lut_dec);
+
     (0..lut.domain_size()).step_by(step).for_each(|i| {
         (0..step).for_each(|_| {
-            assert_eq!(
-                f[i / step] % message_modulus as i64,
-                lut.data[0].raw()[0] / (1 << (log_scale % basek)) as i64
-            );
-            lut.rotate(module, -1);
+            assert_eq!(f[i / step] % message_modulus as i64, lut_dec[i]);
         });
     });
 }
 
 pub(crate) fn test_lut_extended<B: Backend>(module: &Module<B>)
 where
-    Module<B>: VecZnxRotateInplace + VecZnxNormalizeInplace<B> + VecZnxNormalizeTmpBytes + VecZnxSwithcDegree + VecZnxCopy,
+    Module<B>: VecZnxRotateInplace
+        + VecZnxNormalizeInplace<B>
+        + VecZnxNormalizeTmpBytes
+        + VecZnxSwithcDegree
+        + VecZnxCopy
+        + VecZnxDecodeVeci64,
     B: ScratchOwnedAllocImpl<B> + ScratchOwnedBorrowImpl<B>,
 {
     let n: usize = module.n();
@@ -69,15 +80,16 @@
     let half_step: i64 = lut.domain_size().div_round(message_modulus << 1) as i64;
     lut.rotate(&module, half_step);
 
-    let step: usize = lut.domain_size().div_round(message_modulus);
+    let step: usize = module.n().div_round(message_modulus);
+
+    let mut lut_dec: Vec<i64> = vec![0i64; module.n()];
 
-    (0..lut.domain_size()).step_by(step).for_each(|i| {
-        (0..step).for_each(|_| {
-            assert_eq!(
-                f[i / step] % message_modulus as i64,
-                lut.data[0].raw()[0] / (1 << (log_scale % basek)) as i64
-            );
-            lut.rotate(&module, -1);
+    (0..extension_factor).for_each(|ext| {
+        module.decode_vec_i64(basek, &lut.data[ext], 0, log_scale, &mut lut_dec);
+        (0..module.n()).step_by(step).for_each(|i| {
+            (0..step).for_each(|_| {
+                assert_eq!(f[i / step] % message_modulus as i64, lut_dec[i]);
+            });
         });
     });
 }

@@ -0,0 +1,508 @@
+use std::{collections::HashMap, time::Instant, usize};
+
+use backend::hal::{
+    api::{
+        ScratchAvailable, TakeMatZnx, TakeScalarZnx, TakeSvpPPol, TakeVecZnx, TakeVecZnxBig, TakeVecZnxDft, TakeVecZnxDftSlice,
+        TakeVecZnxSlice, VecZnxAddInplace, VecZnxAddScalarInplace, VecZnxAutomorphism, VecZnxAutomorphismInplace,
+        VecZnxBigAutomorphismInplace, VecZnxBigSubSmallBInplace, VecZnxCopy, VecZnxDftCopy, VecZnxDftToVecZnxBigTmpA,
+        VecZnxNegateInplace, VecZnxNormalizeInplace, VecZnxNormalizeTmpBytes, VecZnxRotateInplace, VecZnxRshInplace, VecZnxSub,
+        VecZnxSubABInplace, VecZnxSwithcDegree,
+    },
+    layouts::{Backend, Data, DataMut, DataRef, Module, Scratch},
+    oep::{ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl},
+};
+use sampling::source::Source;
+
+use crate::{
+    AutomorphismKey, AutomorphismKeyEncryptSkFamily, AutomorphismKeyExec, BlindRotationKeyCGGI, BlindRotationKeyCGGIExec,
+    BlindRotationKeyCGGIExecLayoutFamily, CCGIBlindRotationFamily, GGSWCiphertext, GGSWEncryptSkFamily, GLWECiphertext, GLWEOps,
+    GLWESecret, GLWESecretExec, GLWESecretFamily, GLWETensorKey, GLWETensorKeyEncryptSkFamily, GLWETensorKeyExec,
+    GLWETraceFamily, Infos, LWECiphertext, LWESecret, LookUpTable, LookUpTableRotationDirection, TakeGGLWE, TakeGLWECt,
+    cggi_blind_rotate,
+};
+
+pub struct CircuitBootstrappingKeyCGGI<D: Data> {
+    pub(crate) brk: BlindRotationKeyCGGI<D>,
+    pub(crate) tsk: GLWETensorKey<Vec<u8>>,
+    pub(crate) atk: HashMap<i64, AutomorphismKey<Vec<u8>>>,
+}
+
+impl CircuitBootstrappingKeyCGGI<Vec<u8>> {
+    pub fn generate<DLwe, DGlwe, B: Backend>(
+        module: &Module<B>,
+        basek: usize,
+        sk_lwe: &LWESecret<DLwe>,
+        sk_glwe: &GLWESecret<DGlwe>,
+        k_brk: usize,
+        rows_brk: usize,
+        k_trace: usize,
+        rows_trace: usize,
+        k_tsk: usize,
+        rows_tsk: usize,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch<B>,
+    ) -> Self
+    where
+        Module<B>: GLWESecretFamily<B>
+            + GGSWEncryptSkFamily<B>
+            + VecZnxAddScalarInplace
+            + AutomorphismKeyEncryptSkFamily<B>
+            + VecZnxAutomorphism
+            + VecZnxSwithcDegree
+            + GLWETensorKeyEncryptSkFamily<B>,
+        DLwe: DataRef,
+        DGlwe: DataRef,
+        Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx + TakeScalarZnx + TakeSvpPPol<B> + TakeVecZnxBig<B>,
+    {
+        let mut auto_keys: HashMap<i64, AutomorphismKey<Vec<u8>>> = HashMap::new();
+        let gal_els: Vec<i64> = GLWECiphertext::trace_galois_elements(&module);
+        gal_els.iter().for_each(|gal_el| {
+            let mut key: AutomorphismKey<Vec<u8>> =
+                AutomorphismKey::alloc(sk_glwe.n(), basek, k_trace, rows_trace, 1, sk_glwe.rank());
+            key.encrypt_sk(
+                &module, *gal_el, &sk_glwe, source_xa, source_xe, sigma, scratch,
+            );
+            auto_keys.insert(*gal_el, key);
+        });
+
+        let sk_glwe_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk_glwe);
+
+        let mut brk: BlindRotationKeyCGGI<Vec<u8>> = BlindRotationKeyCGGI::alloc(
+            sk_glwe.n(),
+            sk_lwe.n(),
+            basek,
+            k_brk,
+            rows_brk,
+            sk_glwe.rank(),
+        );
+        brk.generate_from_sk(
+            module,
+            &sk_glwe_exec,
+            sk_lwe,
+            source_xa,
+            source_xe,
+            sigma,
+            scratch,
+        );
+
+        let mut tsk: GLWETensorKey<Vec<u8>> = GLWETensorKey::alloc(sk_glwe.n(), basek, k_tsk, rows_tsk, 1, sk_glwe.rank());
+        tsk.encrypt_sk(module, &sk_glwe, source_xa, source_xe, sigma, scratch);
+
+        Self {
+            brk,
+            atk: auto_keys,
+            tsk,
+        }
+    }
+}
+
+pub struct CircuitBootstrappingKeyCGGIExec<D: Data, B: Backend> {
+    pub(crate) brk: BlindRotationKeyCGGIExec<D, B>,
+    pub(crate) tsk: GLWETensorKeyExec<Vec<u8>, B>,
+    pub(crate) atk: HashMap<i64, AutomorphismKeyExec<Vec<u8>, B>>,
+}
+
+impl<B: Backend> CircuitBootstrappingKeyCGGIExec<Vec<u8>, B> {
+    pub fn from<DataOther: DataRef>(
+        module: &Module<B>,
+        other: &CircuitBootstrappingKeyCGGI<DataOther>,
+        scratch: &mut Scratch<B>,
+    ) -> CircuitBootstrappingKeyCGGIExec<Vec<u8>, B>
+    where
+        Module<B>: BlindRotationKeyCGGIExecLayoutFamily<B>,
+    {
+        let brk: BlindRotationKeyCGGIExec<Vec<u8>, B> = BlindRotationKeyCGGIExec::from(module, &other.brk, scratch);
+        let tsk: GLWETensorKeyExec<Vec<u8>, B> = GLWETensorKeyExec::from(module, &other.tsk, scratch);
+        let mut atk: HashMap<i64, AutomorphismKeyExec<Vec<u8>, B>> = HashMap::new();
+        for (key, value) in &other.atk {
+            atk.insert(*key, AutomorphismKeyExec::from(module, value, scratch));
+        }
+        CircuitBootstrappingKeyCGGIExec { brk, tsk, atk }
+    }
+}
+
+pub trait CGGICircuitBootstrapFamily<B: Backend> = VecZnxRotateInplace
+    + VecZnxNormalizeInplace<B>
+    + VecZnxNormalizeTmpBytes
+    + CCGIBlindRotationFamily<B>
+    + VecZnxSwithcDegree
+    + VecZnxBigAutomorphismInplace<B>
+    + VecZnxRshInplace
+    + VecZnxDftCopy<B>
+    + VecZnxDftToVecZnxBigTmpA<B>
+    + VecZnxSub
+    + VecZnxAddInplace
+    + VecZnxNegateInplace
+    + VecZnxCopy
+    + VecZnxSubABInplace
+    + GLWETraceFamily<B>
+    + VecZnxRotateInplace
+    + VecZnxAutomorphismInplace
+    + VecZnxBigSubSmallBInplace<B>;
+
+pub fn circuit_bootstrap_to_constant_cggi<DRes, DLwe, DBrk, B: Backend>(
+    module: &Module<B>,
+    res: &mut GGSWCiphertext<DRes>,
+    lwe: &LWECiphertext<DLwe>,
+    log_domain: usize,
+    extension_factor: usize,
+    key: &CircuitBootstrappingKeyCGGIExec<DBrk, B>,
+    scratch: &mut Scratch<B>,
+) where
+    DRes: DataMut,
+    DLwe: DataRef,
+    DBrk: DataRef,
+    Module<B>: CGGICircuitBootstrapFamily<B>,
+    B: ScratchOwnedAllocImpl<B> + ScratchOwnedBorrowImpl<B>,
+    Scratch<B>: TakeVecZnx
+        + TakeVecZnxDftSlice<B>
+        + TakeVecZnxBig<B>
+        + TakeVecZnxDft<B>
+        + TakeMatZnx
+        + ScratchAvailable
+        + TakeVecZnxSlice,
+{
+    circuit_bootstrap_core_cggi(
+        false,
+        module,
+        0,
+        res,
+        lwe,
+        log_domain,
+        extension_factor,
+        key,
+        scratch,
+    );
+}
+
+pub fn circuit_bootstrap_to_exponent_cggi<DRes, DLwe, DBrk, B: Backend>(
+    module: &Module<B>,
+    log_gap_out: usize,
+    res: &mut GGSWCiphertext<DRes>,
+    lwe: &LWECiphertext<DLwe>,
+    log_domain: usize,
+    extension_factor: usize,
+    key: &CircuitBootstrappingKeyCGGIExec<DBrk, B>,
+    scratch: &mut Scratch<B>,
+) where
+    DRes: DataMut,
+    DLwe: DataRef,
+    DBrk: DataRef,
+    Module<B>: CGGICircuitBootstrapFamily<B>,
+    B: ScratchOwnedAllocImpl<B> + ScratchOwnedBorrowImpl<B>,
+    Scratch<B>: TakeVecZnx
+        + TakeVecZnxDftSlice<B>
+        + TakeVecZnxBig<B>
+        + TakeVecZnxDft<B>
+        + TakeMatZnx
+        + ScratchAvailable
+        + TakeVecZnxSlice,
+{
+    circuit_bootstrap_core_cggi(
+        true,
+        module,
+        log_gap_out,
+        res,
+        lwe,
+        log_domain,
+        extension_factor,
+        key,
+        scratch,
+    );
+}
+
+pub fn circuit_bootstrap_core_cggi<DRes, DLwe, DBrk, B: Backend>(
+    to_exponent: bool,
+    module: &Module<B>,
+    log_gap_out: usize,
+    res: &mut GGSWCiphertext<DRes>,
+    lwe: &LWECiphertext<DLwe>,
+    log_domain: usize,
+    extension_factor: usize,
+    key: &CircuitBootstrappingKeyCGGIExec<DBrk, B>,
+    scratch: &mut Scratch<B>,
+) where
+    DRes: DataMut,
+    DLwe: DataRef,
+    DBrk: DataRef,
+    Module<B>: CGGICircuitBootstrapFamily<B>,
+    B: ScratchOwnedAllocImpl<B> + ScratchOwnedBorrowImpl<B>,
+    Scratch<B>: TakeGGLWE<B>
+        + TakeVecZnxDftSlice<B>
+        + TakeVecZnxBig<B>
+        + TakeVecZnxDft<B>
+        + TakeVecZnx
+        + ScratchAvailable
+        + TakeVecZnxSlice,
+{
+    #[cfg(debug_assertions)]
+    {
+        use crate::Infos;
+
+        assert_eq!(res.n(), key.brk.n());
+        assert_eq!(lwe.basek(), key.brk.basek());
+        assert_eq!(res.basek(), key.brk.basek());
+    }
+
+    let n: usize = res.n();
+    let basek: usize = res.basek();
+    let rows: usize = res.rows();
+    let rank: usize = res.rank();
+    let k: usize = res.k();
+
+    let alpha: usize = rows.next_power_of_two();
+
+    let mut f: Vec<i64> = vec![0i64; (1 << log_domain) * alpha];
+
+    if to_exponent {
+        (0..rows).for_each(|i| {
+            f[i] = 1 << (basek * (rows - 1 - i));
+        });
+    } else {
+        (0..1 << log_domain).for_each(|j| {
+            (0..rows).for_each(|i| {
+                f[j * alpha + i] = j as i64 * (1 << (basek * (rows - 1 - i)));
+            });
+        });
+    }
+
+    // Lut precision, basically must be able to hold the decomposition power basis of the GGSW
+    let mut lut: LookUpTable = LookUpTable::alloc(n, basek, basek * rows, extension_factor);
+    lut.set(module, &f, basek * rows);
+
+    if to_exponent {
+        lut.set_rotation_direction(LookUpTableRotationDirection::Right);
+    }
+
+    // TODO: separate GGSW k from output of blind rotation k
+    let (mut res_glwe, scratch1) = scratch.take_glwe_ct(n, basek, k, rank);
+    let (mut tmp_gglwe, scratch2) = scratch1.take_gglwe(n, basek, k, rows, 1, rank, rank);
+
+    let now: Instant = Instant::now();
+    cggi_blind_rotate(module, &mut res_glwe, &lwe, &lut, &key.brk, scratch2);
+    println!("cggi_blind_rotate: {} ms", now.elapsed().as_millis());
+
+    let gap: usize = 2 * lut.drift / lut.extension_factor();
+
+    let log_gap_in: usize = (usize::BITS - (gap * alpha - 1).leading_zeros()) as _;
+
+    (0..rows).for_each(|i| {
+        let mut tmp_glwe: GLWECiphertext<&mut [u8]> = tmp_gglwe.at_mut(i, 0);
+
+        if to_exponent {
+            let now: Instant = Instant::now();
+
+            // Isolates i-th LUT and moves coefficients according to requested gap.
+            post_process(
+                module,
+                &mut tmp_glwe,
+                &res_glwe,
+                log_gap_in,
+                log_gap_out,
+                log_domain,
+                &key.atk,
+                scratch2,
+            );
+            println!("post_process: {} ms", now.elapsed().as_millis());
+        } else {
+            tmp_glwe.trace(module, 0, module.log_n(), &res_glwe, &key.atk, scratch2);
+        }
+
+        if i < rows {
+            res_glwe.rotate_inplace(module, -(gap as i64));
+        }
+    });
+
+    // Expands GGLWE to GGSW using GGLWE(s^2)
+    res.from_gglwe(module, &tmp_gglwe, &key.tsk, scratch2);
+}
+
+fn post_process<DataRes, DataA, B: Backend>(
+    module: &Module<B>,
+    res: &mut GLWECiphertext<DataRes>,
+    a: &GLWECiphertext<DataA>,
+    log_gap_in: usize,
+    log_gap_out: usize,
+    log_domain: usize,
+    auto_keys: &HashMap<i64, AutomorphismKeyExec<Vec<u8>, B>>,
+    scratch: &mut Scratch<B>,
+) where
+    DataRes: DataMut,
+    DataA: DataRef,
+    Module<B>: CGGICircuitBootstrapFamily<B>,
+    Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx,
+{
+    let log_n: usize = module.log_n();
+
+    let mut cts: HashMap<usize, GLWECiphertext<Vec<u8>>> = HashMap::new();
+
+    // First partial trace, vanishes all coefficients which are not multiples of gap_in
+    // [1, 1, 1, 1, 0, 0, 0, ..., 0, 0, -1, -1, -1, -1] -> [1, 0, 0, 0, 0, 0, 0, ..., 0, 0, 0, 0, 0, 0]
+    res.trace(
+        module,
+        module.log_n() - log_gap_in as usize + 1,
+        log_n,
+        &a,
+        auto_keys,
+        scratch,
+    );
+
+    // TODO: optimize with packing and final partial trace
+    // If gap_out < gap_in, then we need to repack, i.e. reduce the cap between coefficients.
+    if log_gap_in != log_gap_out {
+        let steps: i32 = 1 << log_domain;
+        (0..steps).for_each(|i| {
+            if i != 0 {
+                res.rotate_inplace(module, -(1 << log_gap_in));
+            }
+            cts.insert(i as usize * (1 << log_gap_out), res.clone());
+        });
+
+        let now: Instant = Instant::now();
+        pack(module, &mut cts, log_gap_out, auto_keys, scratch);
+        println!("pack: {} ms", now.elapsed().as_millis());
+        let packed: GLWECiphertext<Vec<u8>> = cts.remove(&0).unwrap();
+        res.trace(
+            module,
+            log_n - log_gap_out,
+            log_n,
+            &packed,
+            auto_keys,
+            scratch,
+        );
+    }
+}
+
+pub fn pack<D: DataMut, B: Backend>(
+    module: &Module<B>,
+    cts: &mut HashMap<usize, GLWECiphertext<D>>,
+    log_gap_out: usize,
+    auto_keys: &HashMap<i64, AutomorphismKeyExec<Vec<u8>, B>>,
+    scratch: &mut Scratch<B>,
+) where
+    Module<B>: CGGICircuitBootstrapFamily<B>,
+    Scratch<B>: TakeVecZnx + TakeVecZnxDft<B> + ScratchAvailable,
+{
+    let log_n: usize = module.log_n();
+
+    let basek: usize = cts.get(&0).unwrap().basek();
+    let k: usize = cts.get(&0).unwrap().k();
+    let rank: usize = cts.get(&0).unwrap().rank();
+
+    (0..log_n - log_gap_out).for_each(|i| {
+        let now: Instant = Instant::now();
+
+        let t = 16.min(1 << (log_n - 1 - i));
+
+        let auto_key: &AutomorphismKeyExec<Vec<u8>, B>;
+        if i == 0 {
+            auto_key = auto_keys.get(&-1).unwrap()
+        } else {
+            auto_key = auto_keys.get(&module.galois_element(1 << (i - 1))).unwrap();
+        }
+
+        (0..t).for_each(|j| {
+            let mut a: Option<GLWECiphertext<D>> = cts.remove(&j);
+            let mut b: Option<GLWECiphertext<D>> = cts.remove(&(j + t));
+
+            combine(
+                module,
+                basek,
+                k,
+                rank,
+                a.as_mut(),
+                b.as_mut(),
+                i,
+                auto_key,
+                scratch,
+            );
+
+            if let Some(a) = a {
+                cts.insert(j, a);
+            } else if let Some(b) = b {
+                cts.insert(j, b);
+            }
+        });
+
+        println!("combine: {} us", now.elapsed().as_micros());
+    });
+}
+
+fn combine<A: DataMut, D: DataMut, DataAK: DataRef, B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k: usize,
+    rank: usize,
+    a: Option<&mut GLWECiphertext<A>>,
+    b: Option<&mut GLWECiphertext<D>>,
+    i: usize,
+    auto_key: &AutomorphismKeyExec<DataAK, B>,
+    scratch: &mut Scratch<B>,
+) where
+    Module<B>: CGGICircuitBootstrapFamily<B>,
+    Scratch<B>: TakeVecZnx + TakeVecZnxDft<B> + ScratchAvailable,
+{
+    // Goal is to evaluate: a = a + b*X^t + phi(a - b*X^t))
+    // We also use the identity: AUTO(a * X^t, g) = -X^t * AUTO(a, g)
+    // where t = 2^(log_n - i - 1) and g = 5^{2^(i - 1)}
+    // Different cases for wether a and/or b are zero.
+    //
+    // Implicite RSH without modulus switch, introduces extra I(X) * Q/2 on decryption.
+    // Necessary so that the scaling of the plaintext remains constant.
+    // It however is ok to do so here because coefficients are eventually
+    // either mapped to garbage or twice their value which vanishes I(X)
+    // since 2*(I(X) * Q/2) = I(X) * Q = 0 mod Q.
+    if let Some(a) = a {
+        let n: usize = a.n();
+        let log_n: usize = (u64::BITS - (n - 1).leading_zeros()) as _;
+        let t: i64 = 1 << (log_n - i - 1);
+
+        if let Some(b) = b {
+            let (mut tmp_b, scratch_1) = scratch.take_glwe_ct(n, basek, k, rank);
+
+            // a = a * X^-t
+            a.rotate_inplace(module, -t);
+
+            // tmp_b = a * X^-t - b
+            tmp_b.sub(module, a, b);
+            tmp_b.rsh(module, 1);
+
+            // a = a * X^-t + b
+            a.add_inplace(module, b);
+            a.rsh(module, 1);
+
+            tmp_b.normalize_inplace(module, scratch_1);
+
+            // tmp_b = phi(a * X^-t - b)
+            tmp_b.automorphism_inplace(module, auto_key, scratch_1);
+
+            // a = a * X^-t + b - phi(a * X^-t - b)
+            a.sub_inplace_ab(module, &tmp_b);
+            a.normalize_inplace(module, scratch_1);
+
+            // a = a + b * X^t - phi(a * X^-t - b) * X^t
+            //   = a + b * X^t - phi(a * X^-t - b) * - phi(X^t)
+            //   = a + b * X^t + phi(a - b * X^t)
+            a.rotate_inplace(module, t);
+        } else {
+            a.rsh(module, 1);
+            // a = a + phi(a)
+            a.automorphism_add_inplace(module, auto_key, scratch);
+        }
+    } else {
+        if let Some(b) = b {
+            let n: usize = b.n();
+            let log_n: usize = (u64::BITS - (n - 1).leading_zeros()) as _;
+            let t: i64 = 1 << (log_n - i - 1);
+
+            let (mut tmp_b, scratch_1) = scratch.take_glwe_ct(n, basek, k, rank);
+            tmp_b.rotate(module, t, b);
+            tmp_b.rsh(module, 1);
+
+            // a = (b* X^t - phi(b* X^t))
+            b.automorphism_sub_ba(module, &tmp_b, auto_key, scratch_1);
+        }
+    }
+}

@@ -0,0 +1,6 @@
+mod circuit_bootstrapping;
+
+pub use circuit_bootstrapping::*;
+
+#[cfg(test)]
+mod test_fft64;

@@ -0,0 +1,357 @@
+use std::time::Instant;
+
+use backend::{
+    hal::{
+        api::{
+            ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddNormal, VecZnxAddScalarInplace, VecZnxAutomorphism,
+            VecZnxEncodeCoeffsi64, VecZnxFillUniform, VecZnxNormalizeInplace, VecZnxRotateInplace, VecZnxStd, VecZnxSwithcDegree,
+            ZnxView, ZnxViewMut,
+        },
+        layouts::{Backend, Module, ScalarZnx, ScratchOwned},
+        oep::{
+            ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeMatZnxImpl, TakeScalarZnxImpl,
+            TakeSvpPPolImpl, TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxDftSliceImpl, TakeVecZnxImpl, TakeVecZnxSliceImpl,
+        },
+    },
+    implementation::cpu_spqlios::FFT64,
+};
+use sampling::source::Source;
+
+use crate::{
+    AutomorphismKeyEncryptSkFamily, BlindRotationKeyCGGIExecLayoutFamily, GGSWAssertNoiseFamily, GGSWCiphertext,
+    GGSWCiphertextExec, GGSWEncryptSkFamily, GLWECiphertext, GLWEDecryptFamily, GLWEPlaintext, GLWESecret, GLWESecretExec,
+    GLWESecretFamily, GLWETensorKeyEncryptSkFamily, LWECiphertext, LWESecret,
+    circuit_bootstrapping::circuit_bootstrapping::{
+        CGGICircuitBootstrapFamily, CircuitBootstrappingKeyCGGI, CircuitBootstrappingKeyCGGIExec,
+        circuit_bootstrap_to_constant_cggi, circuit_bootstrap_to_exponent_cggi,
+    },
+    lwe::LWEPlaintext,
+};
+
+#[test]
+fn test_to_exponent() {
+    let module: Module<FFT64> = Module::<FFT64>::new(256);
+    to_exponent(&module);
+}
+
+fn to_exponent<B: Backend>(module: &Module<B>)
+where
+    Module<B>: GLWESecretFamily<B>
+        + VecZnxEncodeCoeffsi64
+        + VecZnxFillUniform
+        + VecZnxAddNormal
+        + VecZnxNormalizeInplace<B>
+        + GLWESecretFamily<B>
+        + GGSWEncryptSkFamily<B>
+        + VecZnxAddScalarInplace
+        + AutomorphismKeyEncryptSkFamily<B>
+        + VecZnxAutomorphism
+        + VecZnxSwithcDegree
+        + GLWETensorKeyEncryptSkFamily<B>
+        + BlindRotationKeyCGGIExecLayoutFamily<B>
+        + CGGICircuitBootstrapFamily<B>
+        + GLWEDecryptFamily<B>
+        + GGSWAssertNoiseFamily<B>
+        + VecZnxStd,
+    B: ScratchOwnedAllocImpl<B>
+        + ScratchOwnedBorrowImpl<B>
+        + TakeVecZnxDftImpl<B>
+        + ScratchAvailableImpl<B>
+        + TakeVecZnxImpl<B>
+        + TakeScalarZnxImpl<B>
+        + TakeSvpPPolImpl<B>
+        + TakeVecZnxBigImpl<B>
+        + TakeVecZnxDftSliceImpl<B>
+        + TakeMatZnxImpl<B>
+        + TakeVecZnxSliceImpl<B>,
+{
+    let n: usize = module.n();
+    let basek: usize = 17;
+    let extension_factor: usize = 1;
+    let rank: usize = 1;
+    let sigma: f64 = 3.2;
+
+    let n_lwe: usize = 77;
+    let k_lwe_pt: usize = 4;
+    let k_lwe_ct: usize = 22;
+    let block_size: usize = 7;
+
+    let k_brk: usize = 5 * basek;
+    let rows_brk: usize = 4;
+
+    let k_trace: usize = 5 * basek;
+    let rows_trace: usize = 4;
+
+    let k_tsk: usize = 5 * basek;
+    let rows_tsk: usize = 4;
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(1 << 23);
+
+    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(block_size, &mut source_xs);
+
+    let mut sk_glwe: GLWESecret<Vec<u8>> = GLWESecret::alloc(n, rank);
+    sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
+
+    let sk_glwe_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk_glwe);
+
+    let data: i64 = 1;
+
+    let mut pt_lwe: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(basek, k_lwe_pt);
+    module.encode_coeff_i64(basek, &mut pt_lwe.data, 0, k_lwe_pt + 2, 0, data, k_lwe_pt);
+
+    println!("pt_lwe: {}", pt_lwe.data);
+
+    let mut ct_lwe: LWECiphertext<Vec<u8>> = LWECiphertext::alloc(n_lwe, basek, k_lwe_ct);
+    ct_lwe.encrypt_sk(
+        module,
+        &pt_lwe,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+    );
+
+    let now: Instant = Instant::now();
+    let cbt_key: CircuitBootstrappingKeyCGGI<Vec<u8>> = CircuitBootstrappingKeyCGGI::generate(
+        module,
+        basek,
+        &sk_lwe,
+        &sk_glwe,
+        k_brk,
+        rows_brk,
+        k_trace,
+        rows_trace,
+        k_tsk,
+        rows_tsk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+    println!("CBT-KGEN: {} ms", now.elapsed().as_millis());
+
+    let k_ggsw_res: usize = 4 * basek;
+    let rows_ggsw_res: usize = 2;
+
+    let mut res: GGSWCiphertext<Vec<u8>> = GGSWCiphertext::alloc(n, basek, k_ggsw_res, rows_ggsw_res, 1, rank);
+
+    let log_gap_out = 1;
+
+    let cbt_exec: CircuitBootstrappingKeyCGGIExec<Vec<u8>, B> =
+        CircuitBootstrappingKeyCGGIExec::from(module, &cbt_key, scratch.borrow());
+
+    let now: Instant = Instant::now();
+    circuit_bootstrap_to_exponent_cggi(
+        module,
+        log_gap_out,
+        &mut res,
+        &ct_lwe,
+        k_lwe_pt,
+        extension_factor,
+        &cbt_exec,
+        scratch.borrow(),
+    );
+    println!("CBT: {} ms", now.elapsed().as_millis());
+
+    // X^{data * 2^log_gap_out}
+    let mut pt_ggsw: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(n, 1);
+    pt_ggsw.at_mut(0, 0)[0] = 1;
+    module.vec_znx_rotate_inplace(data * (1 << log_gap_out), &mut pt_ggsw.as_vec_znx_mut(), 0);
+
+    res.print_noise(module, &sk_glwe_exec, &pt_ggsw);
+
+    let k_glwe: usize = k_ggsw_res;
+
+    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(n, basek, k_glwe, rank);
+    let mut pt_glwe: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(n, basek, basek);
+    pt_glwe.data.at_mut(0, 0)[0] = 1 << (basek - 2);
+
+    ct_glwe.encrypt_sk(
+        module,
+        &pt_glwe,
+        &sk_glwe_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let res_exec: GGSWCiphertextExec<Vec<u8>, B> = GGSWCiphertextExec::from(module, &res, scratch.borrow());
+
+    ct_glwe.external_product_inplace(module, &res_exec, scratch.borrow());
+
+    let mut pt_res: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(n, basek, k_glwe);
+    ct_glwe.decrypt(module, &mut pt_res, &sk_glwe_exec, scratch.borrow());
+
+    // Parameters are set such that the first limb should be noiseless.
+    let mut pt_want: Vec<i64> = vec![0i64; module.n()];
+    pt_want[data as usize * (1 << log_gap_out)] = pt_glwe.data.at(0, 0)[0];
+    assert_eq!(pt_res.data.at(0, 0), pt_want);
+}
+
+#[test]
+fn test_to_constant() {
+    let module: Module<FFT64> = Module::<FFT64>::new(256);
+    to_constant(&module);
+}
+
+fn to_constant<B: Backend>(module: &Module<B>)
+where
+    Module<B>: GLWESecretFamily<B>
+        + VecZnxEncodeCoeffsi64
+        + VecZnxFillUniform
+        + VecZnxAddNormal
+        + VecZnxNormalizeInplace<B>
+        + GLWESecretFamily<B>
+        + GGSWEncryptSkFamily<B>
+        + VecZnxAddScalarInplace
+        + AutomorphismKeyEncryptSkFamily<B>
+        + VecZnxAutomorphism
+        + VecZnxSwithcDegree
+        + GLWETensorKeyEncryptSkFamily<B>
+        + BlindRotationKeyCGGIExecLayoutFamily<B>
+        + CGGICircuitBootstrapFamily<B>
+        + GLWEDecryptFamily<B>
+        + GGSWAssertNoiseFamily<B>
+        + VecZnxStd,
+    B: ScratchOwnedAllocImpl<B>
+        + ScratchOwnedBorrowImpl<B>
+        + TakeVecZnxDftImpl<B>
+        + ScratchAvailableImpl<B>
+        + TakeVecZnxImpl<B>
+        + TakeScalarZnxImpl<B>
+        + TakeSvpPPolImpl<B>
+        + TakeVecZnxBigImpl<B>
+        + TakeVecZnxDftSliceImpl<B>
+        + TakeMatZnxImpl<B>
+        + TakeVecZnxSliceImpl<B>,
+{
+    let n = module.n();
+    let basek: usize = 14;
+    let extension_factor: usize = 1;
+    let rank: usize = 2;
+    let sigma: f64 = 3.2;
+
+    let n_lwe: usize = 77;
+    let k_lwe_pt: usize = 1;
+    let k_lwe_ct: usize = 13;
+    let block_size: usize = 7;
+
+    let k_brk: usize = 5 * basek;
+    let rows_brk: usize = 3;
+
+    let k_trace: usize = 5 * basek;
+    let rows_trace: usize = 4;
+
+    let k_tsk: usize = 5 * basek;
+    let rows_tsk: usize = 4;
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(1 << 23);
+
+    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(block_size, &mut source_xs);
+
+    let mut sk_glwe: GLWESecret<Vec<u8>> = GLWESecret::alloc(n, rank);
+    sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
+
+    let sk_glwe_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk_glwe);
+
+    let data: i64 = 1;
+
+    let mut pt_lwe: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(basek, k_lwe_pt);
+    module.encode_coeff_i64(basek, &mut pt_lwe.data, 0, k_lwe_pt + 2, 0, data, k_lwe_pt);
+
+    println!("pt_lwe: {}", pt_lwe.data);
+
+    let mut ct_lwe: LWECiphertext<Vec<u8>> = LWECiphertext::alloc(n_lwe, basek, k_lwe_ct);
+    ct_lwe.encrypt_sk(
+        module,
+        &pt_lwe,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+    );
+
+    let now: Instant = Instant::now();
+    let cbt_key: CircuitBootstrappingKeyCGGI<Vec<u8>> = CircuitBootstrappingKeyCGGI::generate(
+        module,
+        basek,
+        &sk_lwe,
+        &sk_glwe,
+        k_brk,
+        rows_brk,
+        k_trace,
+        rows_trace,
+        k_tsk,
+        rows_tsk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+    println!("CBT-KGEN: {} ms", now.elapsed().as_millis());
+
+    let k_ggsw_res: usize = 4 * basek;
+    let rows_ggsw_res: usize = 3;
+
+    let mut res: GGSWCiphertext<Vec<u8>> = GGSWCiphertext::alloc(n, basek, k_ggsw_res, rows_ggsw_res, 1, rank);
+
+    let cbt_exec: CircuitBootstrappingKeyCGGIExec<Vec<u8>, B> =
+        CircuitBootstrappingKeyCGGIExec::from(module, &cbt_key, scratch.borrow());
+
+    let now: Instant = Instant::now();
+    circuit_bootstrap_to_constant_cggi(
+        module,
+        &mut res,
+        &ct_lwe,
+        k_lwe_pt,
+        extension_factor,
+        &cbt_exec,
+        scratch.borrow(),
+    );
+    println!("CBT: {} ms", now.elapsed().as_millis());
+
+    // X^{data * 2^log_gap_out}
+    let mut pt_ggsw: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(n, 1);
+    pt_ggsw.at_mut(0, 0)[0] = data;
+
+    res.print_noise(module, &sk_glwe_exec, &pt_ggsw);
+
+    let k_glwe: usize = k_ggsw_res;
+
+    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(n, basek, k_glwe, rank);
+    let mut pt_glwe: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(n, basek, basek);
+    pt_glwe.data.at_mut(0, 0)[0] = 1 << (basek - k_lwe_pt - 1);
+
+    ct_glwe.encrypt_sk(
+        module,
+        &pt_glwe,
+        &sk_glwe_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let res_exec: GGSWCiphertextExec<Vec<u8>, B> = GGSWCiphertextExec::from(module, &res, scratch.borrow());
+
+    ct_glwe.external_product_inplace(module, &res_exec, scratch.borrow());
+
+    let mut pt_res: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(n, basek, k_glwe);
+    ct_glwe.decrypt(module, &mut pt_res, &sk_glwe_exec, scratch.borrow());
+
+    // Parameters are set such that the first limb should be noiseless.
+    let mut pt_want: Vec<i64> = vec![0i64; module.n()];
+    pt_want[0] = pt_glwe.data.at(0, 0)[0] * data;
+    assert_eq!(pt_res.data.at(0, 0), pt_want);
+}

@@ -0,0 +1,1 @@
+mod circuit_bootstrapping;

@@ -366,6 +366,27 @@ {
         let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
         pairs * GLWESwitchingKeyExec::bytes_of(module, n, basek, k, rows, digits, 1, rank)
     }
+
+    pub fn from<D: DataRef>(
+        module: &Module<B>,
+        other: &GLWETensorKey<D>,
+        scratch: &mut Scratch<B>,
+    ) -> GLWETensorKeyExec<Vec<u8>, B>
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        let mut tsk_exec: GLWETensorKeyExec<Vec<u8>, B> = Self::alloc(
+            module,
+            other.n(),
+            other.basek(),
+            other.k(),
+            other.rows(),
+            other.digits(),
+            other.rank(),
+        );
+        tsk_exec.prepare(module, other, scratch);
+        tsk_exec
+    }
 }
 
 impl<D: Data, B: Backend> Infos for GLWETensorKeyExec<D, B> {

@@ -108,32 +108,8 @@ )
             )
         };
 
-        let n: usize = auto_key.n();
-        let rank: usize = self.rank();
-        let cols: usize = rank + 1;
-
-        // Keyswitch the j-th row of the col 0
-        (0..lhs.rows()).for_each(|row_i| {
-            // Key-switch column 0, i.e.
-            // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0, a1, a2) -> (-(a0pi^-1(s0) + a1pi^-1(s1) + a2pi^-1(s2)) + M[i], a0, a1, a2)
-            self.at_mut(row_i, 0)
-                .automorphism(module, &lhs.at(row_i, 0), auto_key, scratch);
-
-            // Isolates DFT(AUTO(a[i]))
-            let (mut ci_dft, scratch1) = scratch.take_vec_znx_dft(n, cols, self.size());
-            (0..cols).for_each(|i| {
-                module.vec_znx_dft_from_vec_znx(1, 0, &mut ci_dft, i, &self.at(row_i, 0).data, i);
-            });
-
-            // Generates
-            //
-            // col 1: (-(b0s0 + b1s1 + b2s2)    , b0 + pi(M[i]), b1           , b2           )
-            // col 2: (-(c0s0 + c1s1 + c2s2)    , c0           , c1 + pi(M[i]), c2           )
-            // col 3: (-(d0s0 + d1s1 + d2s2)    , d0           , d1           , d2 + pi(M[i]))
-            (1..cols).for_each(|col_j| {
-                self.expand_row(module, row_i, col_j, &ci_dft, tensor_key, scratch1);
-            });
-        })
+        self.automorphism_internal(module, lhs, auto_key, scratch);
+        self.expand_row(module, tensor_key, scratch);
     }
 
     pub fn automorphism_inplace<DataKsk: DataRef, DataTsk: DataRef, B: Backend>(
@@ -150,5 +126,24 @@ unsafe {
             let self_ptr: *mut GGSWCiphertext<DataSelf> = self as *mut GGSWCiphertext<DataSelf>;
             self.automorphism(module, &*self_ptr, auto_key, tensor_key, scratch);
         }
+    }
+
+    fn automorphism_internal<DataLhs: DataRef, DataAk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        lhs: &GGSWCiphertext<DataLhs>,
+        auto_key: &AutomorphismKeyExec<DataAk, B>,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GLWEKeyswitchFamily<B> + GGSWKeySwitchFamily<B> + VecZnxAutomorphismInplace + VecZnxNormalizeTmpBytes,
+        Scratch<B>: ScratchAvailable + TakeVecZnxDft<B> + TakeVecZnxBig<B>,
+    {
+        // Keyswitch the j-th row of the col 0
+        (0..lhs.rows()).for_each(|row_i| {
+            // Key-switch column 0, i.e.
+            // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0, a1, a2) -> (-(a0pi^-1(s0) + a1pi^-1(s1) + a2pi^-1(s2)) + M[i], a0, a1, a2)
+            self.at_mut(row_i, 0)
+                .automorphism(module, &lhs.at(row_i, 0), auto_key, scratch);
+        });
     }
 }

@@ -1,12 +1,14 @@
 use backend::hal::{
     api::{
-        ScratchAvailable, TakeVecZnxBig, TakeVecZnxDft, VecZnxBigAllocBytes, VecZnxDftAddInplace, VecZnxDftCopy,
-        VecZnxDftToVecZnxBigTmpA, VecZnxNormalizeTmpBytes, ZnxInfos,
+        ScratchAvailable, TakeVecZnx, TakeVecZnxBig, TakeVecZnxDft, VecZnxBigAllocBytes, VecZnxCopy, VecZnxDftAddInplace,
+        VecZnxDftCopy, VecZnxDftToVecZnxBigTmpA, VecZnxNormalizeTmpBytes, ZnxInfos,
     },
-    layouts::{Backend, DataMut, DataRef, Module, Scratch, VecZnx, VecZnxDft, VmpPMat},
+    layouts::{Backend, DataMut, DataRef, Module, Scratch, VecZnx, VmpPMat},
 };
 
-use crate::{GGSWCiphertext, GLWECiphertext, GLWEKeyswitchFamily, GLWESwitchingKeyExec, GLWETensorKeyExec, Infos};
+use crate::{
+    GGLWECiphertext, GGSWCiphertext, GLWECiphertext, GLWEKeyswitchFamily, GLWEOps, GLWESwitchingKeyExec, GLWETensorKeyExec, Infos,
+};
 
 pub trait GGSWKeySwitchFamily<B> =
     GLWEKeyswitchFamily<B> + VecZnxBigAllocBytes + VecZnxDftCopy<B> + VecZnxDftAddInplace<B> + VecZnxDftToVecZnxBigTmpA<B>;
@@ -40,7 +42,7 @@ rank,
             tsk_size,
         );
         let tmp_idft: usize = module.vec_znx_big_alloc_bytes(n, 1, tsk_size);
-        let norm: usize = module.vec_znx_normalize_tmp_bytes(module.n());
+        let norm: usize = module.vec_znx_normalize_tmp_bytes(n);
         tmp_dft_i + ((tmp_a + vmp) | (tmp_idft + norm))
     }
 
@@ -89,25 +91,72 @@ }
 }
 
 impl<DataSelf: DataMut> GGSWCiphertext<DataSelf> {
-    pub(crate) fn expand_row<DataCi: DataRef, DataTsk: DataRef, B: Backend>(
+    pub fn from_gglwe<DataA, DataTsk, B: Backend>(
         &mut self,
         module: &Module<B>,
-        row_i: usize,
-        col_j: usize,
-        ci_dft: &VecZnxDft<DataCi, B>,
+        a: &GGLWECiphertext<DataA>,
         tsk: &GLWETensorKeyExec<DataTsk, B>,
         scratch: &mut Scratch<B>,
     ) where
-        Module<B>: GGSWKeySwitchFamily<B> + VecZnxNormalizeTmpBytes,
-        Scratch<B>: TakeVecZnxDft<B> + TakeVecZnxBig<B> + ScratchAvailable,
+        DataA: DataRef,
+        DataTsk: DataRef,
+        Module<B>: GGSWKeySwitchFamily<B> + VecZnxNormalizeTmpBytes + VecZnxCopy,
+        Scratch<B>: TakeVecZnxDft<B> + TakeVecZnxBig<B> + ScratchAvailable + TakeVecZnx,
     {
-        let cols: usize = self.rank() + 1;
-
         #[cfg(debug_assertions)]
         {
-            assert_eq!(self.n(), tsk.n());
+            assert_eq!(self.rank(), a.rank());
+            assert_eq!(self.rows(), a.rows());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(a.n(), module.n());
+            assert_eq!(tsk.n(), module.n());
         }
+        (0..self.rows()).for_each(|row_i| {
+            self.at_mut(row_i, 0).copy(module, &a.at(row_i, 0));
+        });
+        self.expand_row(module, tsk, scratch);
+    }
 
+    pub fn keyswitch<DataLhs: DataRef, DataKsk: DataRef, DataTsk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        lhs: &GGSWCiphertext<DataLhs>,
+        ksk: &GLWESwitchingKeyExec<DataKsk, B>,
+        tsk: &GLWETensorKeyExec<DataTsk, B>,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GLWEKeyswitchFamily<B> + GGSWKeySwitchFamily<B> + VecZnxNormalizeTmpBytes,
+        Scratch<B>: TakeVecZnxDft<B> + TakeVecZnxBig<B> + ScratchAvailable,
+    {
+        self.keyswitch_internal(module, lhs, ksk, scratch);
+        self.expand_row(module, tsk, scratch);
+    }
+
+    pub fn keyswitch_inplace<DataKsk: DataRef, DataTsk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        ksk: &GLWESwitchingKeyExec<DataKsk, B>,
+        tsk: &GLWETensorKeyExec<DataTsk, B>,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GLWEKeyswitchFamily<B> + GGSWKeySwitchFamily<B> + VecZnxNormalizeTmpBytes,
+        Scratch<B>: TakeVecZnxDft<B> + TakeVecZnxBig<B> + ScratchAvailable,
+    {
+        unsafe {
+            let self_ptr: *mut GGSWCiphertext<DataSelf> = self as *mut GGSWCiphertext<DataSelf>;
+            self.keyswitch(module, &*self_ptr, ksk, tsk, scratch);
+        }
+    }
+
+    pub fn expand_row<DataTsk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        tsk: &GLWETensorKeyExec<DataTsk, B>,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GGSWKeySwitchFamily<B> + VecZnxNormalizeTmpBytes,
+        Scratch<B>: TakeVecZnxDft<B> + TakeVecZnxBig<B> + ScratchAvailable,
+    {
         assert!(
             scratch.available()
                 >= GGSWCiphertext::expand_row_scratch_space(
@@ -121,145 +170,124 @@ tsk.rank()
                 )
         );
 
-        // Example for rank 3:
-        //
-        // Note: M is a vector (m, Bm, B^2m, B^3m, ...), so each column is
-        // actually composed of that many rows and we focus on a specific row here
-        // implicitely given ci_dft.
-        //
-        // # Input
-        //
-        // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0    , a1    , a2    )
-        // col 1: (0, 0, 0, 0)
-        // col 2: (0, 0, 0, 0)
-        // col 3: (0, 0, 0, 0)
-        //
-        // # Output
-        //
-        // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0       , a1       , a2       )
-        // col 1: (-(b0s0 + b1s1 + b2s2)       , b0 + M[i], b1       , b2       )
-        // col 2: (-(c0s0 + c1s1 + c2s2)       , c0       , c1 + M[i], c2       )
-        // col 3: (-(d0s0 + d1s1 + d2s2)       , d0       , d1       , d2 + M[i])
-
         let n: usize = self.n();
-        let digits: usize = tsk.digits();
+        let rank: usize = self.rank();
+        let cols: usize = rank + 1;
 
-        let (mut tmp_dft_i, scratch1) = scratch.take_vec_znx_dft(n, cols, tsk.size());
-        let (mut tmp_a, scratch2) = scratch1.take_vec_znx_dft(n, 1, ci_dft.size().div_ceil(digits));
+        // Keyswitch the j-th row of the col 0
+        (0..self.rows()).for_each(|row_i| {
+            // Pre-compute DFT of (a0, a1, a2)
+            let (mut ci_dft, scratch1) = scratch.take_vec_znx_dft(n, cols, self.size());
+            (0..cols).for_each(|i| {
+                module.vec_znx_dft_from_vec_znx(1, 0, &mut ci_dft, i, &self.at(row_i, 0).data, i);
+            });
 
-        {
-            // Performs a key-switch for each combination of s[i]*s[j], i.e. for a0, a1, a2
-            //
-            // # Example for col=1
-            //
-            // a0 * (-(f0s0 + f1s1 + f1s2) + s0^2, f0, f1, f2) = (-(a0f0s0 + a0f1s1 + a0f1s2) + a0s0^2, a0f0, a0f1, a0f2)
-            // +
-            // a1 * (-(g0s0 + g1s1 + g1s2) + s0s1, g0, g1, g2) = (-(a1g0s0 + a1g1s1 + a1g1s2) + a1s0s1, a1g0, a1g1, a1g2)
-            // +
-            // a2 * (-(h0s0 + h1s1 + h1s2) + s0s2, h0, h1, h2) = (-(a2h0s0 + a2h1s1 + a2h1s2) + a2s0s2, a2h0, a2h1, a2h2)
-            // =
-            // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0, x1, x2)
-            (1..cols).for_each(|col_i| {
-                let pmat: &VmpPMat<DataTsk, B> = &tsk.at(col_i - 1, col_j - 1).key.data; // Selects Enc(s[i]s[j])
+            (1..cols).for_each(|col_j| {
+                // Example for rank 3:
+                //
+                // Note: M is a vector (m, Bm, B^2m, B^3m, ...), so each column is
+                // actually composed of that many rows and we focus on a specific row here
+                // implicitely given ci_dft.
+                //
+                // # Input
+                //
+                // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0    , a1    , a2    )
+                // col 1: (0, 0, 0, 0)
+                // col 2: (0, 0, 0, 0)
+                // col 3: (0, 0, 0, 0)
+                //
+                // # Output
+                //
+                // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0       , a1       , a2       )
+                // col 1: (-(b0s0 + b1s1 + b2s2)       , b0 + M[i], b1       , b2       )
+                // col 2: (-(c0s0 + c1s1 + c2s2)       , c0       , c1 + M[i], c2       )
+                // col 3: (-(d0s0 + d1s1 + d2s2)       , d0       , d1       , d2 + M[i])
 
-                // Extracts a[i] and multipies with Enc(s[i]s[j])
-                (0..digits).for_each(|di| {
-                    tmp_a.set_size((ci_dft.size() + di) / digits);
+                let digits: usize = tsk.digits();
 
-                    // Small optimization for digits > 2
-                    // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
-                    // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(digits-1) * B}.
-                    // As such we can ignore the last digits-2 limbs safely of the sum of vmp products.
-                    // It is possible to further ignore the last digits-1 limbs, but this introduce
-                    // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
-                    // noise is kept with respect to the ideal functionality.
-                    tmp_dft_i.set_size(tsk.size() - ((digits - di) as isize - 2).max(0) as usize);
+                let (mut tmp_dft_i, scratch2) = scratch1.take_vec_znx_dft(n, cols, tsk.size());
+                let (mut tmp_a, scratch3) = scratch2.take_vec_znx_dft(n, 1, ci_dft.size().div_ceil(digits));
 
-                    module.vec_znx_dft_copy(digits, digits - 1 - di, &mut tmp_a, 0, ci_dft, col_i);
-                    if di == 0 && col_i == 1 {
-                        module.vmp_apply(&mut tmp_dft_i, &tmp_a, pmat, scratch2);
-                    } else {
-                        module.vmp_apply_add(&mut tmp_dft_i, &tmp_a, pmat, di, scratch2);
-                    }
+                {
+                    // Performs a key-switch for each combination of s[i]*s[j], i.e. for a0, a1, a2
+                    //
+                    // # Example for col=1
+                    //
+                    // a0 * (-(f0s0 + f1s1 + f1s2) + s0^2, f0, f1, f2) = (-(a0f0s0 + a0f1s1 + a0f1s2) + a0s0^2, a0f0, a0f1, a0f2)
+                    // +
+                    // a1 * (-(g0s0 + g1s1 + g1s2) + s0s1, g0, g1, g2) = (-(a1g0s0 + a1g1s1 + a1g1s2) + a1s0s1, a1g0, a1g1, a1g2)
+                    // +
+                    // a2 * (-(h0s0 + h1s1 + h1s2) + s0s2, h0, h1, h2) = (-(a2h0s0 + a2h1s1 + a2h1s2) + a2s0s2, a2h0, a2h1, a2h2)
+                    // =
+                    // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0, x1, x2)
+                    (1..cols).for_each(|col_i| {
+                        let pmat: &VmpPMat<DataTsk, B> = &tsk.at(col_i - 1, col_j - 1).key.data; // Selects Enc(s[i]s[j])
+
+                        // Extracts a[i] and multipies with Enc(s[i]s[j])
+                        (0..digits).for_each(|di| {
+                            tmp_a.set_size((ci_dft.size() + di) / digits);
+
+                            // Small optimization for digits > 2
+                            // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
+                            // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(digits-1) * B}.
+                            // As such we can ignore the last digits-2 limbs safely of the sum of vmp products.
+                            // It is possible to further ignore the last digits-1 limbs, but this introduce
+                            // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
+                            // noise is kept with respect to the ideal functionality.
+                            tmp_dft_i.set_size(tsk.size() - ((digits - di) as isize - 2).max(0) as usize);
+
+                            module.vec_znx_dft_copy(digits, digits - 1 - di, &mut tmp_a, 0, &ci_dft, col_i);
+                            if di == 0 && col_i == 1 {
+                                module.vmp_apply(&mut tmp_dft_i, &tmp_a, pmat, scratch3);
+                            } else {
+                                module.vmp_apply_add(&mut tmp_dft_i, &tmp_a, pmat, di, scratch3);
+                            }
+                        });
+                    });
+                }
+
+                // Adds -(sum a[i] * s[i]) + m)  on the i-th column of tmp_idft_i
+                //
+                // (-(x0s0 + x1s1 + x2s2) + a0s0s0 + a1s0s1 + a2s0s2, x0, x1, x2)
+                // +
+                // (0, -(a0s0 + a1s1 + a2s2) + M[i], 0, 0)
+                // =
+                // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0 -(a0s0 + a1s1 + a2s2) + M[i], x1, x2)
+                // =
+                // (-(x0s0 + x1s1 + x2s2), x0 + M[i], x1, x2)
+                module.vec_znx_dft_add_inplace(&mut tmp_dft_i, col_j, &ci_dft, 0);
+                let (mut tmp_idft, scratch3) = scratch2.take_vec_znx_big(n, 1, tsk.size());
+                (0..cols).for_each(|i| {
+                    module.vec_znx_dft_to_vec_znx_big_tmp_a(&mut tmp_idft, 0, &mut tmp_dft_i, i);
+                    module.vec_znx_big_normalize(
+                        self.basek(),
+                        &mut self.at_mut(row_i, col_j).data,
+                        i,
+                        &tmp_idft,
+                        0,
+                        scratch3,
+                    );
                 });
-            });
-        }
-
-        // Adds -(sum a[i] * s[i]) + m)  on the i-th column of tmp_idft_i
-        //
-        // (-(x0s0 + x1s1 + x2s2) + a0s0s0 + a1s0s1 + a2s0s2, x0, x1, x2)
-        // +
-        // (0, -(a0s0 + a1s1 + a2s2) + M[i], 0, 0)
-        // =
-        // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0 -(a0s0 + a1s1 + a2s2) + M[i], x1, x2)
-        // =
-        // (-(x0s0 + x1s1 + x2s2), x0 + M[i], x1, x2)
-        module.vec_znx_dft_add_inplace(&mut tmp_dft_i, col_j, ci_dft, 0);
-        let (mut tmp_idft, scratch2) = scratch1.take_vec_znx_big(n, 1, tsk.size());
-        (0..cols).for_each(|i| {
-            module.vec_znx_dft_to_vec_znx_big_tmp_a(&mut tmp_idft, 0, &mut tmp_dft_i, i);
-            module.vec_znx_big_normalize(
-                self.basek(),
-                &mut self.at_mut(row_i, col_j).data,
-                i,
-                &tmp_idft,
-                0,
-                scratch2,
-            );
-        });
+            })
+        })
     }
 
-    pub fn keyswitch<DataLhs: DataRef, DataKsk: DataRef, DataTsk: DataRef, B: Backend>(
+    fn keyswitch_internal<DataLhs: DataRef, DataKsk: DataRef, B: Backend>(
         &mut self,
         module: &Module<B>,
         lhs: &GGSWCiphertext<DataLhs>,
         ksk: &GLWESwitchingKeyExec<DataKsk, B>,
-        tsk: &GLWETensorKeyExec<DataTsk, B>,
         scratch: &mut Scratch<B>,
     ) where
         Module<B>: GLWEKeyswitchFamily<B> + GGSWKeySwitchFamily<B> + VecZnxNormalizeTmpBytes,
         Scratch<B>: TakeVecZnxDft<B> + TakeVecZnxBig<B> + ScratchAvailable,
     {
-        let n: usize = self.n();
-        let rank: usize = self.rank();
-        let cols: usize = rank + 1;
-
         // Keyswitch the j-th row of the col 0
         (0..lhs.rows()).for_each(|row_i| {
             // Key-switch column 0, i.e.
             // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0, a1, a2) -> (-(a0s0' + a1s1' + a2s2') + M[i], a0, a1, a2)
             self.at_mut(row_i, 0)
                 .keyswitch(module, &lhs.at(row_i, 0), ksk, scratch);
-
-            // Pre-compute DFT of (a0, a1, a2)
-            let (mut ci_dft, scratch1) = scratch.take_vec_znx_dft(n, cols, self.size());
-            (0..cols).for_each(|i| {
-                module.vec_znx_dft_from_vec_znx(1, 0, &mut ci_dft, i, &self.at(row_i, 0).data, i);
-            });
-            // Generates
-            //
-            // col 1: (-(b0s0' + b1s1' + b2s2')    , b0 + M[i], b1       , b2       )
-            // col 2: (-(c0s0' + c1s1' + c2s2')    , c0       , c1 + M[i], c2       )
-            // col 3: (-(d0s0' + d1s1' + d2s2')    , d0       , d1       , d2 + M[i])
-            (1..cols).for_each(|col_j| {
-                self.expand_row(module, row_i, col_j, &ci_dft, tsk, scratch1);
-            });
         })
-    }
-
-    pub fn keyswitch_inplace<DataKsk: DataRef, DataTsk: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        ksk: &GLWESwitchingKeyExec<DataKsk, B>,
-        tsk: &GLWETensorKeyExec<DataTsk, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: GLWEKeyswitchFamily<B> + GGSWKeySwitchFamily<B> + VecZnxNormalizeTmpBytes,
-        Scratch<B>: TakeVecZnxDft<B> + TakeVecZnxBig<B> + ScratchAvailable,
-    {
-        unsafe {
-            let self_ptr: *mut GGSWCiphertext<DataSelf> = self as *mut GGSWCiphertext<DataSelf>;
-            self.keyswitch(module, &*self_ptr, ksk, tsk, scratch);
-        }
     }
 }

@@ -71,3 +71,53 @@ });
         });
     }
 }
+
+impl<D: DataRef> GGSWCiphertext<D> {
+    pub fn print_noise<B: Backend, DataSk, DataScalar>(
+        &self,
+        module: &Module<B>,
+        sk_exec: &GLWESecretExec<DataSk, B>,
+        pt_want: &ScalarZnx<DataScalar>,
+    ) where
+        DataSk: DataRef,
+        DataScalar: DataRef,
+        Module<B>: GGSWAssertNoiseFamily<B> + VecZnxAddScalarInplace + VecZnxSubABInplace + VecZnxStd,
+        B: TakeVecZnxDftImpl<B> + TakeVecZnxBigImpl<B> + ScratchOwnedAllocImpl<B> + ScratchOwnedBorrowImpl<B>,
+    {
+        let basek: usize = self.basek();
+        let k: usize = self.k();
+        let digits: usize = self.digits();
+
+        let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(self.n(), basek, k);
+        let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(self.n(), basek, k);
+        let mut pt_dft: VecZnxDft<Vec<u8>, B> = module.vec_znx_dft_alloc(self.n(), 1, self.size());
+        let mut pt_big: VecZnxBig<Vec<u8>, B> = module.vec_znx_big_alloc(self.n(), 1, self.size());
+
+        let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+            GLWECiphertext::decrypt_scratch_space(module, self.n(), basek, k) | module.vec_znx_normalize_tmp_bytes(module.n()),
+        );
+
+        (0..self.rank() + 1).for_each(|col_j| {
+            (0..self.rows()).for_each(|row_i| {
+                module.vec_znx_add_scalar_inplace(&mut pt.data, 0, (digits - 1) + row_i * digits, pt_want, 0);
+
+                // mul with sk[col_j-1]
+                if col_j > 0 {
+                    module.vec_znx_dft_from_vec_znx(1, 0, &mut pt_dft, 0, &pt.data, 0);
+                    module.svp_apply_inplace(&mut pt_dft, 0, &sk_exec.data, col_j - 1);
+                    module.vec_znx_dft_to_vec_znx_big_tmp_a(&mut pt_big, 0, &mut pt_dft, 0);
+                    module.vec_znx_big_normalize(basek, &mut pt.data, 0, &pt_big, 0, scratch.borrow());
+                }
+
+                self.at(row_i, col_j)
+                    .decrypt(module, &mut pt_have, &sk_exec, scratch.borrow());
+
+                module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt.data, 0);
+
+                let std_pt: f64 = module.vec_znx_std(basek, &pt_have.data, 0).log2();
+                println!("{}", std_pt);
+                pt.data.zero();
+            });
+        });
+    }
+}

@@ -25,3 +25,4 @@ pub use packing::*;
 pub use plaintext::*;
 pub use public_key::*;
 pub use secret::*;
+pub use trace::*;

@@ -5,10 +5,7 @@ api::{ScratchAvailable, TakeVecZnxDft, VecZnxBigAutomorphismInplace, VecZnxCopy, VecZnxRshInplace},
     layouts::{Backend, DataMut, DataRef, Module, Scratch},
 };
 
-use crate::{
-    AutomorphismKeyExec, GLWECiphertext, GLWECiphertextToMut, GLWECiphertextToRef, GLWEKeyswitchFamily, GLWEOps, Infos,
-    SetMetaData,
-};
+use crate::{AutomorphismKeyExec, GLWECiphertext, GLWECiphertextToMut, GLWEKeyswitchFamily, GLWEOps, Infos, SetMetaData};
 
 pub trait GLWETraceFamily<B: Backend> = GLWEKeyswitchFamily<B> + VecZnxCopy + VecZnxRshInplace + VecZnxBigAutomorphismInplace<B>;
 
@@ -70,7 +67,6 @@ lhs: &GLWECiphertext<DataLhs>,
         auto_keys: &HashMap<i64, AutomorphismKeyExec<DataAK, B>>,
         scratch: &mut Scratch<B>,
     ) where
-        GLWECiphertext<DataLhs>: GLWECiphertextToRef + Infos + VecZnxRshInplace,
         Module<B>: GLWETraceFamily<B>,
         Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable,
     {

@@ -1,5 +1,6 @@
 #![feature(trait_alias)]
 mod blind_rotation;
+mod circuit_bootstrapping;
 mod dist;
 mod elem;
 mod gglwe;
@@ -12,6 +13,7 @@
 use crate::dist::Distribution;
 
 pub use blind_rotation::*;
+pub use circuit_bootstrapping::*;
 pub use elem::*;
 pub use gglwe::*;
 pub use ggsw::*;