@@ -12,6 +12,12 @@ fn elwise_mul_mut(&self, a: &mut [Self::Element], b: &[Self::Element]);
     fn elwise_neg_mut(&self, a: &mut [Self::Element]);
     /// inplace mutates `a`: a = a + b*c
     fn elwise_fma_mut(&self, a: &mut [Self::Element], b: &[Self::Element], c: &[Self::Element]);
+    fn elwise_fma_scalar_mut(
+        &self,
+        a: &mut [Self::Element],
+        b: &[Self::Element],
+        c: &Self::Element,
+    );
 
     fn modulus(&self) -> Self::Element;
 }
@@ -166,6 +172,17 @@
     fn elwise_fma_mut(&self, a: &mut [Self::Element], b: &[Self::Element], c: &[Self::Element]) {
         izip!(a.iter_mut(), b.iter(), c.iter()).for_each(|(ai, bi, ci)| {
             *ai = self.add_mod_fast(*ai, self.mul_mod_fast(*bi, *ci));
+        });
+    }
+
+    fn elwise_fma_scalar_mut(
+        &self,
+        a: &mut [Self::Element],
+        b: &[Self::Element],
+        c: &Self::Element,
+    ) {
+        izip!(a.iter_mut(), b.iter()).for_each(|(ai, bi)| {
+            *ai = self.add_mod_fast(*ai, self.mul_mod_fast(*bi, *c));
         });
     }
 

@@ -0,0 +1,360 @@
+use std::collections::HashMap;
+
+use num_traits::{FromPrimitive, One, PrimInt, ToPrimitive, Zero};
+
+use crate::{
+    backend::{ArithmeticOps, VectorOps},
+    decomposer::Decomposer,
+    lwe::lwe_key_switch,
+    ntt::Ntt,
+    rgsw::{galois_auto, rlwe_by_rgsw, IsTrivial},
+    Matrix, MatrixEntity, MatrixMut, Row, RowMut,
+};
+
+struct BoolEvaluator {}
+
+impl BoolEvaluator {}
+
+trait PbsKey {
+    type M: Matrix;
+
+    fn rgsw_ct_secret_el(&self, si: usize) -> &Self::M;
+    fn galois_key_for_auto(&self, k: isize) -> &Self::M;
+    fn auto_map_index(&self, k: isize) -> &[usize];
+    fn auto_map_sign(&self, k: isize) -> &[bool];
+}
+
+/// LMKCY+ Blind rotation
+///
+/// gk_to_si: [-g^0, -g^1, .., -g^{q/2-1}, g^0, ..., g^{q/2-1}]
+fn blind_rotation<
+    MT: IsTrivial + MatrixMut,
+    Mmut: MatrixMut<MatElement = MT::MatElement> + Matrix,
+    D: Decomposer<Element = MT::MatElement>,
+    NttOp: Ntt<Element = MT::MatElement>,
+    ModOp: ArithmeticOps<Element = MT::MatElement> + VectorOps<Element = MT::MatElement>,
+    K: PbsKey<M = Mmut>,
+>(
+    trivial_rlwe_test_poly: &mut MT,
+    scratch_matrix_dplus2_ring: &mut Mmut,
+    g: isize,
+    w: usize,
+    q: usize,
+    gk_to_si: &[Vec<usize>],
+    decomposer: &D,
+    ntt_op: &NttOp,
+    mod_op: &ModOp,
+    pbs_key: &K,
+) where
+    <Mmut as Matrix>::R: RowMut,
+    Mmut::MatElement: Copy + Zero,
+    <MT as Matrix>::R: RowMut,
+{
+    let q_by_2 = q / 2;
+
+    // -(g^k)
+    for i in 1..q_by_2 {
+        gk_to_si[q_by_2 + i].iter().for_each(|s_index| {
+            rlwe_by_rgsw(
+                trivial_rlwe_test_poly,
+                pbs_key.rgsw_ct_secret_el(*s_index),
+                scratch_matrix_dplus2_ring,
+                decomposer,
+                ntt_op,
+                mod_op,
+            );
+        });
+
+        galois_auto(
+            trivial_rlwe_test_poly,
+            pbs_key.galois_key_for_auto(g),
+            scratch_matrix_dplus2_ring,
+            pbs_key.auto_map_index(g),
+            pbs_key.auto_map_sign(g),
+            mod_op,
+            ntt_op,
+            decomposer,
+        );
+    }
+
+    // -(g^0)
+    gk_to_si[q_by_2].iter().for_each(|s_index| {
+        rlwe_by_rgsw(
+            trivial_rlwe_test_poly,
+            pbs_key.rgsw_ct_secret_el(*s_index),
+            scratch_matrix_dplus2_ring,
+            decomposer,
+            ntt_op,
+            mod_op,
+        );
+    });
+    galois_auto(
+        trivial_rlwe_test_poly,
+        pbs_key.galois_key_for_auto(-g),
+        scratch_matrix_dplus2_ring,
+        pbs_key.auto_map_index(-g),
+        pbs_key.auto_map_sign(-g),
+        mod_op,
+        ntt_op,
+        decomposer,
+    );
+
+    // +(g^k)
+    for i in 1..q_by_2 {
+        gk_to_si[i].iter().for_each(|s_index| {
+            rlwe_by_rgsw(
+                trivial_rlwe_test_poly,
+                pbs_key.rgsw_ct_secret_el(*s_index),
+                scratch_matrix_dplus2_ring,
+                decomposer,
+                ntt_op,
+                mod_op,
+            );
+        });
+
+        galois_auto(
+            trivial_rlwe_test_poly,
+            pbs_key.galois_key_for_auto(g),
+            scratch_matrix_dplus2_ring,
+            pbs_key.auto_map_index(g),
+            pbs_key.auto_map_sign(g),
+            mod_op,
+            ntt_op,
+            decomposer,
+        );
+    }
+
+    // +(g^0)
+    gk_to_si[0].iter().for_each(|s_index| {
+        rlwe_by_rgsw(
+            trivial_rlwe_test_poly,
+            pbs_key.rgsw_ct_secret_el(gk_to_si[q_by_2][*s_index]),
+            scratch_matrix_dplus2_ring,
+            decomposer,
+            ntt_op,
+            mod_op,
+        );
+    });
+}
+
+trait Parameters {
+    type Element;
+    type D: Decomposer<Element = Self::Element>;
+    fn rlwe_q(&self) -> Self::Element;
+    fn lwe_q(&self) -> Self::Element;
+    fn br_q(&self) -> usize;
+    fn d_rgsw(&self) -> usize;
+    fn d_lwe(&self) -> usize;
+    fn rlwe_n(&self) -> usize;
+    fn lwe_n(&self) -> usize;
+    // Embedding fator for ring X^{q}+1 inside
+    fn embedding_factor(&self) -> usize;
+    // generator g
+    fn g(&self) -> isize;
+    fn decomoposer_lwe(&self) -> &Self::D;
+    fn decomoposer_rlwe(&self) -> &Self::D;
+    /// Maps a \in Z^*_{2q} to discrete log k, with generator g (i.e. g^k =
+    /// a). Returned vector is of size q that stores dlog of a at `vec[a]`.
+    /// For any a, k is s.t. a = g^{k}, then k is expressed as k. If k is s.t a
+    /// = -g^{k/2}, then k is expressed as k=k+q/2
+    fn g_k_dlog_map(&self) -> &[usize];
+}
+
+/// - Mod down
+/// - key switching
+/// - mod down
+/// - blind rotate
+fn pbs<
+    M: Matrix + MatrixMut + MatrixEntity,
+    MT: MatrixMut<MatElement = M::MatElement, R = M::R> + IsTrivial + MatrixEntity,
+    P: Parameters<Element = M::MatElement>,
+    NttOp: Ntt<Element = M::MatElement>,
+    ModOp: ArithmeticOps<Element = M::MatElement> + VectorOps<Element = M::MatElement>,
+    K: PbsKey<M = M>,
+>(
+    parameters: &P,
+    test_vec: &M::R,
+    lwe_in: &mut M::R,
+    lwe_ksk: &M,
+    scratch_lwen_plus1: &mut M::R,
+    scratch_matrix_dplus2_ring: &mut M,
+    modop_lweq: &ModOp,
+    modop_rlweq: &ModOp,
+    nttop_rlweq: &NttOp,
+    pbs_key: K,
+) where
+    <M as Matrix>::R: RowMut,
+    <MT as Matrix>::R: RowMut,
+    M::MatElement: PrimInt + ToPrimitive + FromPrimitive + One + Copy + Zero,
+{
+    let rlwe_q = parameters.rlwe_q();
+    let lwe_q = parameters.lwe_q();
+    let br_q = parameters.br_q();
+    let rlwe_qf64 = rlwe_q.to_f64().unwrap();
+    let lwe_qf64 = lwe_q.to_f64().unwrap();
+    let br_qf64 = br_q.to_f64().unwrap();
+    let rlwe_n = parameters.rlwe_n();
+
+    // moddown Q -> Q_ks
+    lwe_in.as_mut().iter_mut().for_each(|v| {
+        *v =
+            M::MatElement::from_f64(((v.to_f64().unwrap() * lwe_qf64) / rlwe_qf64).round()).unwrap()
+    });
+
+    // key switch
+    // let mut lwe_out = M::zeros(1, parameters.lwe_n() + 1);
+    scratch_lwen_plus1.as_mut().fill(M::MatElement::zero());
+    lwe_key_switch(
+        scratch_lwen_plus1,
+        lwe_in,
+        lwe_ksk,
+        modop_lweq,
+        parameters.decomoposer_lwe(),
+    );
+
+    // odd mowdown Q_ks -> q
+    let g_k_dlog_map = parameters.g_k_dlog_map();
+    let mut g_k_si = vec![vec![]; br_q];
+    scratch_lwen_plus1
+        .as_ref()
+        .iter()
+        .skip(1)
+        .enumerate()
+        .for_each(|(index, v)| {
+            let odd_v = mod_switch_odd(v.to_f64().unwrap(), lwe_qf64, br_qf64);
+            let k = g_k_dlog_map[odd_v];
+            g_k_si[k].push(index);
+        });
+
+    // handle b and set trivial test RLWE
+    let g = parameters.g() as usize;
+    let g_times_b = (g * mod_switch_odd(
+        scratch_lwen_plus1.as_ref()[0].to_f64().unwrap(),
+        lwe_qf64,
+        br_qf64,
+    )) % (br_q);
+    // v = (v(X) * X^{g*b}) mod X^{q/2}+1
+    let br_qby2 = br_q / 2;
+    let mut gb_monomial_sign = true;
+    let mut gb_monomial_exp = g_times_b;
+    // X^{g*b} mod X^{q}+1
+    if gb_monomial_exp > br_qby2 {
+        gb_monomial_exp -= br_qby2;
+        gb_monomial_sign = false
+    }
+    // monomial mul
+    let mut trivial_rlwe_test_poly = MT::zeros(2, rlwe_n);
+    if parameters.embedding_factor() == 1 {
+        monomial_mul(
+            test_vec.as_ref(),
+            trivial_rlwe_test_poly.get_row_mut(1).as_mut(),
+            gb_monomial_exp,
+            gb_monomial_sign,
+            br_q,
+            modop_rlweq,
+        );
+    } else {
+        // use lwe_in to store the `t = v(X) * X^{g*2} mod X^{q/2}+1` temporarily. This
+        // works because q/2 < N (where N is lwe_in LWE dimension) always.
+        monomial_mul(
+            test_vec.as_ref(),
+            &mut lwe_in.as_mut()[..br_qby2],
+            gb_monomial_exp,
+            gb_monomial_sign,
+            br_q,
+            modop_rlweq,
+        );
+
+        // emebed poly `t` in ring X^{q/2}+1 inside the bigger ring X^{N}+1
+        let partb_trivial_rlwe = trivial_rlwe_test_poly.get_row_mut(1);
+        lwe_in.as_ref()[..br_qby2]
+            .iter()
+            .enumerate()
+            .for_each(|(index, v)| {
+                partb_trivial_rlwe[2 * index] = *v;
+            });
+    }
+    // TODO Rotate test input
+
+    // blind rotate
+    blind_rotation(
+        &mut trivial_rlwe_test_poly,
+        scratch_matrix_dplus2_ring,
+        parameters.g(),
+        1,
+        br_q,
+        &g_k_si,
+        parameters.decomoposer_rlwe(),
+        nttop_rlweq,
+        modop_rlweq,
+        &pbs_key,
+    );
+
+    // sample extract
+    sample_extract(lwe_in, &trivial_rlwe_test_poly, modop_rlweq, 0);
+}
+
+fn mod_switch_odd(v: f64, from_q: f64, to_q: f64) -> usize {
+    let odd_v = (((v.to_f64().unwrap() * to_q) / (from_q)).floor())
+        .to_usize()
+        .unwrap();
+    //TODO(Jay): check correctness of this
+    odd_v + (odd_v ^ (usize::one()))
+}
+
+fn sample_extract<M: Matrix + MatrixMut, ModOp: ArithmeticOps<Element = M::MatElement>>(
+    lwe_out: &mut M::R,
+    rlwe_in: &M,
+    mod_op: &ModOp,
+    index: usize,
+) where
+    <M as Matrix>::R: RowMut,
+    M::MatElement: Copy,
+{
+    let ring_size = rlwe_in.dimension().1;
+
+    // index..=0
+    let to = &mut lwe_out.as_mut()[1..];
+    let from = rlwe_in.get_row_slice(0);
+    for i in 0..index + 1 {
+        to[i] = from[index - i];
+    }
+
+    // -(N..index)
+    for i in index + 1..ring_size {
+        to[i] = mod_op.neg(&from[ring_size + index - i]);
+    }
+
+    // set b
+    lwe_out.as_mut()[0] = *rlwe_in.get(1, index);
+}
+
+fn monomial_mul<El, ModOp: ArithmeticOps<Element = El>>(
+    p_in: &[El],
+    p_out: &mut [El],
+    mon_exp: usize,
+    mon_sign: bool,
+    ring_size: usize,
+    mod_op: &ModOp,
+) where
+    El: Copy,
+{
+    debug_assert!(p_in.as_ref().len() == ring_size);
+    debug_assert!(p_in.as_ref().len() == p_out.as_ref().len());
+    debug_assert!(mon_exp < ring_size);
+
+    p_in.as_ref().iter().enumerate().for_each(|(index, v)| {
+        let mut to_index = index + mon_exp;
+        let mut to_sign = mon_sign;
+        if to_index >= ring_size {
+            to_index = to_index - ring_size;
+            to_sign = !to_sign;
+        }
+
+        if !to_sign {
+            p_out.as_mut()[to_index] = mod_op.neg(v);
+        } else {
+            p_out.as_mut()[to_index] = *v;
+        }
+    });
+}

@@ -6,6 +6,7 @@ use random::{RandomGaussianDist, RandomUniformDist};
 use utils::TryConvertFrom;
 
 mod backend;
+mod bool;
 mod decomposer;
 mod lwe;
 mod ntt;
@@ -34,6 +35,10 @@
     fn get(&self, row_idx: usize, column_idx: usize) -> &Self::MatElement {
         &self.as_ref()[row_idx].as_ref()[column_idx]
     }
+
+    fn split_at_row(&self, idx: usize) -> (&[<Self as Matrix>::R], &[<Self as Matrix>::R]) {
+        self.as_ref().split_at(idx)
+    }
 }
 
 pub trait MatrixMut: Matrix + AsMut<[<Self as Matrix>::R]>
@@ -52,7 +57,7 @@ fn set(&mut self, row_idx: usize, column_idx: usize, val: <Self as Matrix>::MatElement) {
         self.as_mut()[row_idx].as_mut()[column_idx] = val;
     }
 
-    fn split_at_row(
+    fn split_at_row_mut(
         &mut self,
         idx: usize,
     ) -> (&mut [<Self as Matrix>::R], &mut [<Self as Matrix>::R]) {
@@ -86,7 +91,26 @@ (self.len(), self[0].len())
     }
 }
 
+impl<T> Matrix for &[Vec<T>] {
+    type MatElement = T;
+    type R = Vec<T>;
+
+    fn dimension(&self) -> (usize, usize) {
+        (self.len(), self[0].len())
+    }
+}
+
+impl<T> Matrix for &mut [Vec<T>] {
+    type MatElement = T;
+    type R = Vec<T>;
+
+    fn dimension(&self) -> (usize, usize) {
+        (self.len(), self[0].len())
+    }
+}
+
 impl<T> MatrixMut for Vec<Vec<T>> {}
+impl<T> MatrixMut for &mut [Vec<T>] {}
 
 impl<T: Zero + Clone> MatrixEntity for Vec<Vec<T>> {
     fn zeros(row: usize, col: usize) -> Self {

@@ -43,36 +43,32 @@ })
     }
 }
 
-fn lwe_key_switch<
+pub(crate) fn lwe_key_switch<
     M: Matrix,
-    Mmut: MatrixMut<MatElement = M::MatElement> + MatrixEntity,
+    Ro: AsMut<[M::MatElement]> + AsRef<[M::MatElement]>,
     Op: VectorOps<Element = M::MatElement> + ArithmeticOps<Element = M::MatElement>,
     D: Decomposer<Element = M::MatElement>,
 >(
-    lwe_out: &mut Mmut,
-    lwe_in: &M,
+    lwe_out: &mut Ro,
+    lwe_in: &Ro,
     lwe_ksk: &M,
     operator: &Op,
     decomposer: &D,
-) where
-    <Mmut as Matrix>::R: RowMut,
-{
-    assert!(lwe_ksk.dimension().0 == ((lwe_in.dimension().1 - 1) * decomposer.d()));
-    assert!(lwe_out.dimension() == (1, lwe_ksk.dimension().1));
-
-    let mut scratch_space = Mmut::zeros(1, lwe_out.dimension().1);
+) {
+    assert!(lwe_ksk.dimension().0 == ((lwe_in.as_ref().len() - 1) * decomposer.d()));
+    assert!(lwe_out.as_ref().len() == lwe_ksk.dimension().1);
 
     let lwe_in_a_decomposed = lwe_in
-        .get_row(0)
+        .as_ref()
+        .iter()
         .skip(1)
         .flat_map(|ai| decomposer.decompose(ai));
     izip!(lwe_in_a_decomposed, lwe_ksk.iter_rows()).for_each(|(ai_j, beta_ij_lwe)| {
-        operator.elwise_scalar_mul(scratch_space.get_row_mut(0), beta_ij_lwe.as_ref(), &ai_j);
-        operator.elwise_add_mut(lwe_out.get_row_mut(0), scratch_space.get_row_slice(0))
+        operator.elwise_fma_scalar_mut(lwe_out.as_mut(), beta_ij_lwe.as_ref(), &ai_j);
     });
 
-    let out_b = operator.add(lwe_out.get(0, 0), lwe_in.get(0, 0));
-    lwe_out.set(0, 0, out_b);
+    let out_b = operator.add(&lwe_out.as_ref()[0], &lwe_in.as_ref()[0]);
+    lwe_out.as_mut()[0] = out_b;
 }
 
 fn lwe_ksk_keygen<
@@ -82,34 +78,34 @@ Op: VectorOps<Element = Mmut::MatElement> + ArithmeticOps<Element = Mmut::MatElement>,
     R: RandomGaussianDist<Mmut::MatElement, Parameters = Mmut::MatElement>
         + RandomUniformDist<[Mmut::MatElement], Parameters = Mmut::MatElement>,
 >(
-    lwe_sk_in: &S,
-    lwe_sk_out: &S,
+    from_lwe_sk: &S,
+    to_lwe_sk: &S,
     ksk_out: &mut Mmut,
     gadget: &[Mmut::MatElement],
     operator: &Op,
     rng: &mut R,
 ) where
     <Mmut as Matrix>::R: RowMut,
-    Mmut: TryConvertFrom<[S::Element], Parameters = Mmut::MatElement>,
+    Mmut::R: TryConvertFrom<[S::Element], Parameters = Mmut::MatElement>,
     Mmut::MatElement: Zero + Debug,
 {
     assert!(
         ksk_out.dimension()
             == (
-                lwe_sk_in.values().len() * gadget.len(),
-                lwe_sk_out.values().len() + 1,
+                from_lwe_sk.values().len() * gadget.len(),
+                to_lwe_sk.values().len() + 1,
             )
     );
 
     let d = gadget.len();
 
     let modulus = VectorOps::modulus(operator);
-    let mut neg_sk_in_m = Mmut::try_convert_from(lwe_sk_in.values(), &modulus);
-    operator.elwise_neg_mut(neg_sk_in_m.get_row_mut(0));
-    let sk_out_m = Mmut::try_convert_from(lwe_sk_out.values(), &modulus);
+    let mut neg_sk_in_m = Mmut::R::try_convert_from(from_lwe_sk.values(), &modulus);
+    operator.elwise_neg_mut(neg_sk_in_m.as_mut());
+    let sk_out_m = Mmut::R::try_convert_from(to_lwe_sk.values(), &modulus);
 
     izip!(
-        neg_sk_in_m.get_row(0),
+        neg_sk_in_m.as_ref(),
         ksk_out.iter_rows_mut().chunks(d).into_iter()
     )
     .for_each(|(neg_sk_in_si, d_ks_lwes)| {
@@ -119,7 +115,7 @@ RandomUniformDist::random_fill(rng, &modulus, &mut lwe.as_mut()[1..]);
 
             // a * z
             let mut az = Mmut::MatElement::zero();
-            izip!(lwe.as_ref()[1..].iter(), sk_out_m.get_row(0)).for_each(|(ai, si)| {
+            izip!(lwe.as_ref()[1..].iter(), sk_out_m.as_ref()).for_each(|(ai, si)| {
                 let ai_si = operator.mul(ai, si);
                 az = operator.add(&az, &ai_si);
             });
@@ -139,59 +135,57 @@ }
 
 /// Encrypts encoded message m as LWE ciphertext
 fn encrypt_lwe<
-    Mmut: MatrixMut + MatrixEntity,
-    R: RandomGaussianDist<Mmut::MatElement, Parameters = Mmut::MatElement>
-        + RandomUniformDist<[Mmut::MatElement], Parameters = Mmut::MatElement>,
+    Ro: Row + RowMut,
+    R: RandomGaussianDist<Ro::Element, Parameters = Ro::Element>
+        + RandomUniformDist<[Ro::Element], Parameters = Ro::Element>,
     S: Secret,
-    Op: ArithmeticOps<Element = Mmut::MatElement>,
+    Op: ArithmeticOps<Element = Ro::Element>,
 >(
-    lwe_out: &mut Mmut,
-    m: Mmut::MatElement,
+    lwe_out: &mut Ro,
+    m: &Ro::Element,
     s: &S,
     operator: &Op,
     rng: &mut R,
 ) where
-    Mmut: TryConvertFrom<[S::Element], Parameters = Mmut::MatElement>,
-    Mmut::MatElement: Zero,
-    <Mmut as Matrix>::R: RowMut,
+    Ro: TryConvertFrom<[S::Element], Parameters = Ro::Element>,
+    Ro::Element: Zero,
 {
-    let s = Mmut::try_convert_from(s.values(), &operator.modulus());
-    assert!(s.dimension().0 == (lwe_out.dimension().0));
-    assert!(s.dimension().1 == (lwe_out.dimension().1 - 1));
+    let s = Ro::try_convert_from(s.values(), &operator.modulus());
+    assert!(s.as_ref().len() == (lwe_out.as_ref().len() - 1));
 
     // a*s
-    RandomUniformDist::random_fill(rng, &operator.modulus(), &mut lwe_out.get_row_mut(0)[1..]);
-    let mut sa = Mmut::MatElement::zero();
-    izip!(lwe_out.get_row(0).skip(1), s.get_row(0)).for_each(|(ai, si)| {
+    RandomUniformDist::random_fill(rng, &operator.modulus(), &mut lwe_out.as_mut()[1..]);
+    let mut sa = Ro::Element::zero();
+    izip!(lwe_out.as_mut().iter().skip(1), s.as_ref()).for_each(|(ai, si)| {
         let tmp = operator.mul(ai, si);
         sa = operator.add(&tmp, &sa);
     });
 
     // b = a*s + e + m
-    let mut e = Mmut::MatElement::zero();
+    let mut e = Ro::Element::zero();
     RandomGaussianDist::random_fill(rng, &operator.modulus(), &mut e);
-    let b = operator.add(&operator.add(&sa, &e), &m);
-    lwe_out.set(0, 0, b);
+    let b = operator.add(&operator.add(&sa, &e), m);
+    lwe_out.as_mut()[0] = b;
 }
 
-fn decrypt_lwe<M: Matrix, Op: ArithmeticOps<Element = M::MatElement>, S: Secret>(
-    lwe_ct: &M,
+fn decrypt_lwe<Ro: Row, Op: ArithmeticOps<Element = Ro::Element>, S: Secret>(
+    lwe_ct: &Ro,
     s: &S,
     operator: &Op,
-) -> M::MatElement
+) -> Ro::Element
 where
-    M: TryConvertFrom<[S::Element], Parameters = M::MatElement>,
-    M::MatElement: Zero,
+    Ro: TryConvertFrom<[S::Element], Parameters = Ro::Element>,
+    Ro::Element: Zero,
 {
-    let s = M::try_convert_from(s.values(), &operator.modulus());
+    let s = Ro::try_convert_from(s.values(), &operator.modulus());
 
-    let mut sa = M::MatElement::zero();
-    izip!(lwe_ct.get_row(0).skip(1), s.get_row(0)).for_each(|(ai, si)| {
+    let mut sa = Ro::Element::zero();
+    izip!(lwe_ct.as_ref().iter().skip(1), s.as_ref()).for_each(|(ai, si)| {
         let tmp = operator.mul(ai, si);
         sa = operator.add(&tmp, &sa);
     });
 
-    let b = &lwe_ct.get_row_slice(0)[0];
+    let b = &lwe_ct.as_ref()[0];
     operator.sub(b, &sa)
 }
 
@@ -222,8 +216,8 @@
         // encrypt
         for m in 0..1u64 << logp {
             let encoded_m = m << (logq - logp);
-            let mut lwe_ct = vec![vec![0u64; lwe_n + 1]];
-            encrypt_lwe(&mut lwe_ct, encoded_m, &lwe_sk, &modq_op, &mut rng);
+            let mut lwe_ct = vec![0u64; lwe_n + 1];
+            encrypt_lwe(&mut lwe_ct, &encoded_m, &lwe_sk, &modq_op, &mut rng);
             let encoded_m_back = decrypt_lwe(&lwe_ct, &lwe_sk, &modq_op);
             let m_back = ((((encoded_m_back as f64) * ((1 << logp) as f64)) / q as f64).round()
                 as u64)
@@ -265,12 +259,12 @@
             for m in 0..(1 << logp) {
                 // encrypt using lwe_sk_in
                 let encoded_m = m << (logq - logp);
-                let mut lwe_in_ct = vec![vec![0u64; lwe_in_n + 1]];
-                encrypt_lwe(&mut lwe_in_ct, encoded_m, &lwe_sk_in, &modq_op, &mut rng);
+                let mut lwe_in_ct = vec![0u64; lwe_in_n + 1];
+                encrypt_lwe(&mut lwe_in_ct, &encoded_m, &lwe_sk_in, &modq_op, &mut rng);
 
                 // key switch from lwe_sk_in to lwe_sk_out
                 let decomposer = DefaultDecomposer::new(1u64 << logq, logb, d_ks);
-                let mut lwe_out_ct = vec![vec![0u64; lwe_out_n + 1]];
+                let mut lwe_out_ct = vec![0u64; lwe_out_n + 1];
                 lwe_key_switch(&mut lwe_out_ct, &lwe_in_ct, &ksk, &modq_op, &decomposer);
 
                 // decrypt lwe_out_ct using lwe_sk_out

@@ -1,10 +1,11 @@
 use std::{
+    clone,
     fmt::Debug,
     ops::{Neg, Sub},
 };
 
 use itertools::{izip, Itertools};
-use num_traits::{PrimInt, ToPrimitive};
+use num_traits::{PrimInt, ToPrimitive, Zero};
 
 use crate::{
     backend::{ArithmeticOps, VectorOps},
@@ -15,6 +16,48 @@ utils::{fill_random_ternary_secret_with_hamming_weight, TryConvertFrom, WithLocal},
     Matrix, MatrixEntity, MatrixMut, RowMut, Secret,
 };
 
+struct RlweCiphertext<M>(M, bool);
+
+impl<M: Matrix> Matrix for RlweCiphertext<M> {
+    type MatElement = M::MatElement;
+    type R = M::R;
+
+    fn dimension(&self) -> (usize, usize) {
+        self.0.dimension()
+    }
+}
+
+impl<M: MatrixMut> MatrixMut for RlweCiphertext<M> where <M as Matrix>::R: RowMut {}
+
+impl<M: Matrix> AsRef<[<M as Matrix>::R]> for RlweCiphertext<M> {
+    fn as_ref(&self) -> &[<M as Matrix>::R] {
+        self.0.as_ref()
+    }
+}
+
+impl<M: MatrixMut> AsMut<[<M as Matrix>::R]> for RlweCiphertext<M>
+where
+    <M as Matrix>::R: RowMut,
+{
+    fn as_mut(&mut self) -> &mut [<M as Matrix>::R] {
+        self.0.as_mut()
+    }
+}
+
+impl<M> IsTrivial for RlweCiphertext<M> {
+    fn is_trivial(&self) -> bool {
+        self.1
+    }
+    fn set_not_trivial(&mut self) {
+        self.1 = false;
+    }
+}
+
+pub trait IsTrivial {
+    fn is_trivial(&self) -> bool;
+    fn set_not_trivial(&mut self);
+}
+
 struct RlweSecret {
     values: Vec<i32>,
 }
@@ -70,7 +113,7 @@ ///   ciphertexts as [RLWE'_A(-from_s) || RLWE'_B(-from_s)]
 /// - neg_from_s_eval: Negative of secret polynomial to key switch from in
 ///   evaluation domain
 /// - to_s_eval: secret polynomial to key switch to in evalution domain.
-fn rlwe_ksk_gen<
+pub(crate) fn rlwe_ksk_gen<
     Mmut: MatrixMut + MatrixEntity,
     ModOp: ArithmeticOps<Element = Mmut::MatElement> + VectorOps<Element = Mmut::MatElement>,
     NttOp: Ntt<Element = Mmut::MatElement>,
@@ -98,7 +141,7 @@
     let mut scratch_space = Mmut::zeros(1, ring_size);
 
     // RLWE'_{to_s}(-from_s)
-    let (part_a, part_b) = ksk_out.split_at_row(d);
+    let (part_a, part_b) = ksk_out.split_at_row_mut(d);
     izip!(part_a.iter_mut(), part_b.iter_mut(), gadget_vector.iter()).for_each(
         |(ai, bi, beta_i)| {
             // sample ai and transform to evaluation
@@ -130,7 +173,7 @@ },
     );
 }
 
-fn galois_key_gen<
+pub(crate) fn galois_key_gen<
     Mmut: MatrixMut + MatrixEntity,
     ModOp: ArithmeticOps<Element = Mmut::MatElement> + VectorOps<Element = Mmut::MatElement>,
     NttOp: Ntt<Element = Mmut::MatElement>,
@@ -179,17 +222,16 @@ rlwe_ksk_gen(ksk_out, &neg_s_auto, &s, gadget_vector, mod_op, ntt_op, rng);
 }
 
 /// Sends RLWE_{s}(X) -> RLWE_{s}(X^k) where k is some galois element
-fn galois_auto<
-    M: Matrix,
-    Mmut: MatrixMut<MatElement = M::MatElement>,
-    ModOp: ArithmeticOps<Element = M::MatElement> + VectorOps<Element = M::MatElement>,
-    NttOp: Ntt<Element = M::MatElement>,
-    D: Decomposer<Element = M::MatElement>,
+pub(crate) fn galois_auto<
+    MT: Matrix + IsTrivial + MatrixMut,
+    Mmut: MatrixMut<MatElement = MT::MatElement>,
+    ModOp: ArithmeticOps<Element = MT::MatElement> + VectorOps<Element = MT::MatElement>,
+    NttOp: Ntt<Element = MT::MatElement>,
+    D: Decomposer<Element = MT::MatElement>,
 >(
-    rlwe_in: &M,
-    ksk: &M,
-    rlwe_out: &mut Mmut,
-    a_rlwe_decomposed: &mut Mmut,
+    rlwe_in: &mut MT,
+    ksk: &Mmut,
+    scratch_matrix_dplus2_ring: &mut Mmut,
     auto_map_index: &[usize],
     auto_map_sign: &[bool],
     mod_op: &ModOp,
@@ -197,10 +239,13 @@ ntt_op: &NttOp,
     decomposer: &D,
 ) where
     <Mmut as Matrix>::R: RowMut,
-    M::MatElement: Copy,
+    <MT as Matrix>::R: RowMut,
+    MT::MatElement: Copy + Zero,
 {
     let d = decomposer.d();
 
+    let (scratch_matrix_d_ring, tmp_rlwe_out) = scratch_matrix_dplus2_ring.split_at_row_mut(d);
+
     // send b(X) -> b(X^k)
     izip!(
         rlwe_in.get_row(1),
@@ -209,45 +254,69 @@ auto_map_sign.iter()
     )
     .for_each(|(el_in, to_index, sign)| {
         if !*sign {
-            rlwe_out.set(1, *to_index, mod_op.neg(el_in));
+            tmp_rlwe_out[1].as_mut()[*to_index] = mod_op.neg(el_in);
         } else {
-            rlwe_out.set(1, *to_index, *el_in);
+            tmp_rlwe_out[1].as_mut()[*to_index] = *el_in;
+            // scratch_matrix_dplus2_ring.set(d + 1, *to_index, *el_in);
         }
     });
 
-    // send a(X) -> a(X^k) and decompose a(X^k)
-    izip!(
-        rlwe_in.get_row(0),
-        auto_map_index.iter(),
-        auto_map_sign.iter()
-    )
-    .for_each(|(el_in, to_index, sign)| {
-        let el_out = if !*sign { mod_op.neg(el_in) } else { *el_in };
+    if !rlwe_in.is_trivial() {
+        // send a(X) -> a(X^k) and decompose a(X^k)
+        izip!(
+            rlwe_in.get_row(0),
+            auto_map_index.iter(),
+            auto_map_sign.iter()
+        )
+        .for_each(|(el_in, to_index, sign)| {
+            let el_out = if !*sign { mod_op.neg(el_in) } else { *el_in };
+
+            let el_out_decomposed = decomposer.decompose(&el_out);
+            for j in 0..d {
+                scratch_matrix_d_ring[j].as_mut()[*to_index] = el_out_decomposed[j];
+            }
+        });
+
+        // transform decomposed a(X^k) to evaluation domain
+        scratch_matrix_d_ring.iter_mut().for_each(|r| {
+            ntt_op.forward(r.as_mut());
+        });
 
-        let el_out_decomposed = decomposer.decompose(&el_out);
-        for j in 0..d {
-            a_rlwe_decomposed.set(j, *to_index, el_out_decomposed[j]);
-        }
-    });
+        // RLWE(m^k) = a', b'; RLWE(m) = a, b
+        // key switch: (a * RLWE'(s(X^k)))
+        let (ksk_a, ksk_b) = ksk.split_at_row(d);
+        tmp_rlwe_out[0].as_mut().fill(Mmut::MatElement::zero());
+        // a' = decomp<a> * RLWE'_A(s(X^k))
+        routine::<Mmut, ModOp>(
+            tmp_rlwe_out[0].as_mut(),
+            scratch_matrix_d_ring,
+            ksk_a,
+            mod_op,
+        );
+        // send b(X^k) to evaluation domain
+        ntt_op.forward(tmp_rlwe_out[1].as_mut());
+        // b' = b(X^k)
+        // b' += decomp<a(X^k)> * RLWE'_B(s(X^k))
+        routine::<Mmut, ModOp>(
+            tmp_rlwe_out[1].as_mut(),
+            scratch_matrix_d_ring,
+            ksk_b,
+            mod_op,
+        );
 
-    // transform decomposed a(X^k) to evaluation domain
-    a_rlwe_decomposed.iter_rows_mut().for_each(|r| {
-        ntt_op.forward(r.as_mut());
-    });
+        // transform RLWE(m^k) to coefficient domain
+        tmp_rlwe_out
+            .iter_mut()
+            .for_each(|r| ntt_op.backward(r.as_mut()));
 
-    // key switch (a(X^k) * RLWE'(s(X^k)))
-    izip!(a_rlwe_decomposed.iter_rows(), ksk.iter_rows().take(d)).for_each(|(a, b)| {
-        mod_op.elwise_fma_mut(rlwe_out.get_row_mut(0), a.as_ref(), b.as_ref());
-    });
-    ntt_op.forward(rlwe_out.get_row_mut(1));
-    izip!(a_rlwe_decomposed.iter_rows(), ksk.iter_rows().skip(d)).for_each(|(a, b)| {
-        mod_op.elwise_fma_mut(rlwe_out.get_row_mut(1), a.as_ref(), b.as_ref());
-    });
+        rlwe_in
+            .get_row_mut(0)
+            .copy_from_slice(tmp_rlwe_out[0].as_ref());
+    }
 
-    // transform RLWE(-s(X^k) * a(X^k)) to coefficient domain
-    rlwe_out
-        .iter_rows_mut()
-        .for_each(|r| ntt_op.backward(r.as_mut()));
+    rlwe_in
+        .get_row_mut(1)
+        .copy_from_slice(tmp_rlwe_out[1].as_ref());
 }
 
 /// Encrypts message m as a RGSW ciphertext.
@@ -256,7 +325,7 @@ /// - m_eval: is `m` is evaluation domain
 /// - out_rgsw: RGSW(m) is stored as single matrix of dimension (d_rgsw * 4,
 ///   ring_size). The matrix has the following structure [RLWE'_A(-sm) ||
 ///   RLWE'_B(-sm) || RLWE'_A(m) || RLWE'_B(m)]^T
-fn encrypt_rgsw<
+pub(crate) fn encrypt_rgsw<
     Mmut: MatrixMut + MatrixEntity,
     M: Matrix<MatElement = Mmut::MatElement> + Clone,
     S: Secret,
@@ -283,7 +352,7 @@ assert!(out_rgsw.dimension() == (d * 4, ring_size));
     assert!(m_eval.dimension() == (1, ring_size));
 
     // RLWE(-sm), RLWE(-sm)
-    let (rlwe_dash_nsm, rlwe_dash_m) = out_rgsw.split_at_row(d * 2);
+    let (rlwe_dash_nsm, rlwe_dash_m) = out_rgsw.split_at_row_mut(d * 2);
 
     let mut s_eval = Mmut::try_convert_from(s.values(), &q);
     ntt_op.forward(s_eval.get_row_mut(0).as_mut());
@@ -364,7 +433,7 @@ ///
 /// - rgsw_in: RGSW(m') in evaluation domain
 /// - rlwe_in_decomposed: decomposed RLWE(m) in evaluation domain
 /// - rlwe_out: returned RLWE(mm') in evaluation domain
-fn rlwe_in_decomposed_evaluation_domain_mul_rgsw_rlwe_out_evaluation_domain<
+pub(crate) fn rlwe_in_decomposed_evaluation_domain_mul_rgsw_rlwe_out_evaluation_domain<
     Mmut: MatrixMut + MatrixEntity,
     M: Matrix<MatElement = Mmut::MatElement> + Clone,
     ModOp: VectorOps<Element = Mmut::MatElement>,
@@ -381,7 +450,7 @@ let d_rgsw = rgsw_in.dimension().0 / 4;
     assert!(rlwe_in_decomposed_eval.dimension() == (2 * d_rgsw, ring_size));
     assert!(rlwe_out_eval.dimension() == (2, ring_size));
 
-    let (a_rlwe_out, b_rlwe_out) = rlwe_out_eval.split_at_row(1);
+    let (a_rlwe_out, b_rlwe_out) = rlwe_out_eval.split_at_row_mut(1);
 
     // a * RLWE'(-sm)
     let a_rlwe_dash_nsm = rgsw_in.iter_rows().take(d_rgsw);
@@ -420,82 +489,165 @@ mod_op.elwise_fma_mut(b_rlwe_out[0].as_mut(), a.as_ref(), b.as_ref());
     });
 }
 
-fn decompose_rlwe<
-    M: Matrix + Clone,
-    Mmut: MatrixMut<MatElement = M::MatElement> + MatrixEntity,
-    D: Decomposer<Element = M::MatElement>,
->(
-    rlwe_in: &M,
+pub(crate) fn routine<M: Matrix + ?Sized, ModOp: VectorOps<Element = M::MatElement>>(
+    write_to_row: &mut [M::MatElement],
+    matrix_a: &[M::R],
+    matrix_b: &[M::R],
+    mod_op: &ModOp,
+) {
+    izip!(matrix_a.iter(), matrix_b.iter()).for_each(|(a, b)| {
+        mod_op.elwise_fma_mut(write_to_row, a.as_ref(), b.as_ref());
+    });
+}
+
+// pub(crate) fn decompose_rlwe<
+//     M: Matrix + Clone,
+//     Mmut: MatrixMut<MatElement = M::MatElement> + MatrixEntity,
+//     D: Decomposer<Element = M::MatElement>,
+// >(
+//     rlwe_in: &M,
+//     decomposer: &D,
+//     rlwe_in_decomposed: &mut Mmut,
+// ) where
+//     M::MatElement: Copy,
+//     <Mmut as Matrix>::R: RowMut,
+// {
+//     let d_rgsw = decomposer.d();
+//     let ring_size = rlwe_in.dimension().1;
+//     assert!(rlwe_in_decomposed.dimension() == (2 * d_rgsw, ring_size));
+
+//     // Decompose rlwe_in
+//     for ri in 0..ring_size {
+//         // ai
+//         let ai_decomposed = decomposer.decompose(rlwe_in.get(0, ri));
+//         for j in 0..d_rgsw {
+//             rlwe_in_decomposed.set(j, ri, ai_decomposed[j]);
+//         }
+
+//         // bi
+//         let bi_decomposed = decomposer.decompose(rlwe_in.get(1, ri));
+//         for j in 0..d_rgsw {
+//             rlwe_in_decomposed.set(j + d_rgsw, ri, bi_decomposed[j]);
+//         }
+//     }
+// }
+
+/// Decomposes ring polynomial r(X) into d polynomials using decomposer into
+/// output matrix decomp_r
+///
+/// Note that decomposition of r(X) requires decomposition of each of
+/// coefficients.
+///
+/// - decomp_r: must have dimensions d x ring_size. i^th decomposed polynomial
+///   will be stored at i^th row.
+pub(crate) fn decompose_r<M: Matrix + MatrixMut, D: Decomposer<Element = M::MatElement>>(
+    r: &[M::MatElement],
+    decomp_r: &mut [M::R],
     decomposer: &D,
-    rlwe_in_decomposed: &mut Mmut,
 ) where
+    <M as Matrix>::R: RowMut,
     M::MatElement: Copy,
-    <Mmut as Matrix>::R: RowMut,
 {
-    let d_rgsw = decomposer.d();
-    let ring_size = rlwe_in.dimension().1;
-    assert!(rlwe_in_decomposed.dimension() == (2 * d_rgsw, ring_size));
+    let ring_size = r.len();
+    let d = decomposer.d();
 
-    // Decompose rlwe_in
     for ri in 0..ring_size {
-        // ai
-        let ai_decomposed = decomposer.decompose(rlwe_in.get(0, ri));
-        for j in 0..d_rgsw {
-            rlwe_in_decomposed.set(j, ri, ai_decomposed[j]);
-        }
-
-        // bi
-        let bi_decomposed = decomposer.decompose(rlwe_in.get(1, ri));
-        for j in 0..d_rgsw {
-            rlwe_in_decomposed.set(j + d_rgsw, ri, bi_decomposed[j]);
+        let el_decomposed = decomposer.decompose(&r[ri]);
+        for j in 0..d {
+            decomp_r[j].as_mut()[ri] = el_decomposed[j];
         }
     }
 }
 
-/// Returns RLWE(m0m1) = RLWE(m0) x RGSW(m1)
+/// Returns RLWE(m0m1) = RLWE(m0) x RGSW(m1). Mutates rlwe_in inplace to equal
+/// RLWE(m0m1)
 ///
 /// - rlwe_in: is RLWE(m0) with polynomials in coefficient domain
 /// - rgsw_in: is RGSW(m1) with polynomials in evaluation domain
-/// - rlwe_out: is output RLWE(m0m1) with polynomials in coefficient domain
-/// - rlwe_in_decomposed: is a matrix of dimension (d_rgsw * 2, ring_size) used
-///   as scratch space to store decomposed RLWE(m0)
-fn rlwe_by_rgsw<
-    M: Matrix + Clone,
-    Mmut: MatrixMut<MatElement = M::MatElement> + MatrixEntity,
-    D: Decomposer<Element = M::MatElement>,
-    ModOp: VectorOps<Element = M::MatElement>,
-    NttOp: Ntt<Element = M::MatElement>,
+/// - scratch_matrix_d_ring: is a matrix of dimension (d_rgsw, ring_size) used
+///   as scratch space to store decomposed Ring elements temporarily
+pub(crate) fn rlwe_by_rgsw<
+    Mmut: MatrixMut,
+    MT: Matrix<MatElement = Mmut::MatElement> + MatrixMut<MatElement = Mmut::MatElement> + IsTrivial,
+    D: Decomposer<Element = Mmut::MatElement>,
+    ModOp: VectorOps<Element = Mmut::MatElement>,
+    NttOp: Ntt<Element = Mmut::MatElement>,
 >(
-    rlwe_in: &M,
-    rgsw_in: &M,
-    rlwe_out: &mut Mmut,
-    rlwe_in_decomposed: &mut Mmut,
+    rlwe_in: &mut MT,
+    rgsw_in: &Mmut,
+    scratch_matrix_dplus2_ring: &mut Mmut,
     decomposer: &D,
     ntt_op: &NttOp,
     mod_op: &ModOp,
 ) where
-    M::MatElement: Copy,
+    Mmut::MatElement: Copy + Zero,
     <Mmut as Matrix>::R: RowMut,
+    <MT as Matrix>::R: RowMut,
 {
-    decompose_rlwe(rlwe_in, decomposer, rlwe_in_decomposed);
-
-    // transform rlwe_in decomposed to evaluation domain
-    rlwe_in_decomposed
-        .iter_rows_mut()
-        .for_each(|r| ntt_op.forward(r.as_mut()));
+    let d_rgsw = decomposer.d();
+    assert!(scratch_matrix_dplus2_ring.dimension() == (d_rgsw + 2, rlwe_in.dimension().1));
 
     // decomposed RLWE x RGSW
-    rlwe_in_decomposed_evaluation_domain_mul_rgsw_rlwe_out_evaluation_domain(
-        rgsw_in,
-        rlwe_in_decomposed,
-        rlwe_out,
+    let (rlwe_dash_nsm, rlwe_dash_m) = rgsw_in.split_at_row(d_rgsw * 2);
+    let (scratch_matrix_d_ring, scratch_rlwe_out) =
+        scratch_matrix_dplus2_ring.split_at_row_mut(d_rgsw);
+    scratch_rlwe_out[0].as_mut().fill(Mmut::MatElement::zero());
+    scratch_rlwe_out[1].as_mut().fill(Mmut::MatElement::zero());
+    // RLWE_in = a_in, b_in; RLWE_out = a_out, b_out
+    if !rlwe_in.is_trivial() {
+        // a_in = 0 when RLWE_in is trivial RLWE ciphertext
+        // decomp<a_in>
+        decompose_r::<Mmut, D>(rlwe_in.get_row_slice(0), scratch_matrix_d_ring, decomposer);
+        scratch_matrix_d_ring
+            .iter_mut()
+            .for_each(|r| ntt_op.forward(r.as_mut()));
+        // a_out += decomp<a_in> \cdot RLWE_A'(-sm)
+        routine::<Mmut, ModOp>(
+            scratch_rlwe_out[0].as_mut(),
+            scratch_matrix_d_ring.as_ref(),
+            &rlwe_dash_nsm[..d_rgsw],
+            mod_op,
+        );
+        // b_out += decomp<a_in> \cdot RLWE_B'(-sm)
+        routine::<Mmut, ModOp>(
+            scratch_rlwe_out[1].as_mut(),
+            scratch_matrix_d_ring.as_ref(),
+            &rlwe_dash_nsm[d_rgsw..],
+            mod_op,
+        );
+    }
+    // decomp<b_in>
+    decompose_r::<Mmut, D>(rlwe_in.get_row_slice(1), scratch_matrix_d_ring, decomposer);
+    scratch_matrix_d_ring
+        .iter_mut()
+        .for_each(|r| ntt_op.forward(r.as_mut()));
+    // a_out += decomp<b_in> \cdot RLWE_A'(m)
+    routine::<Mmut, ModOp>(
+        scratch_rlwe_out[0].as_mut(),
+        scratch_matrix_d_ring.as_ref(),
+        &rlwe_dash_m[..d_rgsw],
+        mod_op,
+    );
+    // b_out += decomp<b_in> \cdot RLWE_B'(m)
+    routine::<Mmut, ModOp>(
+        scratch_rlwe_out[1].as_mut(),
+        scratch_matrix_d_ring.as_ref(),
+        &rlwe_dash_m[d_rgsw..],
         mod_op,
     );
 
     // transform rlwe_out to coefficient domain
-    rlwe_out
-        .iter_rows_mut()
+    scratch_rlwe_out
+        .iter_mut()
         .for_each(|r| ntt_op.backward(r.as_mut()));
+
+    rlwe_in
+        .get_row_mut(0)
+        .copy_from_slice(scratch_rlwe_out[0].as_mut());
+    rlwe_in
+        .get_row_mut(1)
+        .copy_from_slice(scratch_rlwe_out[1].as_mut());
+    rlwe_in.set_not_trivial();
 }
 
 /// Encrypt polynomial m(X) as RLWE ciphertext.
@@ -503,7 +655,7 @@ ///
 /// - rlwe_out: returned RLWE ciphertext RLWE(m) in coefficient domain. RLWE
 ///   ciphertext is a matirx with first row consiting polynomial `a` and the
 ///   second rows consting polynomial `b`
-fn encrypt_rlwe<
+pub(crate) fn encrypt_rlwe<
     Mmut: Matrix + MatrixMut + Clone,
     ModOp: VectorOps<Element = Mmut::MatElement>,
     NttOp: Ntt<Element = Mmut::MatElement>,
@@ -547,7 +699,7 @@
 /// Decrypts degree 1 RLWE ciphertext RLWE(m) and returns m
 ///
 /// - rlwe_ct: input degree 1 ciphertext RLWE(m).
-fn decrypt_rlwe<
+pub(crate) fn decrypt_rlwe<
     Mmut: MatrixMut + Clone,
     M: Matrix<MatElement = Mmut::MatElement>,
     ModOp: VectorOps<Element = Mmut::MatElement>,
@@ -587,7 +739,7 @@ }
 
 // Measures noise in degree 1 RLWE ciphertext against encoded ideal message
 // encoded_m
-fn measure_noise<
+pub(crate) fn measure_noise<
     Mmut: MatrixMut + Matrix + MatrixEntity,
     ModOp: VectorOps<Element = Mmut::MatElement>,
     NttOp: Ntt<Element = Mmut::MatElement>,
@@ -657,8 +809,9 @@ backend::ModularOpsU64,
         decomposer::{gadget_vector, DefaultDecomposer},
         ntt::{self, Ntt, NttBackendU64},
         random::{DefaultSecureRng, RandomUniformDist},
-        rgsw::measure_noise,
+        rgsw::{measure_noise, RlweCiphertext},
         utils::{generate_prime, negacyclic_mul},
+        Matrix,
     };
 
     use super::{
@@ -718,15 +871,14 @@ &mod_op,
             &ntt_op,
             &mut rng,
         );
+        let mut rlwe_in_ct = RlweCiphertext(rlwe_in_ct, false);
 
         // RLWE(m0m1) = RLWE(m0) x RGSW(m1)
-        let mut rlwe_out_ct = vec![vec![0u64; ring_size as usize]; 2];
-        let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw * 2];
+        let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw + 2];
         let decomposer = DefaultDecomposer::new(q, logb, d_rgsw);
         rlwe_by_rgsw(
-            &rlwe_in_ct,
+            &mut rlwe_in_ct,
             &rgsw_ct,
-            &mut rlwe_out_ct,
             &mut scratch_space,
             &decomposer,
             &ntt_op,
@@ -735,7 +887,7 @@ );
 
         // Decrypt RLWE(m0m1)
         let mut encoded_m0m1_back = vec![vec![0u64; ring_size as usize]];
-        decrypt_rlwe(&rlwe_out_ct, &s, &mut encoded_m0m1_back, &ntt_op, &mod_op);
+        decrypt_rlwe(&rlwe_in_ct, &s, &mut encoded_m0m1_back, &ntt_op, &mod_op);
         let m0m1_back = encoded_m0m1_back[0]
             .iter()
             .map(|v| (((*v as f64 * p as f64) / (q as f64)).round() as u64) % p)
@@ -797,14 +949,13 @@ &mut rng,
         );
 
         // Send RLWE_{s}(m) -> RLWE_{s}(m^k)
-        let mut rlwe_m_k = vec![vec![0u64; ring_size as usize]; 2];
-        let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw];
+        let mut rlwe_m = RlweCiphertext(rlwe_m, false);
+        let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw + 2];
         let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size as usize, auto_k);
         let decomposer = DefaultDecomposer::new(q, logb, d_rgsw);
         galois_auto(
-            &rlwe_m,
+            &mut rlwe_m,
             &ksk_out,
-            &mut rlwe_m_k,
             &mut scratch_space,
             &auto_map_index,
             &auto_map_sign,
@@ -812,6 +963,8 @@ &mod_op,
             &ntt_op,
             &decomposer,
         );
+
+        let rlwe_m_k = rlwe_m;
 
         // Decrypt RLWE_{s}(m^k) and check
         let mut encoded_m_k_back = vec![vec![0u64; ring_size as usize]];
@@ -834,13 +987,13 @@ },
         );
 
         {
-            let encoded_m_k = m_k
-                .iter()
-                .map(|v| ((*v as f64 * q as f64) / p as f64).round() as u64)
-                .collect_vec();
+            // let encoded_m_k = m_k
+            //     .iter()
+            //     .map(|v| ((*v as f64 * q as f64) / p as f64).round() as u64)
+            //     .collect_vec();
 
-            let noise = measure_noise(&rlwe_m_k, &vec![encoded_m_k], &ntt_op, &mod_op, &s);
-            println!("Ksk noise: {noise}");
+            // let noise = measure_noise(&rlwe_m_k, &vec![encoded_m_k], &ntt_op,
+            // &mod_op, &s); println!("Ksk noise: {noise}");
         }
 
         // FIXME(Jay): Galios autormophism will incur high error unless we fix in

@@ -189,3 +189,24 @@
         vec![row0]
     }
 }
+
+impl TryConvertFrom<[i32]> for Vec<u64> {
+    type Parameters = u64;
+    fn try_convert_from(value: &[i32], parameters: &Self::Parameters) -> Self {
+        value
+            .iter()
+            .map(|v| {
+                let is_neg = v.is_negative();
+                let v_u64 = v.abs() as u64;
+
+                assert!(v_u64 < *parameters);
+
+                if is_neg {
+                    parameters - v_u64
+                } else {
+                    v_u64
+                }
+            })
+            .collect_vec()
+    }
+}