diff --git a/math/src/lib.rs b/math/src/lib.rs
index 8ee8bd7..e98dc31 100644
--- a/math/src/lib.rs
+++ b/math/src/lib.rs
@@ -229,4 +229,41 @@ pub mod macros{
             }
         };
     }
+
+    #[macro_export]
+    macro_rules! apply_vsv {
+
+        ($self:expr, $f:expr, $a:expr, $c:expr, $b:expr, $CHUNK:expr) => {
+
+            let n: usize = $a.len();
+            debug_assert!($b.len() == n, "invalid argument b: b.len() = {} != a.len() = {}", $b.len(), n);
+            debug_assert!(CHUNK&(CHUNK-1) == 0, "invalid CHUNK const: not a power of two");
+
+            match CHUNK{
+                8 => {
+                    
+                    izip!($a.chunks_exact(8), $b.chunks_exact_mut(8)).for_each(|(a, b)| {
+                        $f(&$self, &a[0], $c, &mut b[0]);
+                        $f(&$self, &a[1], $c, &mut b[1]);
+                        $f(&$self, &a[2], $c, &mut b[2]);
+                        $f(&$self, &a[3], $c, &mut b[3]);
+                        $f(&$self, &a[4], $c, &mut b[4]);
+                        $f(&$self, &a[5], $c, &mut b[5]);
+                        $f(&$self, &a[6], $c, &mut b[6]);
+                        $f(&$self, &a[7], $c, &mut b[7]);
+                    });
+
+                    let m = n - (n&7);
+                    izip!($a[m..].iter(), $b[m..].iter_mut()).for_each(|(a, b)| {
+                        $f(&$self, a, $c, b);
+                    });
+                },
+                _=>{
+                    izip!($a.iter(), $b.iter_mut()).for_each(|(a, b)| {
+                        $f(&$self, a, $c, b);
+                    });
+                }
+            }
+        };
+    }
 }
\ No newline at end of file
diff --git a/math/src/modulus.rs b/math/src/modulus.rs
index 8b14a0d..f516678 100644
--- a/math/src/modulus.rs
+++ b/math/src/modulus.rs
@@ -94,6 +94,9 @@ pub trait WordOperations<O>{
 
     // Assigns (a + 2q - b) * c to d.
     fn word_sum_aqqmb_prod_c_barrett_assign_d<const REDUCE:REDUCEMOD>(&self, a: &O, b: &O, c: &barrett::Barrett<O>, d: &mut O);
+
+    // Assigns (a + 2q - b) * c to b.
+    fn word_sum_aqqmb_prod_c_barrett_assign_b<const REDUCE:REDUCEMOD>(&self, a: &u64, c: &barrett::Barrett<u64>, b: &mut u64);
 }
 
 pub trait VecOperations<O>{
@@ -136,6 +139,9 @@ pub trait VecOperations<O>{
 
     // Assigns (a[i] + 2q - b[i]) * c to d[i].
     fn vec_sum_aqqmb_prod_c_scalar_barrett_assign_d<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b: &[u64], c: &barrett::Barrett<u64>, d: &mut [u64]);
+
+    // Assigns (a[i] + 2q - b[i]) * c to b[i].
+    fn vec_sum_aqqmb_prod_c_scalar_barrett_assign_b<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], c: &barrett::Barrett<u64>, b: &mut [u64]);
 }
 
 
diff --git a/math/src/modulus/impl_u64/operations.rs b/math/src/modulus/impl_u64/operations.rs
index 3acf34c..6711a75 100644
--- a/math/src/modulus/impl_u64/operations.rs
+++ b/math/src/modulus/impl_u64/operations.rs
@@ -5,7 +5,7 @@ use crate::modulus::ReduceOnce;
 use crate::modulus::montgomery::Montgomery;
 use crate::modulus::barrett::Barrett;
 use crate::modulus::REDUCEMOD;
-use crate::{apply_v, apply_vv, apply_vvv, apply_sv, apply_svv, apply_vvsv};
+use crate::{apply_v, apply_vv, apply_vvv, apply_sv, apply_svv, apply_vvsv, apply_vsv};
 use itertools::izip;
 
 impl WordOperations<u64> for Prime<u64>{
@@ -86,6 +86,12 @@ impl WordOperations<u64> for Prime<u64>{
         *d = self.two_q.wrapping_sub(*b).wrapping_add(*a);
         self.barrett.mul_external_assign::<REDUCE>(*c, d);
     }
+
+    #[inline(always)]
+    fn word_sum_aqqmb_prod_c_barrett_assign_b<const REDUCE:REDUCEMOD>(&self, a: &u64, c: &Barrett<u64>, b: &mut u64){
+        *b = self.two_q.wrapping_sub(*b).wrapping_add(*a);
+        self.barrett.mul_external_assign::<REDUCE>(*c, b);
+    }
 }
 
 impl VecOperations<u64> for Prime<u64>{
@@ -160,4 +166,8 @@ impl VecOperations<u64> for Prime<u64>{
     fn vec_sum_aqqmb_prod_c_scalar_barrett_assign_d<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b: &[u64], c: &Barrett<u64>, d: &mut [u64]){
         apply_vvsv!(self, Self::word_sum_aqqmb_prod_c_barrett_assign_d::<REDUCE>, a, b, c, d, CHUNK);
     }
+
+    fn vec_sum_aqqmb_prod_c_scalar_barrett_assign_b<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], c: &Barrett<u64>, b: &mut [u64]){
+        apply_vsv!(self, Self::word_sum_aqqmb_prod_c_barrett_assign_b::<REDUCE>, a, c, b, CHUNK);
+    }
 }
diff --git a/math/src/poly.rs b/math/src/poly.rs
index d153249..2d63277 100644
--- a/math/src/poly.rs
+++ b/math/src/poly.rs
@@ -1,10 +1,11 @@
 pub mod poly;
+use std::cmp::PartialEq;
 
-#[derive(Clone, Debug, PartialEq, Eq)]
+#[derive(Clone, Debug, Eq)]
 pub struct Poly<O>(pub Vec<O>);
 
 impl<O> Poly<O>where
-    O: Default + Clone,
+    O: Default + Clone + Copy,
     {
     pub fn new(n: usize) -> Self{
         Self(vec![O::default();n])
@@ -20,15 +21,45 @@ impl<O> Poly<O>where
     }
 
     pub fn n(&self) -> usize{
-        return self.0.len()
+        (usize::BITS - self.0.len().leading_zeros()) as usize
+    }
+
+    pub fn log_n(&self) -> usize{
+        self.0.len()-1
+    }
+
+    pub fn resize(&mut self, n:usize){
+        self.0.resize(n, O::default());
+    }
+
+    pub fn set_all(&mut self, v: &O){
+        self.0.fill(*v)
+    }
+
+    pub fn zero(&mut self){
+        self.set_all(&O::default())
+    }
+
+    pub fn copy_from(&mut self, other: &Poly<O>){
+        if std::ptr::eq(self, other){
+            return
+        }
+        self.resize(other.n());
+        self.0.copy_from_slice(&other.0)
     }
 }
 
-#[derive(Clone, Debug, PartialEq, Eq)]
+impl<O: PartialEq> PartialEq for Poly<O> {
+    fn eq(&self, other: &Self) -> bool {
+        std::ptr::eq(self, other) || (self.0 == other.0)
+    }
+}
+
+#[derive(Clone, Debug, Eq)]
 pub struct PolyRNS<O>(pub Vec<Poly<O>>);
 
 impl<O> PolyRNS<O>where
-    O: Default + Clone,
+    O: Default + Clone + Copy,
     {
 
     pub fn new(n: usize, level: usize) -> Self{
@@ -42,6 +73,10 @@ impl<O> PolyRNS<O>where
         self.0[0].n()
     }
 
+    pub fn log_n(&self) -> usize{
+        self.0[0].log_n()
+    }
+
     pub fn level(&self) -> usize{
         self.0.len()-1
     }
@@ -60,13 +95,50 @@ impl<O> PolyRNS<O>where
         }
     }
 
+    pub fn resize(&mut self, level:usize){
+        self.0.resize(level+1, Poly::<O>::new(self.n()));
+    }
+
+    pub fn split_at_mut(&mut self, level:usize) -> (&mut [Poly<O>], &mut [Poly<O>]){
+        self.0.split_at_mut(level)
+    }
+
     pub fn at(&self, level:usize) -> &Poly<O>{
+        assert!(level <= self.level(), "invalid argument level: level={} > self.level()={}", level, self.level());
         &self.0[level]
     }
 
     pub fn at_mut(&mut self, level:usize) -> &mut Poly<O>{
         &mut self.0[level]
     }
+
+    pub fn set_all(&mut self, v: &O){
+        (0..self.level()+1).for_each(|i| self.at_mut(i).set_all(v))
+    }
+
+    pub fn zero(&mut self){
+        self.set_all(&O::default())
+    }
+
+    pub fn copy(&mut self, other: &PolyRNS<O>){
+        if std::ptr::eq(self, other){
+            return
+        }
+        self.resize(other.level());
+        self.copy_level(other.level(), other);
+    }
+
+    pub fn copy_level(&mut self, level:usize, other: &PolyRNS<O>){
+        assert!(self.level() <= level, "invalid argument level: level={} > self.level()={}", level, self.level());
+        assert!(other.level() <= level, "invalid argument level: level={} > other.level()={}", level, other.level());
+        (0..level+1).for_each(|i| self.at_mut(i).copy_from(other.at(i)))
+    }
+}
+
+impl<O: PartialEq> PartialEq for PolyRNS<O> {
+    fn eq(&self, other: &Self) -> bool {
+        std::ptr::eq(self, other) && (self.0 == other.0)
+    }
 }
 
 impl<O> Default for PolyRNS<O>{
diff --git a/math/src/ring.rs b/math/src/ring.rs
index 4a3de26..b62f9a9 100644
--- a/math/src/ring.rs
+++ b/math/src/ring.rs
@@ -2,6 +2,7 @@ pub mod impl_u64;
 
 use crate::modulus::prime::Prime;
 use crate::poly::{Poly, PolyRNS};
+use num_bigint::BigInt;
 use crate::dft::DFT;
 
 
@@ -21,12 +22,9 @@ impl<O> Ring<O>{
     }
 }
 
-
-//pub struct RingRNS<'a, O: Copy>(pub Vec<Box<& 'a Ring<O>>>);
-
 pub struct RingRNS<'a, O>(& 'a [Ring<O>]);
 
-impl<O: Copy> RingRNS<'_, O>{
+impl<O: Copy> RingRNS<'_, O> {
 
     pub fn n(&self) -> usize{
         self.0[0].n()
@@ -39,11 +37,7 @@ impl<O: Copy> RingRNS<'_, O>{
     pub fn max_level(&self) -> usize{
         self.0.len()-1
     }
-
-    pub fn modulus<const LEVEL:usize>(&self) -> O{
-        self.0[LEVEL].modulus.q
-    }
-
+    
     pub fn level(&self) -> usize{
         self.0.len()-1
     }
diff --git a/math/src/ring/impl_u64/rescaling_rns.rs b/math/src/ring/impl_u64/rescaling_rns.rs
index 505d225..3634e00 100644
--- a/math/src/ring/impl_u64/rescaling_rns.rs
+++ b/math/src/ring/impl_u64/rescaling_rns.rs
@@ -1,12 +1,12 @@
 use crate::ring::RingRNS;
-use crate::poly::PolyRNS;
+use crate::poly::{Poly, PolyRNS};
 use crate::modulus::barrett::Barrett;
 use crate::modulus::ONCE;
 extern crate test;
 
 impl RingRNS<'_, u64>{
 
-    /// Updates b to floor(b / q[b.level()]).
+    /// Updates b to floor(a / q[b.level()]).
     /// Expects a and b to be in the NTT domain.
     pub fn div_floor_by_last_modulus_ntt(&self, a: &PolyRNS<u64>, buf: &mut PolyRNS<u64>, b: &mut PolyRNS<u64>){
         assert!(b.level() >= a.level()-1, "invalid input b: b.level()={} < a.level()-1={}", b.level(), a.level()-1);
@@ -21,6 +21,19 @@ impl RingRNS<'_, u64>{
     }
 
     /// Updates b to floor(b / q[b.level()]).
+    /// Expects b to be in the NTT domain.
+    pub fn div_floor_by_last_modulus_ntt_inplace(&self, buf: &mut PolyRNS<u64>, b: &mut PolyRNS<u64>){
+        let level = self.level();
+        self.0[level].intt::<true>(b.at(level), buf.at_mut(0));
+        let rescaling_constants: Vec<Barrett<u64>> = self.rescaling_constant();
+        let (buf_ntt_q_scaling, buf_ntt_qi_scaling) = buf.0.split_at_mut(1);
+        for (i, r) in self.0[0..level].iter().enumerate(){
+            r.ntt::<true>(&buf_ntt_q_scaling[0], &mut buf_ntt_qi_scaling[0]);
+            r.sum_aqqmb_prod_c_scalar_barrett_inplace::<ONCE>(&buf_ntt_qi_scaling[0], &rescaling_constants[i], b.at_mut(i));
+        }
+    }
+
+    /// Updates b to floor(a / q[b.level()]).
     pub fn div_floor_by_last_modulus(&self, a: &PolyRNS<u64>, b: &mut PolyRNS<u64>){
         assert!(b.level() >= a.level()-1, "invalid input b: b.level()={} < a.level()-1={}", b.level(), a.level()-1);
         let level = self.level();
@@ -29,6 +42,35 @@ impl RingRNS<'_, u64>{
             r.sum_aqqmb_prod_c_scalar_barrett::<ONCE>(a.at(level), a.at(i), &rescaling_constants[i], b.at_mut(i));
         }
     }
+
+    /// Updates a to floor(b / q[b.level()]).
+    pub fn div_floor_by_last_modulus_inplace(&self, a: &mut PolyRNS<u64>){
+        let level = self.level();
+        let rescaling_constants: Vec<Barrett<u64>> = self.rescaling_constant();
+        let (a_i, a_level) = a.split_at_mut(level);
+        for (i, r) in self.0[0..level].iter().enumerate(){
+            r.sum_aqqmb_prod_c_scalar_barrett_inplace::<ONCE>(&a_level[0], &rescaling_constants[i], &mut a_i[i]);
+        }
+    }
+
+    pub fn div_floor_by_last_moduli(&self, nb_moduli:usize, a: &PolyRNS<u64>, b: &mut PolyRNS<u64>){
+        if nb_moduli == 0{
+            if a != b{
+                b.copy(a);
+            }
+        }else{
+            self.div_floor_by_last_modulus(a, b);
+            (1..nb_moduli).for_each(|i|{self.at_level(self.level()-i).div_floor_by_last_modulus_inplace(b)});
+        }
+    }
+
+    pub fn div_floor_by_last_moduli_inplace(&self, nb_moduli:usize, a: &mut PolyRNS<u64>){
+        (0..nb_moduli).for_each(|i|{self.at_level(self.level()-i).div_floor_by_last_modulus_inplace(a)});
+    }
+
+    pub fn div_round_by_last_modulus_ntt(&self, a: &PolyRNS<u64>, buf: &mut PolyRNS<u64>, b: &mut PolyRNS<u64>){
+        let level = self.level();
+    }
 }
 
 
diff --git a/math/src/ring/impl_u64/ring.rs b/math/src/ring/impl_u64/ring.rs
index ed6934d..b04d901 100644
--- a/math/src/ring/impl_u64/ring.rs
+++ b/math/src/ring/impl_u64/ring.rs
@@ -139,4 +139,11 @@ impl Ring<u64>{
         debug_assert!(d.n() == self.n(), "d.n()={} != n={}", d.n(), self.n());
         self.modulus.vec_sum_aqqmb_prod_c_scalar_barrett_assign_d::<CHUNK, REDUCE>(&a.0, &b.0, c, &mut d.0);
     }
+
+    #[inline(always)]
+    pub fn sum_aqqmb_prod_c_scalar_barrett_inplace<const REDUCE:REDUCEMOD>(&self, a: &Poly<u64>, c: &Barrett<u64>, b: &mut Poly<u64>){
+        debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
+        debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
+        self.modulus.vec_sum_aqqmb_prod_c_scalar_barrett_assign_b::<CHUNK, REDUCE>(&a.0, c, &mut b.0);
+    }
 }
\ No newline at end of file
diff --git a/math/src/ring/impl_u64/ring_rns.rs b/math/src/ring/impl_u64/ring_rns.rs
index b4b6339..dc82615 100644
--- a/math/src/ring/impl_u64/ring_rns.rs
+++ b/math/src/ring/impl_u64/ring_rns.rs
@@ -19,6 +19,12 @@ impl<'a> RingRNS<'a, u64>{
         RingRNS(rings)
     }
 
+    pub fn modulus(&self) -> BigInt{
+        let mut modulus = BigInt::from(1);
+        self.0.iter().enumerate().for_each(|(_, r)|modulus *= BigInt::from(r.modulus.q));
+        modulus
+    }
+
     pub fn rescaling_constant(&self) -> Vec<Barrett<u64>> {
         let level = self.level();
         let q_scale: u64 = self.0[level].modulus.q;
@@ -30,6 +36,32 @@ impl<'a> RingRNS<'a, u64>{
         assert!(level <= a.level(), "invalid level: level={} > a.level()={}", level, a.level());
         (0..level).for_each(|i|{self.0[i].from_bigint(coeffs, step, a.at_mut(i))});
     }
+
+    pub fn set_bigint_from_poly(&self, a: &PolyRNS<u64>, step: usize, coeffs: &mut [BigInt]){
+        assert!(step <= a.n(), "invalid step: step={} > a.n()={}", step, a.n());
+        assert!(coeffs.len() <= a.n() / step, "invalid coeffs: coeffs.len()={} > a.n()/step={}", coeffs.len(), a.n()/step);
+
+        let mut inv_crt: Vec<BigInt> = vec![BigInt::default(); self.level()+1];
+        let q_big: BigInt = self.modulus();
+        let q_big_half: BigInt = &q_big>>1;
+
+        inv_crt.iter_mut().enumerate().for_each(|(i, a)|{
+            let qi_big = BigInt::from(self.0[i].modulus.q);
+            *a = (&q_big / &qi_big);
+            *a *= a.modinv(&qi_big).unwrap();
+        });
+
+        (0..self.n()).step_by(step).enumerate().for_each(|(i, j)|{
+            coeffs[j] = BigInt::from(a.at(0).0[i]) * &inv_crt[0];
+            (1..self.level()+1).for_each(|k|{
+                coeffs[j] += BigInt::from(a.at(k).0[i] * &inv_crt[k]);
+            });
+            coeffs[j] %= &q_big;
+            if &coeffs[j] >= &q_big_half{
+                coeffs[j] -= &q_big;
+            }
+        });
+    }
 }
 
 impl RingRNS<'_, u64>{