@@ -1,10 +1,9 @@
 use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion};
 use math::poly::PolyRNS;
-use math::ring::impl_u64::ring_rns::new_rings;
-use math::ring::{Ring, RingRNS};
+use math::ring::RingRNS;
 
 fn div_floor_by_last_modulus_ntt_true(c: &mut Criterion) {
-    fn runner(r: RingRNS<u64>) -> Box<dyn FnMut() + '_> {
+    fn runner(r: RingRNS<u64>) -> Box<dyn FnMut()> {
         let a: PolyRNS<u64> = r.new_polyrns();
         let mut b: PolyRNS<u64> = r.new_polyrns();
         let mut c: PolyRNS<u64> = r.new_polyrns();
@@ -22,8 +21,8 @@ 0x1fffffffffc80001u64,
             0x1fffffffffb40001,
             0x1fffffffff500001,
         ];
-        let rings: Vec<Ring<u64>> = new_rings(n, moduli);
-        let ring_rns: RingRNS<'_, u64> = RingRNS::new(&rings);
+
+        let ring_rns: RingRNS<u64> = RingRNS::new(n, moduli);
 
         let runners = [(format!("prime/n={}/level={}", n, ring_rns.level()), {
             runner(ring_rns)

@@ -1,11 +1,10 @@
 use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion};
 use math::poly::PolyRNS;
-use math::ring::impl_u64::ring_rns::new_rings;
-use math::ring::{Ring, RingRNS};
+use math::ring::RingRNS;
 use sampling::source::Source;
 
 fn fill_uniform(c: &mut Criterion) {
-    fn runner(r: RingRNS<u64>) -> Box<dyn FnMut() + '_> {
+    fn runner(r: RingRNS<u64>) -> Box<dyn FnMut()> {
         let mut a: PolyRNS<u64> = r.new_polyrns();
         let seed: [u8; 32] = [0; 32];
         let mut source: Source = Source::new(seed);
@@ -25,8 +24,8 @@ 0x1fffffffffc80001u64,
             0x1fffffffffb40001,
             0x1fffffffff500001,
         ];
-        let rings: Vec<Ring<u64>> = new_rings(n, moduli);
-        let ring_rns: RingRNS<'_, u64> = RingRNS::new(&rings);
+
+        let ring_rns: RingRNS<u64> = RingRNS::new(n, moduli);
 
         let runners = [(format!("prime/n={}/level={}", n, ring_rns.level()), {
             runner(ring_rns)

@@ -19,7 +19,7 @@ four_q: O,
 }
 
 impl Table<u64> {
-    pub fn new(prime: Prime<u64>, nth_root: u64) -> Self {
+    pub fn new(prime: Prime<u64>, nth_root: u64) -> Table<u64> {
         assert!(
             nth_root & (nth_root - 1) == 0,
             "invalid argument: nth_root = {} is not a power of two",

@@ -4,6 +4,7 @@ use crate::dft::DFT;
 use crate::modulus::prime::Prime;
 use crate::poly::{Poly, PolyRNS};
 use num::traits::Unsigned;
+use std::sync::Arc;
 
 pub struct Ring<O: Unsigned> {
     pub n: usize,
@@ -21,9 +22,9 @@ Poly::<u64>::new(self.n())
     }
 }
 
-pub struct RingRNS<'a, O: Unsigned>(pub &'a [Ring<O>]);
+pub struct RingRNS<O: Unsigned>(pub Vec<Arc<Ring<O>>>);
 
-impl<O: Unsigned> RingRNS<'_, O> {
+impl<O: Unsigned> RingRNS<O> {
     pub fn n(&self) -> usize {
         self.0[0].n()
     }
@@ -42,6 +43,6 @@ }
 
     pub fn at_level(&self, level: usize) -> RingRNS<O> {
         assert!(level <= self.0.len());
-        RingRNS(&self.0[..level + 1])
+        RingRNS(self.0[..level + 1].to_vec())
     }
 }

@@ -6,7 +6,7 @@ use crate::ring::RingRNS;
 use crate::scalar::ScalarRNS;
 extern crate test;
 
-impl RingRNS<'_, u64> {
+impl RingRNS<u64> {
     /// Updates b to floor(a / q[b.level()]).
     pub fn div_floor_by_last_modulus<const NTT: bool>(
         &self,

@@ -5,19 +5,16 @@ use crate::poly::PolyRNS;
 use crate::ring::{Ring, RingRNS};
 use crate::scalar::ScalarRNS;
 use num_bigint::BigInt;
+use std::sync::Arc;
 
-pub fn new_rings(n: usize, moduli: Vec<u64>) -> Vec<Ring<u64>> {
-    assert!(!moduli.is_empty(), "moduli cannot be empty");
-    let rings: Vec<Ring<u64>> = moduli
-        .into_iter()
-        .map(|prime| Ring::new(n, prime, 1))
-        .collect();
-    return rings;
-}
-
-impl<'a> RingRNS<'a, u64> {
-    pub fn new(rings: &'a [Ring<u64>]) -> Self {
-        RingRNS(rings)
+impl RingRNS<u64> {
+    pub fn new(n: usize, moduli: Vec<u64>) -> Self {
+        assert!(!moduli.is_empty(), "moduli cannot be empty");
+        let rings: Vec<Arc<Ring<u64>>> = moduli
+            .into_iter()
+            .map(|prime| Arc::new(Ring::new(n, prime, 1)))
+            .collect();
+        return RingRNS(rings);
     }
 
     pub fn modulus(&self) -> BigInt {
@@ -92,7 +89,7 @@ });
     }
 }
 
-impl RingRNS<'_, u64> {
+impl RingRNS<u64> {
     pub fn ntt_inplace<const LAZY: bool>(&self, a: &mut PolyRNS<u64>) {
         self.0
             .iter()
@@ -122,7 +119,7 @@ .for_each(|(i, ring)| ring.intt::<LAZY>(&a.0[i], &mut b.0[i]));
     }
 }
 
-impl RingRNS<'_, u64> {
+impl RingRNS<u64> {
     #[inline(always)]
     pub fn add<const REDUCE: REDUCEMOD>(
         &self,

@@ -12,7 +12,7 @@ .for_each(|a| *a = source.next_u64n(max, mask));
     }
 }
 
-impl RingRNS<'_, u64> {
+impl RingRNS<u64> {
     pub fn fill_uniform(&self, source: &mut Source, a: &mut PolyRNS<u64>) {
         self.0
             .iter()

@@ -1,6 +1,5 @@
 use math::poly::PolyRNS;
-use math::ring::impl_u64::ring_rns::new_rings;
-use math::ring::{Ring, RingRNS};
+use math::ring::RingRNS;
 use num_bigint::BigInt;
 use num_bigint::Sign;
 use sampling::source::Source;
@@ -9,8 +8,7 @@ #[test]
 fn rescaling_rns_u64() {
     let n = 1 << 10;
     let moduli: Vec<u64> = vec![0x1fffffffffc80001u64, 0x1fffffffffe00001u64];
-    let rings: Vec<Ring<u64>> = new_rings(n, moduli);
-    let ring_rns: RingRNS<'_, u64> = RingRNS::new(&rings);
+    let ring_rns: RingRNS<u64> = RingRNS::new(n, moduli);
 
     test_div_floor_by_last_modulus::<false>(&ring_rns);
     test_div_floor_by_last_modulus::<true>(&ring_rns);