diff --git a/Cargo.toml b/Cargo.toml
index 0642edd..2bf8179 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -6,3 +6,5 @@ edition = "2021"
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
+lll-rs = "0.2.0"
+rug = "1.27.0"
diff --git a/src/matrix.rs b/src/matrix.rs
index 8098da6..0029e04 100644
--- a/src/matrix.rs
+++ b/src/matrix.rs
@@ -1,7 +1,14 @@
-type Element = f64;
-
+use rug::ops::Pow;
 use std::ops::{Index, IndexMut};
 
+type Element = rug::Integer;
+
+macro_rules! int {
+    ($x:expr) => {
+        rug::Integer::from($x)
+    };
+}
+
 #[derive(Debug, PartialEq)]
 pub struct Matrix {
     pub n: usize,
@@ -22,14 +29,14 @@ impl Matrix {
         let mut values = Vec::with_capacity(n * n);
 
         // First row: [2^noise_bits, ciphertexts[1], ..., ciphertexts[t]]
-        values.push((2.0f64).powi(noise_bits as i32));
+        values.push(int!(2u64).pow(noise_bits as u32));
         values.extend_from_slice(&ciphertexts[1..]);
 
         // -x0 on diagonal, 0 everywhere else
-        let x0 = ciphertexts[0];
+        let x0 = &ciphertexts[0];
         for i in 0..n - 1 {
-            let mut row = vec![0.0; n];
-            row[i] = -x0;
+            let mut row = vec![int!(0); n];
+            row[i] = -x0.clone();
             values.extend(row);
         }
 
@@ -38,7 +45,7 @@ impl Matrix {
 }
 
 impl Index<(usize, usize)> for Matrix {
-    type Output = f64;
+    type Output = Element;
     fn index(&self, index: (usize, usize)) -> &Self::Output {
         &self.values[(self.n * index.0) + index.1]
     }
@@ -58,31 +65,40 @@ mod tests {
         assert_eq!(
             Matrix {
                 n: 2,
-                values: Vec::from([1.0, 2.0, 3.0, 4.0])
+                values: vec![int!(1), int!(2), int!(3), int!(4)],
             },
-            Matrix::new(2, Vec::from([1.0, 2.0, 3.0, 4.0])).unwrap()
+            Matrix::new(2, vec![int!(1), int!(2), int!(3), int!(4)]).unwrap()
         );
-        assert!(Matrix::new(3, Vec::from([1.0, 2.0])).is_none());
+        assert!(Matrix::new(3, vec![int!(1), int!(2)]).is_none());
     }
+
     #[test]
     fn indexes() {
-        let mut m = Matrix::new(2, vec![1.0, 2.0, 3.0, 4.0]).unwrap();
-        assert_eq!(m[(0, 0)], 1.0);
-        assert_eq!(m[(1, 0)], 3.0);
+        let mut m = Matrix::new(2, vec![int!(1), int!(2), int!(3), int!(4)]).unwrap();
 
-        m[(1, 0)] = 5.0;
-        assert_eq!(m[(1, 0)], 5.0);
+        assert_eq!(m[(0, 0)], int!(1));
+        assert_eq!(m[(1, 0)], int!(3));
+
+        m[(1, 0)] = int!(5);
+        assert_eq!(m[(1, 0)], int!(5));
     }
+
     #[test]
     fn test_new_lattice() {
-        let ciphertexts = vec![5.0, 8.0, 12.0]; // x0=5.0, x1=8.0, x2=12.0
+        let ciphertexts = vec![int!(5), int!(8), int!(12)];
         let noise_bits = 2;
 
-        // Expected matrix (3x3):
-        // [ 2^2,   x1,   x2 ] = [4.0, 8.0, 12.0]
-        // [ -x0,    0,    0 ] = [-5.0, 0.0, 0.0]
-        // [   0,  -x0,    0 ] = [0.0, -5.0, 0.0]
-        let expected_values = vec![4.0, 8.0, 12.0, -5.0, 0.0, 0.0, 0.0, -5.0, 0.0];
+        let expected_values = vec![
+            int!(4),
+            int!(8),
+            int!(12),
+            int!(-5),
+            int!(0),
+            int!(0),
+            int!(0),
+            int!(-5),
+            int!(0),
+        ];
 
         let lattice = Matrix::new_lattice(noise_bits, ciphertexts).unwrap();
         assert_eq!(lattice.n, 3);