SDA lattice attack, need to fix LLL part

src/lll.rs

@@ -0,0 +1,22 @@
+use lll_rs::{matrix::Matrix as LLLMatrix, vector::BigVector};
+
+use crate::matrix::Matrix;
+
+impl Matrix {
+    pub fn to_lll_matrix(&self) -> LLLMatrix<BigVector> {
+        let n = self.n;
+        let mut lll_mat = LLLMatrix::init(n, n);
+
+        for row_idx in 0..n {
+            let mut elements = Vec::with_capacity(n);
+
+            for col_idx in 0..n {
+                let val = self[(row_idx, col_idx)].clone();
+                elements.push(val);
+            }
+
+            lll_mat[row_idx] = BigVector::from_vector(elements);
+        }
+        lll_mat
+    }
+}

src/main.rs

@@ -1,5 +1,42 @@
+use rug::Integer;
+use crate::matrix::Matrix;
+use lll_rs::lll::biglll;
+mod lll;
 mod matrix;
 
 fn main() {
-    println!("");
+    // 1. Build lattice matrix basis
+    let ciphertexts = vec![
+Integer::from(37459),
+Integer::from(8227),
+Integer::from(44119),
+Integer::from(22575),
+Integer::from(9249),
+Integer::from(38483),
+Integer::from(26181),
+    ];
+    let noise_bits = 2;
+    let basis_matrix = Matrix::new_lattice(noise_bits, ciphertexts.clone()).unwrap();
+
+    println!("matrix: {:?}", basis_matrix);
+
+    // 2. reduce with LLL
+    let mut lll_matrix = basis_matrix.to_lll_matrix();
+    biglll::lattice_reduce(&mut lll_matrix);
+
+    // 3. Extract shortest vector
+    let shortest_vector = &lll_matrix[0];
+    println!("Shortest vector: {:?}", shortest_vector);
+
+    // 4. q0 candidate
+    let q0 = &shortest_vector[0] / (Integer::from(1) << (noise_bits + 1));
+
+    // 5. Find p
+    // compute r0 = x0 (mod q0)
+    // and p = (x0 − r0)/q0.
+    let x0 = &ciphertexts[0];
+    let r0 = x0 % q0.clone();
+    let p_guess = (x0 - r0) / q0;
+
+    println!("Recovered p: {}", p_guess);
 }

src/matrix.rs

@@ -11,14 +11,14 @@ macro_rules! int {
 
 #[derive(Debug, PartialEq)]
 pub struct Matrix {
-    pub n: usize, //rows
+    pub n: usize, // rows
     pub m: usize, // columns
     values: Vec<Element>,
 }
 
 impl Matrix {
     pub fn new(n: usize, m: usize, values: Vec<Element>) -> Option<Self> {
-        if n*m == values.len() {
+        if n * m == values.len() {
             Some(Matrix { n, m, values })
         } else {
             None
@@ -29,8 +29,8 @@ impl Matrix {
         let n = ciphertexts.len();
         let mut values = Vec::with_capacity(n * n);
 
-        // First row: [2^noise_bits, ciphertexts[1], ..., ciphertexts[t]]
-        values.push(int!(2u64).pow(noise_bits as u32));
+        // First row: [2^(noise_bits+1), ciphertexts[1], ..., ciphertexts[t]]
+        values.push(int!(2u64).pow(noise_bits as u32 + 1));
         values.extend_from_slice(&ciphertexts[1..]);
 
         // -x0 on diagonal, 0 everywhere else
@@ -48,7 +48,7 @@ impl Matrix {
 impl Index<(usize, usize)> for Matrix {
     type Output = Element;
     fn index(&self, index: (usize, usize)) -> &Self::Output {
-        if index.0>=self.m || index.1 >= self.n {
+        if index.0 >= self.m || index.1 >= self.n {
             panic!();
         }
         &self.values[(self.n * index.0) + index.1]
@@ -57,7 +57,7 @@ impl Index<(usize, usize)> for Matrix {
 
 impl IndexMut<(usize, usize)> for Matrix {
     fn index_mut(&mut self, index: (usize, usize)) -> &mut Self::Output {
-        if index.0>=self.m || index.1 >= self.n {
+        if index.0 >= self.m || index.1 >= self.n {
             panic!();
         }
         &mut self.values[(self.n * index.0) + index.1]
@@ -91,7 +91,12 @@ mod tests {
         m[(1, 0)] = int!(5);
         assert_eq!(m[(1, 0)], int!(5));
 
-        let m2 = Matrix::new(3, 2, vec![int!(1), int!(2), int!(3), int!(4), int!(5), int!(6)]).unwrap();
+        let m2 = Matrix::new(
+            3,
+            2,
+            vec![int!(1), int!(2), int!(3), int!(4), int!(5), int!(6)],
+        )
+        .unwrap();
         assert_eq!(m2[(0, 2)], int!(3));
         assert_eq!(m2[(1, 0)], int!(4));
         let result = panic::catch_unwind(|| {
@@ -111,7 +116,7 @@ mod tests {
         let noise_bits = 2;
 
         let expected_values = vec![
-            int!(4),
+            int!(8),
             int!(8),
             int!(12),
             int!(0),