Impl multi-variable lagrange (#5)

1. bugfix for Fervalds algorithm
2. Impl multi-variable lagrange.

1_IP/src/lib.rs

@@ -1,5 +1,6 @@
 /// The interactive proofs case(1.2.1) in chapter 1
-/// In this case, business store data in cloud_provider. Later, before business wants wanna do some computation on cloud_provider, the business check the `data` first.
+/// In this case, business store data in cloud_provider. Later, before business wants wanna do some
+/// computation on cloud_provider, the business check the `data` first.
 mod prover;
 mod utils;
 mod verify;

2_Freivalds_Algorithm/src/lib.rs

@@ -1,18 +1,18 @@
-use crate::matrix::Matrix;
-use crate::prover::Prover;
-use crate::utils::gen_x;
-use rand_core::OsRng;
-
-mod matrix;
 /// For matrix A and B, C = A · B.
 ///
 /// How can one verify that two matrices were multiplied correctly.
 /// First,choose a random `r∈Fp`,and let x=(1,r,r2,...,rn−1).
 /// Then compute `y=Cx` and `z=A·Bx`,outputting YES if y = z and NO otherwise.
+mod matrix;
 mod prover;
 mod utils;
 mod verifier;
 
+use crate::matrix::Matrix;
+use crate::prover::Prover;
+use crate::utils::gen_x;
+use rand_core::OsRng;
+
 #[test]
 fn completeness() {
     let n: usize = std::env::var("n")
@@ -26,7 +26,7 @@ fn completeness() {
     let c = alice.matrix_multiplication();
 
     let x = gen_x(OsRng, n);
-    // z=A·Bx
+    // z=A·(Bx)
     let z = alice.hash(&x);
 
     // verify

2_Freivalds_Algorithm/src/matrix.rs

@@ -1,6 +1,6 @@
 use bls12_381::Scalar;
 use ff::Field;
-use rand_core::{OsRng, RngCore};
+use rand_core::OsRng;
 use std::ops::AddAssign;
 
 /// This define `matrix` (rows * cols) （m × n）
@@ -98,6 +98,7 @@ impl Matrix {
 mod test {
     use crate::matrix::Matrix;
     use bls12_381::Scalar;
+    use ff::PrimeField;
 
     #[test]
     fn test_random_matrix() {
@@ -154,4 +155,18 @@ mod test {
         assert_eq!(row_1, res);
         println!("{:#?}", res);
     }
+
+    #[test]
+    fn test() {
+        let n = 2;
+        let A = Matrix::random(n, n);
+        let B = Matrix::random(n, n);
+        let x = vec![Scalar::from_u128(3), Scalar::from_u128(5)];
+
+        // A*B*x
+        let res1 = Matrix::mul(&A, &B).matrix_mul_vec(&x);
+        // A*(B*x)
+        let res2 = A.matrix_mul_vec(&B.matrix_mul_vec(&x));
+        assert_eq!(res1, res2);
+    }
 }

2_Freivalds_Algorithm/src/prover.rs

@@ -20,9 +20,9 @@ impl Prover {
     }
 
     pub fn hash(&self, x: &Vec<Scalar>) -> Vec<Scalar> {
-        // tmp = Ax
-        let tmp = self.a.matrix_mul_vec(x);
-        // z = B temp
-        self.b.matrix_mul_vec(&tmp)
+        // tmp = Bx
+        let tmp = self.b.matrix_mul_vec(x);
+        // z = A temp = A(Bx)
+        self.a.matrix_mul_vec(&tmp)
     }
 }

2_Reed_Solomon_Fingerprinting/src/lib.rs

@@ -1,16 +1,16 @@
-use crate::prover::Prover;
 /// The Reed-Solomon Fingerprinting case(2.1) in chapter 2
 /// In this case, we'll check whether Alice and Bob has the same file by checking RS-fingerprint.
+mod prover;
+mod utils;
+mod verify;
+
+use crate::prover::Prover;
 use crate::utils::{dump_field_data, read_from_file};
 use crate::verify::Verifier;
 use bls12_381::Scalar;
 use ff::Field;
 use rand_core::{OsRng, RngCore};
 
-mod prover;
-mod utils;
-mod verify;
-
 #[derive(Default, Eq, PartialEq)]
 pub(crate) struct Person {
     data: Vec<Scalar>,