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/*
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This is the java implementation of classic Coppersmith-Freivalds’ algorithm to check whether
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the multiplication of matrix A and B equals the given matrix C. It does it by checking A*(B*r)-(C*r) where r
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is any random column vector consisting only 0/1 as its elements. If this value is zero algorithm prints Yes, No otherwise.
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*/
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//This is a sample program to check whether the matrix c is equal to the multiplication of a and b
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//implementation of Coppersmith Freivalds Algorithm
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import java.util.Random;
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import java.util.Scanner;
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public class Coppersmith_Freivalds_Algorithm
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{
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public static void main(String args[])
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{
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System.out.println("Enter the dimesion of the matrices: ");
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Scanner input = new Scanner(System.in);
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int n = input.nextInt();
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System.out.println("Enter the 1st matrix: ");
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double a[][] = new double[n][n];
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for(int i=0; i<n; i++)
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{
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for(int j=0; j<n; j++)
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{
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a[i][j] = input.nextDouble();
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}
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}
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System.out.println("Enter the 2st matrix: ");
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double b[][] = new double[n][n];
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for(int i=0; i<n; i++)
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{
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for(int j=0; j<n; j++)
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{
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b[i][j] = input.nextDouble();
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}
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}
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System.out.println("Enter the result matrix: ");
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double c[][] = new double[n][n];
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for(int i=0; i<n; i++)
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{
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for(int j=0; j<n; j++)
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{
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c[i][j] = input.nextDouble();
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}
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}
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//random generation of the r vector containing only 0/1 as its elements
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double [][]r = new double[n][1];
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Random random = new Random();
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for(int i=0; i<n; i++)
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{
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r[i][0] = random.nextInt(2);
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}
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//test A * (b*r) - (C*) = 0
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double br[][] = new double[n][1];
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double cr[][] = new double[n][1];
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double abr[][] = new double[n][1];
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br = multiplyVector(b, r, n);
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cr = multiplyVector(c, r, n);
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abr = multiplyVector(a, br, n);
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//check for all zeros in abr
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boolean flag = true;
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for(int i=0; i<n; i++)
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{
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if(abr[i][0] == 0)
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continue;
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else
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flag = false;
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}
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if(flag == true)
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System.out.println("Yes");
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else
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System.out.println("No");
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input.close();
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}
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public static double[][] multiplyVector(double[][] a, double[][] b, int n)
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{
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double result[][] = new double[n][1];
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for (int i = 0; i < n; i++)
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{
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for (int j = 0; j < 1; j++)
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{
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for (int k = 0; k < n; k++)
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{
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result[i][j] = result[i][j] + a[i][k] * b[k][j];
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}
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}
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}
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return result;
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}
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}
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/*
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Output:
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Enter the dimesion of the matrices:
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2
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Enter the 1st matrix:
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2 3
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3 4
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Enter the 2st matrix:
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1 0
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1 2
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Enter the result matrix:
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6 5
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8 7
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