Naor-Reingold Pseudo-Random Function is a function of generating random numbers. Moni Naor and Omer Reingold described efficient constructions for various cryptographic primitives in the private key as well as public-key cryptography.
Example:
Input : N = 5 Output: 9.0, 9.0, 3.0, 9.0, 3.0 Input : N = 7 Output: 9.0, 81.0, 9.0, 9.0, 3.0, 3.0, 9.0
Algorithm:
- Declare the variables p, l, g, n, x and arrays a[] and arr[]
- Take input from the user for generating random numbers
- Generate random numbers and use the defined approach:
Let p and l be prime numbers with l|p−1. Select an element g ε Fp* of multiplicative order l. Then for each n-dimensional vector a = (a0,a1, ..., an). They define the function as: fa(x)=ga0.a1x1a2x2…..anxn ε Fp
- Print the random numbers
Below is the implementation of the Naor-Reingold Pseudo-Random Function:
Java
// Java Program to Implement Naor-Reingold// Pseudo Random Functionimport java.util.*;public class Main {    public static void randomNumbers()    {        // Creating arrays and defining variables        int p = 7, l = 2, g = 3, n = 6, x;          int a[] = { 1, 2, 2, 1 };          int arr[] = new int[4];          Random random = new Random();          int num = 10;        System.out.println("The Random numbers are: ");          // Generating Random Numbers using        // Naor-Reingold Pseudo Random Function approach        for (int i = 0; i < num; i++) {            x = random.nextInt(num) % 16;              for (int j = 3; j >= 0; j--) {                arr[j] = x % 2;                x /= 2;            }            int mult = 1;              for (int k = 0; k < 4; k++) {                mult *= Math.pow(a[k], arr[k]);            }            System.out.print(Math.pow(g, mult) + ", ");        }    }    public static void main(String args[])    {        randomNumbers();    }} |
Output
The Random numbers are: 9.0, 9.0, 3.0, 81.0, 3.0, 81.0, 9.0, 9.0, 3.0, 3.0,
