This is a C++ Program to genrate random numbers using Naor-Reingold random function. Moni Naor and Omer Reingold described efficient constructions for various cryptographic primitives in private key as well as public-key cryptography. Their result is the construction of an efficient pseudorandom function. Let p and l be prime numbers with l |p-1. Select an element g ? {\mathbb F_p}^* of multiplicative order l. Then for each n-dimensional vector a = (a1, …, an)? (\mathbb F_{l})^{n} they define the function

f_{a}(x) = g^{a_{1}^{x_{1}} a_{2}^{x_{2}}…a_{n}^{x_{n}}} \in \mathbb F_p

where x = x1 … xn is the bit representation of integer x, 0 = x = 2^n-1, with some extra leading zeros if necessary.

Here is source code of the C++ Program to Implement Naor-Reingold Pseudo Random Function. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

`#include <iostream>`

`#include <math.h>`

`#include <stdlib.h>`

using namespace std;

int main(int argc, char **argv)

`{`

int p = 7, l = 3, g = 2, n = 4, x;

int a[] = { 1, 2, 2, 1 };

int bin[4];

cout << "The Random numbers are: ";

for (int i = 0; i < 10; i++)

`{`

x = rand() % 16;

for (int j = 3; j >= 0; j--)

`{`

bin[j] = x % 2;

x /= 2;

`}`

int mul = 1;

for (int k = 0; k < 4; k++)

mul *= pow(a[k], bin[k]);

cout << pow(g, mul)<<" ";

`}`

`}`

Output:

$ g++ Naor-Reingold.cpp $ a.out The Random numbers are: 2 4 16 4 2 4 16 16 4 2

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