C++ Program to Implement Naor-Reingold Pseudo Random Function

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];
```
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    cout << "The Random numbers are: ";
```
```
    for (int i = 0; i < 10; i++)
```
```
    {
```
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        x = rand() % 16;
```
```
        for (int j = 3; j >= 0; j--)
```
```
        {
```
```
            bin[j] = x % 2;
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            x /= 2;
```
```
        }
```
```
        int mul = 1;
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```
        for (int k = 0; k < 4; k++)
```
```
            mul *= pow(a[k], bin[k]);
```
```
        cout << pow(g, mul)<<" ";
```
```
    }
```
```
}
```

Output:

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

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