Miller Rabin Primality Test in C++

This C++ Program demonstrates the implementation of Miller Rabin Primality Test.

Here is source code of the C++ Program to demonstrate the implementation of Miller Rabin Primality Test. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
/* 
```

 * C++ Program to Implement Miller Rabin Primality Test

```
 */
```
```
#include <iostream>
```
```
#include <cstring>
```
```
#include <cstdlib>
```
```
#define ll long long
```
```
using namespace std;
```
```
 
```
```
/* 
```

 * calculates (a * b) % c taking into account that a * b might overflow

```
 */
```
```
ll mulmod(ll a, ll b, ll mod)
```
```
{
```
```
    ll x = 0,y = a % mod;
```
```
    while (b > 0)
```
```
    {
```
```
        if (b % 2 == 1)
```
```
        {    
```
```
            x = (x + y) % mod;
```
```
        }
```
```
        y = (y * 2) % mod;
```
```
        b /= 2;
```
```
    }
```
```
    return x % mod;
```
```
}
```
```
/* 
```
```
 * modular exponentiation
```
```
 */
```
```
ll modulo(ll base, ll exponent, ll mod)
```
```
{
```
```
    ll x = 1;
```
```
    ll y = base;
```
```
    while (exponent > 0)
```
```
    {
```
```
        if (exponent % 2 == 1)
```
```
            x = (x * y) % mod;
```
```
        y = (y * y) % mod;
```
```
        exponent = exponent / 2;
```
```
    }
```
```
    return x % mod;
```
```
}
```
```
 
```
```
/*
```

 * Miller-Rabin primality test, iteration signifies the accuracy

```
 */
```
```
bool Miller(ll p,int iteration)
```
```
{
```
```
    if (p < 2)
```
```
    {
```
```
        return false;
```
```
    }
```
```
    if (p != 2 && p % 2==0)
```
```
    {
```
```
        return false;
```
```
    }
```
```
    ll s = p - 1;
```
```
    while (s % 2 == 0)
```
```
    {
```
```
        s /= 2;
```
```
    }
```
```
    for (int i = 0; i < iteration; i++)
```
```
    {
```

        ll a = rand() % (p - 1) + 1, temp = s;

```
        ll mod = modulo(a, temp, p);
```

        while (temp != p - 1 && mod != 1 && mod != p - 1)

```
        {
```
```
            mod = mulmod(mod, mod, p);
```
```
            temp *= 2;
```
```
        }
```

        if (mod != p - 1 && temp % 2 == 0)

```
        {
```
```
            return false;
```
```
        }
```
```
    }
```
```
    return true;
```
```
}
```
```
//Main
```
```
int main()
```
```
{
```
```
    int iteration = 5;
```
```
    ll num;
```

    cout<<"Enter integer to test primality: ";

```
    cin>>num;
```
```
    if (Miller(num, iteration))
```
```
        cout<<num<<" is prime"<<endl;
```
```
    else
```

        cout<<num<<" is not prime"<<endl;

```
    return 0;
```
```
}
```

$ g++ miller_rabin.cpp
$ a.out
 
Enter integer to test primality: 127
127 is prime
 
------------------
(program exited with code: 1)
Press return to continue

Sanfoundry Global Education & Learning Series – 1000 C++ Programs.

If you wish to look at all C++ Programming examples, go to C++ Programs.

« Prev - Modular Exponentiation Algorithm in C++

» Next - C++ Program to Implement Radix Sort

Related Posts:

Recommended Articles: