C++ Program to Implement Solovay-Strassen Primality Test

This C++ Program demonstrates the implementation of Solovay-Strassen Primality Test.

Here is source code of the C++ Program to demonstrate the implementation of Solovay-Strassen 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 Solovay-Strassen Primality Test

```
 */
```
```
#include <cstring>
```
```
#include <iostream>
```
```
#include <cstdlib>
```
```
#define ll long long
```
```
using namespace std;
```
```
/* 
```
```
 * modular exponentiation
```
```
 */
```
```
ll modulo(ll base, ll exponent, ll mod)
```
```
{
```
```
    ll x = 1;
```
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    ll y = base;
```
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    while (exponent > 0)
```
```
    {
```
```
        if (exponent % 2 == 1)
```
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            x = (x * y) % mod;
```
```
        y = (y * y) % mod;
```
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        exponent = exponent / 2;
```
```
    }
```
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    return x % mod;
```
```
}
```
```
/* 
```

 * calculates Jacobian(a/n) n>0 and n is odd

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 */
```
```
int calculateJacobian(ll a,ll n)
```
```
{
```
```
    if (!a) 
```
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        return 0;
```
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    int ans = 1;
```
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    ll temp;
```
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    if (a < 0)
```
```
    {
```
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        a = -a;
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        if (n % 4 == 3) 
```
```
            ans=-ans; 
```
```
    }
```
```
    if (a == 1) 
```
```
        return ans;
```
```
    while (a)
```
```
    {
```
```
        if (a < 0)
```
```
        {
```
```
            a = -a;
```
```
            if (n % 4 == 3) 
```
```
                ans = -ans;  
```
```
        }
```
```
        while (a % 2 == 0)
```
```
        {
```
```
            a = a / 2;
```

            if (n % 8 == 3 || n % 8 == 5)

```
                ans = -ans;    
```
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        }
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        swap(a, n);
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        if (a % 4 == 3 && n % 4 == 3) 
```
```
            ans = -ans;
```
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        a = a % n;
```
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        if (a > n / 2) 
```
```
            a = a - n; 
```
```
    }
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```
    if (n == 1) 
```
```
        return ans;
```
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    return 0; 
```
```
}
```
```
 
```
```
/* 
```
```
 * Solovay-Strassen Primality Test
```

 * Iterations determine the accuracy of the test

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

        ll jacobian = (p + calculateJacobian(a, p)) % p;

        ll mod = modulo(a, (p - 1) / 2, p);

        if (!jacobian || mod != jacobian)

```
        { 
```
```
            return false;
```
```
        }
```
```
    }
```
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    return true;
```
```
}
```
```
//Main
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int main()
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{
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    int iteration = 50;
```
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    ll num;
```

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

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

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

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

$ g++ solovay_strassen.cpp
$ a.out
 
Enter integr to test primality: 219891801103773
219891801103773 is not prime
 
------------------
(program exited with code: 1)
Press return to continue

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