C++ Program to Implement Solovay-Strassen Primality Test

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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.

  1. /* 
  2.  * C++ Program to Implement Solovay-Strassen Primality Test
  3.  */
  4. #include <cstring>
  5. #include <iostream>
  6. #include <cstdlib>
  7. #define ll long long
  8. using namespace std;
  9. /* 
  10.  * modular exponentiation
  11.  */
  12. ll modulo(ll base, ll exponent, ll mod)
  13. {
  14.     ll x = 1;
  15.     ll y = base;
  16.     while (exponent > 0)
  17.     {
  18.         if (exponent % 2 == 1)
  19.             x = (x * y) % mod;
  20.         y = (y * y) % mod;
  21.         exponent = exponent / 2;
  22.     }
  23.     return x % mod;
  24. }
  25. /* 
  26.  * calculates Jacobian(a/n) n>0 and n is odd 
  27.  */
  28. int calculateJacobian(ll a,ll n)
  29. {
  30.     if (!a) 
  31.         return 0;
  32.     int ans = 1;
  33.     ll temp;
  34.     if (a < 0)
  35.     {
  36.         a = -a;
  37.         if (n % 4 == 3) 
  38.             ans=-ans; 
  39.     }
  40.     if (a == 1) 
  41.         return ans;
  42.     while (a)
  43.     {
  44.         if (a < 0)
  45.         {
  46.             a = -a;
  47.             if (n % 4 == 3) 
  48.                 ans = -ans;  
  49.         }
  50.         while (a % 2 == 0)
  51.         {
  52.             a = a / 2;
  53.             if (n % 8 == 3 || n % 8 == 5) 
  54.                 ans = -ans;    
  55.         }
  56.         swap(a, n);
  57.         if (a % 4 == 3 && n % 4 == 3) 
  58.             ans = -ans;
  59.         a = a % n;
  60.         if (a > n / 2) 
  61.             a = a - n; 
  62.     }
  63.     if (n == 1) 
  64.         return ans;
  65.     return 0; 
  66. }
  67.  
  68. /* 
  69.  * Solovay-Strassen Primality Test
  70.  * Iterations determine the accuracy of the test 
  71.  */
  72. bool Solovoy(ll p, int iteration)
  73. {
  74.     if (p < 2) 
  75.         return false;
  76.     if (p != 2 && p % 2 == 0) 
  77.         return false;
  78.     for (int i = 0; i < iteration; i++)
  79.     {
  80.         ll a = rand() % (p - 1) + 1;
  81.         ll jacobian = (p + calculateJacobian(a, p)) % p;
  82.         ll mod = modulo(a, (p - 1) / 2, p);
  83.         if (!jacobian || mod != jacobian)
  84.         { 
  85.             return false;
  86.         }
  87.     }
  88.     return true;
  89. }
  90. //Main
  91. int main()
  92. {
  93.     int iteration = 50;
  94.     ll num;
  95.     cout<<"Enter integr to test primality: ";
  96.     cin>>num;
  97.     if (Solovoy(num, iteration))
  98.         cout<<num<<" is prime"<<endl;
  99.     else
  100.         cout<<num<<" is not prime"<<endl;
  101.     return 0;
  102. }

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$ 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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn