C++ Program to Implement the Solovay-Strassen Primality Test to Check if a Given Number is Prime

Solovay-Strassen Primality Test is used to test a number whether it is a composite or possibly prime number.

Algorithms

Begin
   Declare a function modulo to the long datatype to perform binary calculation.
      Declare m_base, m_exp, m_mod of long datatype and pass them as a parameter.
      Declare two variables a, b of long datatype.
         Initialize a = 1, b = m_base.
      while (m_exp > 0) do
         if (m_exp % 2 == 1) then
            a = (a * b) % m_mod.
         b = (b * b) % m_mod.
         m_exp = m_exp / 2.
      Return a % m_mod.
End
Begin
   Declare a function Jecobian of the int datatype to calculate Jacobian symbol of a given number.
   Declare CJ_a, CJ_n of the long datatype and pass them as a parameter.
   if (!CJ_a) then
      return 0.
   Declare answer of the integer datatype.
      Initialize answer = 1.
   if (CJ_a < 0) then
      CJ_a = -CJ_a.
      if (CJ_n % 4 == 3) then
         answer = -answer.
   if (CJ_a == 1) then
      return answer.
   while (CJ_a) do
      if (CJ_a < 0) then
         CJ_a = -CJ_a.
         if (CJ_n % 4 == 3) then
         answer = -answer.
   while (CJ_a % 2 == 0) do
      CJ_a = CJ_a / 2;
      if (CJ_n % 8 == 3 || CJ_n % 8 == 5) then
         answer = -answer.
   swap(CJ_a, CJ_n)
   if (CJ_a % 4 == 3 && CJ_n % 4 == 3) then
      answer = -answer.
         CJ_a = CJ_a % CJ_n;
   if (CJ_a > CJ_n / 2) then
      CJ_a = CJ_a - CJ_n.
   if (CJ_n == 1) then
      return answer.
End
Begin
   Declare a function Solovoystrassen to the Boolean datatype to perform the Solovay-Strassen Primality Test.
      Declare SS_p to the long datatype and pass as a parameter.
      Declare itr to the integer datatype and pass them as a parameter.
      if (SS_p < 2) then
         return false.
      if (SS_p != 2 && SS_p % 2 == 0) then
         return false.
      for (int i = 0; i < itr; i++)
         long a = rand() % (SS_p - 1) + 1;
         long jacob = (SS_p + Jacobian(a, SS_p)) % SS_p;
         long mod = modulo(a, (SS_p - 1) / 2, SS_p);
      if (!jacob || mod != jacob) then
         return false
      return true.
End
Begin
   Declare iter of the integer datatype.
      Initialize iter = 50.
   Declare num1, num2 of the long datatype.
   Print “Enter the first number:”
   Input the value of num1.
   if (Solovoystrassen(num1, iter)) then
      print the value of num1 and ”is a prime number”.
   Else
      print the value of num1 and ”is a composite number”.
   Print “Enter another number:”
      Input the value of num2.
   if (Solovoystrassen(num2, iter)) then
      print the value of num2 and ”is a prime number”.
   Else
      print the value of num2 and ”is a composite number”.
End.

Example

#include<iostream>
#include <bits/stdc++.h>
using namespace std;
long modulo(long m_base, long m_exp, long m_mod) // modulo
function to perform binary calculation {
   long a = 1;
   long b = m_base;
   while (m_exp > 0) {
      if (m_exp % 2 == 1)
         a = (a * b) % m_mod;
      b = (b * b) % m_mod;
      m_exp = m_exp / 2;
   }
   return a % m_mod;
}
int Jacobian(long CJ_a, long CJ_n) { // calculate Jacobian symbol of a given number 
   if (!CJ_a)
      return 0;// (0/n) = 0
   int answer = 1;
   if (CJ_a < 0) {
      CJ_a = -CJ_a; // (a/n) = (-a/n)*(-1/n)
      if (CJ_n % 4 == 3)
         answer = -answer; // (-1/n) = -1 if n = 3 (mod 4)
   }
   if (CJ_a == 1)
      return answer; // (1/n) = 1
   while (CJ_a)  {
      if (CJ_a < 0) {
         CJ_a = -CJ_a; // (a/n) = (-a/n)*(-1/n)
         if (CJ_n % 4 == 3)
            answer = -answer; // (-1/n) = -1 if n = 3 (mod 4)
      }
      while (CJ_a % 2 == 0) {
         CJ_a = CJ_a / 2;
         if (CJ_n % 8 == 3 || CJ_n % 8 == 5)
            answer = -answer;
      }
      swap(CJ_a, CJ_n);
      if (CJ_a % 4 == 3 && CJ_n % 4 == 3)
         answer = -answer;
      CJ_a = CJ_a % CJ_n;
         if (CJ_a > CJ_n / 2)
            CJ_a = CJ_a - CJ_n;
   }
   if (CJ_n == 1)
      return answer;
   return 0;
}
bool Solovoystrassen(long SS_p, int itr) { //perform the Solovay- Strassen Primality Test
   if (SS_p < 2)
      return false;
   if (SS_p != 2 && SS_p % 2 == 0)
      return false;
   for (int i = 0; i < itr; i++) {
      // Generate a random number a
      long a = rand() % (SS_p - 1) + 1;
      long jacob = (SS_p + Jacobian(a, SS_p)) % SS_p;
      long mod = modulo(a, (SS_p - 1) / 2, SS_p);
      if (!jacob || mod != jacob)
         return false;
   }
   return true;
}
// Driver Code
int main() {
   int iter = 50;
   long num1;
   long num2;
   cout<< "Enter the first number: ";
   cin>>num1;
   cout<<endl;
   if (Solovoystrassen(num1, iter))
      cout<<num1<<" is a prime number\n"<<endl;
   else
      cout<<num1<<" is a composite number\n"<<endl;
      cout<<"Enter another number: ";
   cin>>num2;
   cout<<endl;
   if (Solovoystrassen(num2, iter))
      cout<<num2<<" is a prime number\n"<<endl;
   else
      cout<<num2<<" is a composite number\n"<<endl;
   return 0;
}

Output

Enter the first number: 24
24 is a composite number
Enter another number: 23
23 is a prime number