The result of the encrypted message after implementing RSA is 0 using the GMP library

Question

I am using the GMP library functions in order to implement the RSA algorithm. Here is my code:

const char* random_String() {
    srand (time(NULL)); 
    const char * tab[] = {"Alice", "Bob", "encryption", "decryption"};
    std::cout << sizeof(tab)/sizeof(tab[0]) << std::endl;
    int indice = rand() % (sizeof(tab)/sizeof(tab[0]));
    
    return tab[indice];
}


int main()
{
    mpz_init(d);
    mpz_init(e);
    mpz_init(n);
    
    mpz_init(M);
    mpz_init(c);
    
 
    /* This function creates the keys. The basic algorithm is...
     *
     *  1. Generate two large distinct primes p and q randomly
     *  2. Calculate n = pq and x = (p-1)(q-1)
     *  3. Select a random integer e (1<e<x) such that gcd(e,x) = 1
     *  4. Calculate the unique d such that ed = 1(mod x)
     *  5. Public key pair : (e,n), Private key pair : (d,n)
     *
     */
   mpz_t p,q,op;
   mpz_init(p);
   mpz_init(q);
   mpz_init(op);
    
   char p_str[1000];
   char q_str[1000];
    
   mpz_init_set_str(op, "7060", 10);
   mpz_nextprime(p, op);
   mpz_get_str(p_str,10,p);
   
   mpz_init_set_str(op, "7874", 10);
   mpz_nextprime(q, op);
   mpz_get_str(q_str, 10, q);
   
   std::cout << "Random Prime 'p' = " << p_str <<  std::endl;
   std::cout << "Random Prime 'q' = " << q_str <<  std::endl;

    char n_str[1000];
    mpz_t x;
    mpz_init(x);

    mpz_mul(n,p,q);
    mpz_get_str(n_str,10,n);
    std::cout << "\t n = " << n_str << std::endl;
    
    mpz_t p_minus_1,q_minus_1;
    mpz_init(p_minus_1);
    mpz_init(q_minus_1);

    mpz_sub_ui(p_minus_1,p,(unsigned long int)1);
    mpz_sub_ui(q_minus_1,q,(unsigned long int)1);

    mpz_mul(x,p_minus_1,q_minus_1);
    char phi_str[1000];
    mpz_get_str(phi_str,10,x);
    std::cout << "\t phi(n) = " << phi_str << std::endl;

    mpz_init_set_str(e, "79", 0);
    char e_str[1000];
    mpz_get_str(e_str,10,e);
    std::cout << "\t e = " << e_str << std::endl;
     
    mpz_invert(d, e, x);
    char d_str[1000];
    mpz_get_str(d_str,10,d);
    std::cout << "\t d = " << d_str << std::endl << std::endl;


    std::cout << "Public Keys  (e,n): ( " << e_str <<" , " << n_str << " )" << std::endl;
    std::cout << "Private Keys (d,n): ( " << d_str <<" , " << n_str << " )" << std::endl;
    

    const char* mess = random_String();
    char c_str[1000];

    std::cout << "The message: : " << mess << std::endl;
    mpz_set_str(M, mess, 10);
    mpz_powm(c, M, e, n);
    mpz_get_str(c_str, 10, c);
    std::cout << "The encrypted message: " << c_str << std::endl;
  
}

During the last 5 lines of the code, I encrypt the message with the values that were previously computed and by following the RSA formulas of encryption. The result of the encrypted message is 0, which means that the result of c_str is 0. How comes that it is 0?

Answer 1

This code

mpz_set_str(M, mess, 10);

converts the random string mess to an integer. For this to work the string must consist of decimal digits, but this is not true for any of your random strings. So the function fails and M is unchanged.

If you check the return value of mpz_set_str you will see that it is -1 meaning the function failed.

Basically your conversion to and from your message to an integer will only work if the message is a decimal number. To convert arbitrary strings you should be using the mpz_import and mpz_export functions instead of mpz_set_str and mpz_get_str.