rsa repeated key generation

[jeanpaulw]

Hi, i try to génératre 10 rsa public and privat keys, i get only a repetition of keys, it génerate the same keys,


please would any one help me.

  #include <iostream>
#include <gmpxx.h>
#include <time.h>
#include <string.h>

#define SIZE 100
#define MPZ_T(X) mpz_t X;mpz_init(X)
#define GMP_RANDSTATE_T(X) gmp_randstate_t X;gmp_randinit_default(X);
#define SEPARATEUR ";"
using namespace std;

void keygen(mpz_t & N, mpz_t & C, mpz_t & U);
void randomPrime(mpz_t &prime, int nb, gmp_randstate_t &state);
string encrypt(mpz_t &N, mpz_t &C, string message);
string decrypt(mpz_t &N, mpz_t &U, string message);

int main(int argc, char *argv[])
{
   // string message = "12345678901234567890123456789012345678901234567890123456789012345678901234567890";
   // cout << message << endl;

    //Création des trois variables de type 'mpz_t' qui forment la clée public et la clée privée :

   MPZ_T(N);
    MPZ_T(C);
    MPZ_T(U);

    for(int i = 1; i< 10; i++){


            cout  << "-----------"<<endl;


    keygen(N, C, U);
       cout  << i<<"-----------"<<endl;

    }



//string message2;
   // message2 = encrypt(N, C, message);
     //cout  << endl;
      //cout  << endl;
 //cout << message2 << endl;
 //cout  << endl;
 // cout  << endl;

   // message = decrypt(N, U, message2);
   // cout << message << endl;

    return 0;
}

void keygen(mpz_t & N, mpz_t & C, mpz_t & U)
{
    GMP_RANDSTATE_T(state);
    gmp_randseed_ui(state, (int)time(NULL));

    MPZ_T(P);
    MPZ_T(Q);
    MPZ_T(P2);
    MPZ_T(Q2);
    MPZ_T(M);

    randomPrime(P, SIZE, state);
    randomPrime(Q, SIZE, state);
    mpz_mul(N, P, Q);

    mpz_sub_ui(Q2, Q, 1);
    mpz_sub_ui(P2, P, 1);
    mpz_mul(M, P2, Q2);

    mpz_clear(P2);
    mpz_clear(Q2);

    randomPrime(C, SIZE/2, state);
    mpz_invert(U, C, M);

    mpz_clear(P);
    mpz_clear(Q);
    mpz_clear(M);

     gmp_printf("N : %Zd \n", N);
     gmp_printf("C : %Zd \n", C);
     gmp_printf("U : %Zd \n", U);


    return;
}

void randomPrime(mpz_t & prime, int nb, gmp_randstate_t &state) //Retourne un nombre premier d'une valeur maximal de 'nb'
{
    MPZ_T(rand);
    MPZ_T(sub_rand);
    MPZ_T(max);

    mpz_ui_pow_ui(max, 10, nb);
    MPZ_T(limite);
    mpz_ui_pow_ui(limite, 10, nb-1);
    mpz_mul_ui(limite, limite, 9);

    mpz_urandomm(rand, state, limite);
    mpz_sub(sub_rand, max, rand);
    mpz_nextprime(prime, sub_rand);

    return;
}

string encrypt(mpz_t &N, mpz_t &C, string message)
{
    string encryptMessage;
    MPZ_T(nb);
    for(int i = 0; i < message.size(); i++)
    {
        mpz_set_ui(nb, (int)message[i]);
        mpz_powm(nb, nb, C, N);
        encryptMessage += mpz_class(nb).get_str(10) + SEPARATEUR;
    }
    return encryptMessage;
}

string decrypt(mpz_t & N, mpz_t & U, string message)
{
    string decryptMessage;
    int start = -1, end = message.find(";", 1);
    MPZ_T(current);

    while(end != -1)
    {
        mpz_set_str(current, message.substr(start+1, end-start-1).c_str(), 10); //Extrait le nombre d'entre les deux séparateur
        mpz_powm(current, current, U, N);
        decryptMessage += (char)mpz_get_ui(current);
        start = message.find(SEPARATEUR, start + 1);
        end = message.find(SEPARATEUR, end + 1);
    }
    return decryptMessage;
}

[Enoizat]

I'm pretty sure you've already solved your issue. Anyway...

, i get only a repetition of keys, it génerate the same keys

I don’t know that library, but in ‘traditional’ RNG usually the number generator is initialised only once. Initialising an RNG to time() means the seed remain the same if subsequent calls happen in a very short lapse of time.

The official documentation of gmp_randseed_ui() says something similar:
https://gmplib.org/manual/Random-State-Seeding.html

Traditionally the system time has been used to seed, but care needs to be taken with this. If an application seeds often and the resolution of the system clock is low, then the same sequence of numbers might be repeated.

I don’t know if that’s the problem you’re facing, but you could try:
a) to initialise your RNG only when needed (inside main() or another function you call just once before generating your first key);
b) if you use a POSIX system, to initialise your engine to /dev/random (read the instruction).

I don’t know if this can be of any help.
Good luck.

[jeanpaulw]

Hi, not yet