#include <pbc.h>
#include "pbc_fp.h"
#include "pbc_test.h"

int main(void) {
  mpz_t p, q, N, d;
  mpz_t dmp1, dmq1;
  mpz_t ipmq, iqmp;
  mpz_t adq, adp;

  field_t f;
  element_t a, b;
  double t0, t1, tnaive = 0, tcrt=0;
  int i, n;

  mpz_init(p);
  mpz_init(q);
  mpz_init(N);
  mpz_init(d);
  mpz_init(dmp1);
  mpz_init(dmq1);
  mpz_init(ipmq);
  mpz_init(iqmp);
  mpz_init(adp);
  mpz_init(adq);
  pbc_mpz_randomb(p, 512);
  pbc_mpz_randomb(q, 512);
  mpz_nextprime(p, p);
  mpz_nextprime(q, q);
  mpz_mul(N, p, q);
  mpz_invert(ipmq, p, q);
  mpz_invert(iqmp, q, p);

  field_init_fp(f, N);
  element_init(a, f);
  element_init(b, f);
  n = 10;
  for (i=0; i<n; i++) {
    pbc_mpz_random(d, N);
    element_random(a);
    t0 = pbc_get_time();
    element_pow_mpz(b, a, d);
    t1 = pbc_get_time();
    tnaive += t1 - t0;

    mpz_sub_ui(p, p, 1);
    mpz_sub_ui(q, q, 1);

    mpz_mod(dmp1, d, p);
    mpz_mod(dmq1, d, q);

    mpz_add_ui(p, p, 1);
    mpz_add_ui(q, q, 1);

    element_to_mpz(adq, a);
    element_to_mpz(adp, a);

    t0 = pbc_get_time();
    mpz_powm(adp, adp, d, p);
    mpz_powm(adq, adq, d, q);

    /* textbook CRT
    mpz_mul(adp, adp, q);
    mpz_mul(adp, adp, iqmp);
    mpz_mul(adq, adq, p);
    mpz_mul(adq, adq, ipmq);
    mpz_add(adp, adp, adq);
    */
    // Garner's algorithm
    mpz_sub(adq, adq, adp);
    mpz_mul(adq, adq, ipmq);
    mpz_mod(adq, adq, q);
    mpz_mul(adq, adq, p);
    mpz_add(adp, adp, adq);

    t1 = pbc_get_time();
    tcrt += t1 - t0;
    element_set_mpz(b, adp);
  }
  printf("average RSA exp time = %lf\n", tnaive / n);
  printf("average RSA exp time (CRT) = %lf\n", tcrt / n);
  return 0;
}