Encryption for distributed Boneh-Franklin IBC

void encrypt20(unsigned char * message, char * rid){
  unsigned char u[128], v[20], w[20], tv[20], tw[20];
  unsigned char sig[20], r[20];
  int i;
  element_t temp1;

  element_random(h2gt);
  hash2(sig);                           //    sig now has a random number
                                        //sig = {0,1}l
  hash3(sig, message);                  //    h3zr ~ r
                                        //r = H3(sig, M)
  hash1(rid);                           //hid = H1(ID) ~ ~ h1 = H1(rid)

  element_init_G1(g, pairing);
  element_random(g);

  element_t U;
  element_init_G1(U, pairing);
  element_pow_zn(U, g, h3zr);           //U = g ^ r, then u = U

  element_init_GT(temp1, pairing);
  pairing_apply(temp1, U, h1, pairing); //temp1 = e(U, h1) = e(g^r,hid)
  element_pow_zn(h2gt, temp1, h3zr);    //h2gt = temp1^h3zr ~~ h2gt=temp1^r
  hash2(tv);                            //tv = H2(h3zr) ~ H2(e(g^r,hid)^r)
  for(i=0;i<20;i++){
    v[i] = sig[i]^tv[i];
  }                                     //v = sig XOR tv
  hash4(sig, tw);                       //tw = H4(sig)
  for(i=0;i<20;i++){
    w[i] = message[i]^tw[i];
  }                                     //w = message XOR tw
  element_to_bytes(u, U);
}