void ecdhDecode(ecdhTuple & masked, const key & sharedSec) {
     key sharedSec1 = hash_to_scalar(sharedSec);
     key sharedSec2 = hash_to_scalar(sharedSec1);
     //decode
     sc_sub(masked.mask.bytes, masked.mask.bytes, sharedSec1.bytes);
     sc_sub(masked.amount.bytes, masked.amount.bytes, sharedSec2.bytes);
 }
 bool crypto_ops::check_signature(const hash &prefix_hash, const public_key &pub, const signature &sig) {
   ge_p2 tmp2;
   ge_p3 tmp3;
   ec_scalar c;
   s_comm buf;
   assert(check_key(pub));
   buf.h = prefix_hash;
   buf.key = pub;
   if (ge_frombytes_vartime(&tmp3, &pub) != 0) {
     abort();
   }
   if (sc_check(&sig.c) != 0 || sc_check(&sig.r) != 0) {
     return false;
   }
   ge_double_scalarmult_base_vartime(&tmp2, &sig.c, &tmp3, &sig.r);
   ge_tobytes(&buf.comm, &tmp2);
   hash_to_scalar(&buf, sizeof(s_comm), c);
   sc_sub(&c, &c, &sig.c);
   return sc_isnonzero(&c) == 0;
 }
  bool crypto_ops::check_ring_signature(const hash &prefix_hash, const key_image &image,
    const public_key *const *pubs, size_t pubs_count,
    const signature *sig) {
    size_t i;
    ge_p3 image_unp;
    ge_dsmp image_pre;
    ec_scalar sum, h;
    rs_comm *const buf = reinterpret_cast<rs_comm *>(alloca(rs_comm_size(pubs_count)));
#if !defined(NDEBUG)
    for (i = 0; i < pubs_count; i++) {
      assert(check_key(*pubs[i]));
    }
#endif
    if (ge_frombytes_vartime(&image_unp, &image) != 0) {
      return false;
    }
    ge_dsm_precomp(image_pre, &image_unp);
    sc_0(&sum);
    buf->h = prefix_hash;
    for (i = 0; i < pubs_count; i++) {
      ge_p2 tmp2;
      ge_p3 tmp3;
      if (sc_check(&sig[i].c) != 0 || sc_check(&sig[i].r) != 0) {
        return false;
      }
      if (ge_frombytes_vartime(&tmp3, &*pubs[i]) != 0) {
        abort();
      }
      ge_double_scalarmult_base_vartime(&tmp2, &sig[i].c, &tmp3, &sig[i].r);
      ge_tobytes(&buf->ab[i].a, &tmp2);
      hash_to_ec(*pubs[i], tmp3);
      ge_double_scalarmult_precomp_vartime(&tmp2, &sig[i].r, &tmp3, &sig[i].c, image_pre);
      ge_tobytes(&buf->ab[i].b, &tmp2);
      sc_add(&sum, &sum, &sig[i].c);
    }
    hash_to_scalar(buf, rs_comm_size(pubs_count), h);
    sc_sub(&h, &h, &sum);
    return sc_isnonzero(&h) == 0;
  }
  void crypto_ops::generate_ring_signature(const hash &prefix_hash, const key_image &image,
    const public_key *const *pubs, size_t pubs_count,
    const secret_key &sec, size_t sec_index,
    signature *sig) {
    lock_guard<mutex> lock(random_lock);
    size_t i;
    ge_p3 image_unp;
    ge_dsmp image_pre;
    ec_scalar sum, k, h;
    rs_comm *const buf = reinterpret_cast<rs_comm *>(alloca(rs_comm_size(pubs_count)));
    assert(sec_index < pubs_count);
#if !defined(NDEBUG)
    {
      ge_p3 t;
      public_key t2;
      key_image t3;
      assert(sc_check(&sec) == 0);
      ge_scalarmult_base(&t, &sec);
      ge_p3_tobytes(&t2, &t);
      assert(*pubs[sec_index] == t2);
      generate_key_image(*pubs[sec_index], sec, t3);
      assert(image == t3);
      for (i = 0; i < pubs_count; i++) {
        assert(check_key(*pubs[i]));
      }
    }
#endif
    if (ge_frombytes_vartime(&image_unp, &image) != 0) {
      abort();
    }
    ge_dsm_precomp(image_pre, &image_unp);
    sc_0(&sum);
    buf->h = prefix_hash;
    for (i = 0; i < pubs_count; i++) {
      ge_p2 tmp2;
      ge_p3 tmp3;
      if (i == sec_index) {
        random_scalar(k);
        ge_scalarmult_base(&tmp3, &k);
        ge_p3_tobytes(&buf->ab[i].a, &tmp3);
        hash_to_ec(*pubs[i], tmp3);
        ge_scalarmult(&tmp2, &k, &tmp3);
        ge_tobytes(&buf->ab[i].b, &tmp2);
      } else {
        random_scalar(sig[i].c);
        random_scalar(sig[i].r);
        if (ge_frombytes_vartime(&tmp3, &*pubs[i]) != 0) {
          abort();
        }
        ge_double_scalarmult_base_vartime(&tmp2, &sig[i].c, &tmp3, &sig[i].r);
        ge_tobytes(&buf->ab[i].a, &tmp2);
        hash_to_ec(*pubs[i], tmp3);
        ge_double_scalarmult_precomp_vartime(&tmp2, &sig[i].r, &tmp3, &sig[i].c, image_pre);
        ge_tobytes(&buf->ab[i].b, &tmp2);
        sc_add(&sum, &sum, &sig[i].c);
      }
    }
    hash_to_scalar(buf, rs_comm_size(pubs_count), h);
    sc_sub(&sig[sec_index].c, &h, &sum);
    sc_mulsub(&sig[sec_index].r, &sig[sec_index].c, &sec, &k);
  }