text: // Copyright (c) 2018-2019, CUT coin
  // Copyright (c) 2016, Monero Research Labs
  //
  // Author: Shen Noether <shen.noether@gmx.com>
  //
  // All rights reserved.
  //
  // Redistribution and use in source and binary forms, with or without modification, are
  // permitted provided that the following conditions are met:
  //
  // 1. Redistributions of source code must retain the above copyright notice, this list of
  //    conditions and the following disclaimer.
  //
  // 2. Redistributions in binary form must reproduce the above copyright notice, this list
  //    of conditions and the following disclaimer in the documentation and/or other
  //    materials provided with the distribution.
  //
  // 3. Neither the name of the copyright holder nor the names of its contributors may be
  //    used to endorse or promote products derived from this software without specific
  //    prior written permission.
  //
  // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
  // MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
  // THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  // STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
  // THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  
  #pragma once
  #ifndef RCT_TYPES_H
  #define RCT_TYPES_H
  
  #include <cstddef>
  #include <vector>
  #include <iostream>
  #include <cinttypes>
  #include <sodium/crypto_verify_32.h>
  
  extern "C" {
  #include "crypto/crypto-ops.h"
  #include "crypto/random.h"
  #include "crypto/keccak.h"
  }
  #include "crypto/generic-ops.h"
  #include "crypto/crypto.h"
  
  #include "hex.h"
  #include "span.h"
  #include "serialization/vector.h"
  #include "serialization/debug_archive.h"
  #include "serialization/binary_archive.h"
  #include "serialization/json_archive.h"
  
  
  //Define this flag when debugging to get additional info on the console
  #ifdef DBG
  #define DP(x) dp(x)
  #else
  #define DP(x)
  #endif
  
  //atomic units of moneros
  #define ATOMS 64
  
  //for printing large ints
  
  //Namespace specifically for ring ct code
  namespace rct {
      //basic ops containers
      typedef unsigned char * Bytes;
  
      // Can contain a secret or public key
      //  similar to secret_key / public_key of crypto-ops,
      //  but uses unsigned chars,
      //  also includes an operator for accessing the i'th byte.
      struct key {
          unsigned char & operator[](int i) {
              return bytes[i];
          }
          unsigned char operator[](int i) const {
              return bytes[i];
          }
          bool operator==(const key &k) const { return !crypto_verify_32(bytes, k.bytes); }
          unsigned char bytes[32];
      };
      typedef std::vector<key> keyV; //vector of keys
      typedef std::vector<keyV> keyM; //matrix of keys (indexed by column first)
  
      //containers For CT operations
      //if it's  representing a private ctkey then "dest" contains the secret key of the address
      // while "mask" contains a where C = aG + bH is CT pedersen commitment and b is the amount
      // (store b, the amount, separately
      //if it's representing a public ctkey, then "dest" = P the address, mask = C the commitment
      struct ctkey {
          key dest;
          key mask; //C here if public
      };
      typedef std::vector<ctkey> ctkeyV;
      typedef std::vector<ctkeyV> ctkeyM;
  
      //used for multisig data
      struct multisig_kLRki {
          key k;
          key L;
          key R;
          key ki;
      };
  
      struct multisig_out {
          std::vector<key> c; // for all inputs
  
          BEGIN_SERIALIZE_OBJECT()
            FIELD(c)
          END_SERIALIZE()
      };
  
      //data for passing the amount to the receiver secretly
      // If the pedersen commitment to an amount is C = aG + bH,
      // "mask" contains a 32 byte key a
      // "amount" contains a hex representation (in 32 bytes) of a 64 bit number
      // "senderPk" is not the senders actual public key, but a one-time public key generated for
      // the purpose of the ECDH exchange
      struct ecdhTuple {
          key mask;
          key amount;
          key senderPk;
  
          BEGIN_SERIALIZE_OBJECT()
            FIELD(mask)
            FIELD(amount)
            // FIELD(senderPk) // not serialized, as we do not use it in CUT Coin currently
          END_SERIALIZE()
      };
  
      //containers for representing amounts
      typedef uint64_t xmr_amount;
      typedef unsigned int bits[ATOMS];
      typedef key key64[64];
  
      struct boroSig {
          key64 s0;
          key64 s1;
          key ee;
      };
    
      //Container for precomp
      struct geDsmp {
          ge_dsmp k;
      };
      
      //just contains the necessary keys to represent MLSAG sigs
      //c.f. https://eprint.iacr.org/2015/1098
      struct mgSig {
          keyM ss;
          key cc;
          keyV II;
  
          BEGIN_SERIALIZE_OBJECT()
              FIELD(ss)
              FIELD(cc)
              // FIELD(II) - not serialized, it can be reconstructed
          END_SERIALIZE()
      };
      //contains the data for an Borromean sig
      // also contains the "Ci" values such that
      // \sum Ci = C
      // and the signature proves that each Ci is either
      // a Pedersen commitment to 0 or to 2^i
      //thus proving that C is in the range of [0, 2^64]
      struct rangeSig {
          boroSig asig;
          key64 Ci;
  
          BEGIN_SERIALIZE_OBJECT()
              FIELD(asig)
              FIELD(Ci)
          END_SERIALIZE()
      };
  
      struct Bulletproof
      {
        rct::keyV V;
        rct::key A, S, T1, T2;
        rct::key taux, mu;
        rct::keyV L, R;
        rct::key a, b, t;
  
        Bulletproof() {}
        Bulletproof(const rct::key &V, const rct::key &A, const rct::key &S, const rct::key &T1, const rct::key &T2, const rct::key &taux, const rct::key &mu, const rct::keyV &L, const rct::keyV &R, const rct::key &a, const rct::key &b, const rct::key &t):
          V({V}), A(A), S(S), T1(T1), T2(T2), taux(taux), mu(mu), L(L), R(R), a(a), b(b), t(t) {}
        Bulletproof(const rct::keyV &V, const rct::key &A, const rct::key &S, const rct::key &T1, const rct::key &T2, const rct::key &taux, const rct::key &mu, const rct::keyV &L, const rct::keyV &R, const rct::key &a, const rct::key &b, const rct::key &t):
          V(V), A(A), S(S), T1(T1), T2(T2), taux(taux), mu(mu), L(L), R(R), a(a), b(b), t(t) {}
  
        BEGIN_SERIALIZE_OBJECT()
          // Commitments aren't saved, they're restored via outPk
          // FIELD(V)
          FIELD(A)
          FIELD(S)
          FIELD(T1)
          FIELD(T2)
          FIELD(taux)
          FIELD(mu)
          FIELD(L)
          FIELD(R)
          FIELD(a)
          FIELD(b)
          FIELD(t)
  
          if (L.empty() || L.size() != R.size())
            return false;
        END_SERIALIZE()
      };
  
      size_t n_bulletproof_amounts(const Bulletproof &proof);
      size_t n_bulletproof_max_amounts(const Bulletproof &proof);
      size_t n_bulletproof_amounts(const std::vector<Bulletproof> &proofs);
      size_t n_bulletproof_max_amounts(const std::vector<Bulletproof> &proofs);
  
      //A container to hold all signatures necessary for RingCT
      // rangeSigs holds all the rangeproof data of a transaction
      // MG holds the MLSAG signature of a transaction
      // mixRing holds all the public keypairs (P, C) for a transaction
      // ecdhInfo holds an encoded mask / amount to be passed to each receiver
      // outPk contains public keypairs which are destinations (P, C),
      //  P = address, C = commitment to amount
      enum {
        RCTTypeNull = 0,
        RCTTypeFull = 1,
        RCTTypeSimple = 2,
        RCTTypeBulletproof = 3,
      };
      enum RangeProofType { RangeProofBorromean, RangeProofBulletproof, RangeProofMultiOutputBulletproof, RangeProofPaddedBulletproof };
      struct rctSigBase {
          uint8_t type;
          key message;
          ctkeyM mixRing; //the set of all pubkeys / copy
          //pairs that you mix with
          keyV pseudoOuts; //C - for simple rct
          std::vector<ecdhTuple> ecdhInfo;
          ctkeyV outPk;
          xmr_amount txnFee; // contains b
  
          template<bool W, template <bool> class Archive>
          bool serialize_rctsig_base(Archive<W> &ar, size_t inputs, size_t outputs)
          {
            FIELD(type)
            if (type == RCTTypeNull)
              return true;
            if (type != RCTTypeFull && type != RCTTypeSimple && type != RCTTypeBulletproof)
              return false;
            VARINT_FIELD(txnFee)
            // inputs/outputs not saved, only here for serialization help
            // FIELD(message) - not serialized, it can be reconstructed
            // FIELD(mixRing) - not serialized, it can be reconstructed
            if (type == RCTTypeSimple) // moved to prunable with bulletproofs
            {
              ar.tag("pseudoOuts");
              ar.begin_array();
              PREPARE_CUSTOM_VECTOR_SERIALIZATION(inputs, pseudoOuts);
              if (pseudoOuts.size() != inputs)
                return false;
              for (size_t i = 0; i < inputs; ++i)
              {
                FIELDS(pseudoOuts[i])
                if (inputs - i > 1)
                  ar.delimit_array();
              }
              ar.end_array();
            }
  
            ar.tag("ecdhInfo");
            ar.begin_array();
            PREPARE_CUSTOM_VECTOR_SERIALIZATION(outputs, ecdhInfo);
            if (ecdhInfo.size() != outputs)
              return false;
            for (size_t i = 0; i < outputs; ++i)
            {
              FIELDS(ecdhInfo[i])
              if (outputs - i > 1)
                ar.delimit_array();
            }
            ar.end_array();
  
            ar.tag("outPk");
            ar.begin_array();
            PREPARE_CUSTOM_VECTOR_SERIALIZATION(outputs, outPk);
            if (outPk.size() != outputs)
              return false;
            for (size_t i = 0; i < outputs; ++i)
            {
              FIELDS(outPk[i].mask)
              if (outputs - i > 1)
                ar.delimit_array();
            }
            ar.end_array();
            return true;
          }
      };
      struct rctSigPrunable {
          std::vector<rangeSig> rangeSigs;
          std::vector<Bulletproof> bulletproofs;
          std::vector<mgSig> MGs; // simple rct has N, full has 1
          keyV pseudoOuts; //C - for simple rct
  
          template<bool W, template <bool> class Archive>
          bool serialize_rctsig_prunable(Archive<W> &ar, uint8_t type, size_t inputs, size_t outputs, size_t mixin)
          {
            if (type == RCTTypeNull)
              return true;
            if (type != RCTTypeFull && type != RCTTypeSimple && type != RCTTypeBulletproof)
              return false;
            if (type == RCTTypeBulletproof)
            {
              uint32_t nbp = bulletproofs.size();
              FIELD(nbp)
              ar.tag("bp");
              ar.begin_array();
              if (nbp > outputs)
                return false;
              PREPARE_CUSTOM_VECTOR_SERIALIZATION(nbp, bulletproofs);
              for (size_t i = 0; i < nbp; ++i)
              {
                FIELDS(bulletproofs[i])
                if (nbp - i > 1)
                  ar.delimit_array();
              }
              if (n_bulletproof_max_amounts(bulletproofs) < outputs)
                return false;
              ar.end_array();
            }
            else
            {
              ar.tag("rangeSigs");
              ar.begin_array();
              PREPARE_CUSTOM_VECTOR_SERIALIZATION(outputs, rangeSigs);
              if (rangeSigs.size() != outputs)
                return false;
              for (size_t i = 0; i < outputs; ++i)
              {
                FIELDS(rangeSigs[i])
                if (outputs - i > 1)
                  ar.delimit_array();
              }
              ar.end_array();
            }
  
            ar.tag("MGs");
            ar.begin_array();
            // we keep a byte for size of MGs, because we don't know whether this is
            // a simple or full rct signature, and it's starting to annoy the hell out of me
            size_t mg_elements = (type == RCTTypeSimple || type == RCTTypeBulletproof) ? inputs : 1;
            PREPARE_CUSTOM_VECTOR_SERIALIZATION(mg_elements, MGs);
            if (MGs.size() != mg_elements)
              return false;
            for (size_t i = 0; i < mg_elements; ++i)
            {
              // we save the MGs contents directly, because we want it to save its
              // arrays and matrices without the size prefixes, and the load can't
              // know what size to expect if it's not in the data
              ar.begin_object();
              ar.tag("ss");
              ar.begin_array();
              PREPARE_CUSTOM_VECTOR_SERIALIZATION(mixin + 1, MGs[i].ss);
              if (MGs[i].ss.size() != mixin + 1)
                return false;
              for (size_t j = 0; j < mixin + 1; ++j)
              {
                ar.begin_array();
                size_t mg_ss2_elements = ((type == RCTTypeSimple || type == RCTTypeBulletproof) ? 1 : inputs) + 1;
                PREPARE_CUSTOM_VECTOR_SERIALIZATION(mg_ss2_elements, MGs[i].ss[j]);
                if (MGs[i].ss[j].size() != mg_ss2_elements)
                  return false;
                for (size_t k = 0; k < mg_ss2_elements; ++k)
                {
                  FIELDS(MGs[i].ss[j][k])
                  if (mg_ss2_elements - k > 1)
                    ar.delimit_array();
                }
                ar.end_array();
  
                if (mixin + 1 - j > 1)
                  ar.delimit_array();
              }
              ar.end_array();
  
              ar.tag("cc");
              FIELDS(MGs[i].cc)
              // MGs[i].II not saved, it can be reconstructed
              ar.end_object();
  
              if (mg_elements - i > 1)
                 ar.delimit_array();
            }
            ar.end_array();
            if (type == RCTTypeBulletproof)
            {
              ar.tag("pseudoOuts");
              ar.begin_array();
              PREPARE_CUSTOM_VECTOR_SERIALIZATION(inputs, pseudoOuts);
              if (pseudoOuts.size() != inputs)
                return false;
              for (size_t i = 0; i < inputs; ++i)
              {
                FIELDS(pseudoOuts[i])
                if (inputs - i > 1)
                  ar.delimit_array();
              }
              ar.end_array();
            }
            return true;
          }
  
      };
      struct rctSig: public rctSigBase {
          rctSigPrunable p;
  
          keyV& get_pseudo_outs()
          {
            return type == RCTTypeBulletproof ? p.pseudoOuts : pseudoOuts;
          }
  
          keyV const& get_pseudo_outs() const
          {
            return type == RCTTypeBulletproof ? p.pseudoOuts : pseudoOuts;
          }
      };
  
      //other basepoint H = toPoint(cn_fast_hash(G)), G the basepoint
      static const key H = { {0x8b, 0x65, 0x59, 0x70, 0x15, 0x37, 0x99, 0xaf, 0x2a, 0xea, 0xdc, 0x9f, 0xf1, 0xad, 0xd0, 0xea, 0x6c, 0x72, 0x51, 0xd5, 0x41, 0x54, 0xcf, 0xa9, 0x2c, 0x17, 0x3a, 0x0d, 0xd3, 0x9c, 0x1f, 0x94} };
  
      //H2 contains 2^i H in each index, i.e. H, 2H, 4H, 8H, ...
      //This is used for the range proofG
      //You can regenerate this by running python2 Test.py HPow2 in the MiniNero repo
      static const key64 H2 = {{{0x8b, 0x65, 0x59, 0x70, 0x15, 0x37, 0x99, 0xaf, 0x2a, 0xea, 0xdc, 0x9f, 0xf1, 0xad, 0xd0, 0xea, 0x6c, 0x72, 0x51, 0xd5, 0x41, 0x54, 0xcf, 0xa9, 0x2c, 0x17, 0x3a, 0x0d, 0xd3, 0x9c, 0x1f, 0x94}},
      {{0x8f, 0xaa, 0x44, 0x8a, 0xe4, 0xb3, 0xe2, 0xbb, 0x3d, 0x4d, 0x13, 0x09, 0x09, 0xf5, 0x5f, 0xcd, 0x79, 0x71, 0x1c, 0x1c, 0x83, 0xcd, 0xbc, 0xca, 0xdd, 0x42, 0xcb, 0xe1, 0x51, 0x5e, 0x87, 0x12}},
      {{0x12, 0xa7, 0xd6, 0x2c, 0x77, 0x91, 0x65, 0x4a, 0x57, 0xf3, 0xe6, 0x76, 0x94, 0xed, 0x50, 0xb4, 0x9a, 0x7d, 0x9e, 0x3f, 0xc1, 0xe4, 0xc7, 0xa0, 0xbd, 0xe2, 0x9d, 0x18, 0x7e, 0x9c, 0xc7, 0x1d}},
      {{0x78, 0x9a, 0xb9, 0x93, 0x4b, 0x49, 0xc4, 0xf9, 0xe6, 0x78, 0x5c, 0x6d, 0x57, 0xa4, 0x98, 0xb3, 0xea, 0xd4, 0x43, 0xf0, 0x4f, 0x13, 0xdf, 0x11, 0x0c, 0x54, 0x27, 0xb4, 0xf2, 0x14, 0xc7, 0x39}},
      {{0x77, 0x1e, 0x92, 0x99, 0xd9, 0x4f, 0x02, 0xac, 0x72, 0xe3, 0x8e, 0x44, 0xde, 0x56, 0x8a, 0xc1, 0xdc, 0xb2, 0xed, 0xc6, 0xed, 0xb6, 0x1f, 0x83, 0xca, 0x41, 0x8e, 0x10, 0x77, 0xce, 0x3d, 0xe8}},
      {{0x73, 0xb9, 0x6d, 0xb4, 0x30, 0x39, 0x81, 0x9b, 0xda, 0xf5, 0x68, 0x0e, 0x5c, 0x32, 0xd7, 0x41, 0x48, 0x88, 0x84, 0xd1, 0x8d, 0x93, 0x86, 0x6d, 0x40, 0x74, 0xa8, 0x49, 0x18, 0x2a, 0x8a, 0x64}},
      {{0x8d, 0x45, 0x8e, 0x1c, 0x2f, 0x68, 0xeb, 0xeb, 0xcc, 0xd2, 0xfd, 0x5d, 0x37, 0x9f, 0x5e, 0x58, 0xf8, 0x13, 0x4d, 0xf3, 0xe0, 0xe8, 0x8c, 0xad, 0x3d, 0x46, 0x70, 0x10, 0x63, 0xa8, 0xd4, 0x12}},
      {{0x09, 0x55, 0x1e, 0xdb, 0xe4, 0x94, 0x41, 0x8e, 0x81, 0x28, 0x44, 0x55, 0xd6, 0x4b, 0x35, 0xee, 0x8a, 0xc0, 0x93, 0x06, 0x8a, 0x5f, 0x16, 0x1f, 0xa6, 0x63, 0x75, 0x59, 0x17, 0x7e, 0xf4, 0x04}},
      {{0xd0, 0x5a, 0x88, 0x66, 0xf4, 0xdf, 0x8c, 0xee, 0x1e, 0x26, 0x8b, 0x1d, 0x23, 0xa4, 0xc5, 0x8c, 0x92, 0xe7, 0x60, 0x30, 0x97, 0x86, 0xcd, 0xac, 0x0f, 0xed, 0xa1, 0xd2, 0x47, 0xa9, 0xc9, 0xa7}},
      {{0x55, 0xcd, 0xaa, 0xd5, 0x18, 0xbd, 0x87, 0x1d, 0xd1, 0xeb, 0x7b, 0xc7, 0x02, 0x3e, 0x1d, 0xc0, 0xfd, 0xf3, 0x33, 0x98, 0x64, 0xf8, 0x8f, 0xdd, 0x2d, 0xe2, 0x69, 0xfe, 0x9e, 0xe1, 0x83, 0x2d}},
      {{0xe7, 0x69, 0x7e, 0x95, 0x1a, 0x98, 0xcf, 0xd5, 0x71, 0x2b, 0x84, 0xbb, 0xe5, 0xf3, 0x4e, 0xd7, 0x33, 0xe9, 0x47, 0x3f, 0xcb, 0x68, 0xed, 0xa6, 0x6e, 0x37, 0x88, 0xdf, 0x19, 0x58, 0xc3, 0x06}},
      {{0xf9, 0x2a, 0x97, 0x0b, 0xae, 0x72, 0x78, 0x29, 0x89, 0xbf, 0xc8, 0x3a, 0xdf, 0xaa, 0x92, 0xa4, 0xf4, 0x9c, 0x7e, 0x95, 0x91, 0x8b, 0x3b, 0xba, 0x3c, 0xdc, 0x7f, 0xe8, 0x8a, 0xcc, 0x8d, 0x47}},
      {{0x1f, 0x66, 0xc2, 0xd4, 0x91, 0xd7, 0x5a, 0xf9, 0x15, 0xc8, 0xdb, 0x6a, 0x6d, 0x1c, 0xb0, 0xcd, 0x4f, 0x7d, 0xdc, 0xd5, 0xe6, 0x3d, 0x3b, 0xa9, 0xb8, 0x3c, 0x86, 0x6c, 0x39, 0xef, 0x3a, 0x2b}},
      {{0x3e, 0xec, 0x98, 0x84, 0xb4, 0x3f, 0x58, 0xe9, 0x3e, 0xf8, 0xde, 0xea, 0x26, 0x00, 0x04, 0xef, 0xea, 0x2a, 0x46, 0x34, 0x4f, 0xc5, 0x96, 0x5b, 0x1a, 0x7d, 0xd5, 0xd1, 0x89, 0x97, 0xef, 0xa7}},
      {{0xb2, 0x9f, 0x8f, 0x0c, 0xcb, 0x96, 0x97, 0x7f, 0xe7, 0x77, 0xd4, 0x89, 0xd6, 0xbe, 0x9e, 0x7e, 0xbc, 0x19, 0xc4, 0x09, 0xb5, 0x10, 0x35, 0x68, 0xf2, 0x77, 0x61, 0x1d, 0x7e, 0xa8, 0x48, 0x94}},
      {{0x56, 0xb1, 0xf5, 0x12, 0x65, 0xb9, 0x55, 0x98, 0x76, 0xd5, 0x8d, 0x24, 0x9d, 0x0c, 0x14, 0x6d, 0x69, 0xa1, 0x03, 0x63, 0x66, 0x99, 0x87, 0x4d, 0x3f, 0x90, 0x47, 0x35, 0x50, 0xfe, 0x3f, 0x2c}},
      {{0x1d, 0x7a, 0x36, 0x57, 0x5e, 0x22, 0xf5, 0xd1, 0x39, 0xff, 0x9c, 0xc5, 0x10, 0xfa, 0x13, 0x85, 0x05, 0x57, 0x6b, 0x63, 0x81, 0x5a, 0x94, 0xe4, 0xb0, 0x12, 0xbf, 0xd4, 0x57, 0xca, 0xaa, 0xda}},
      {{0xd0, 0xac, 0x50, 0x7a, 0x86, 0x4e, 0xcd, 0x05, 0x93, 0xfa, 0x67, 0xbe, 0x7d, 0x23, 0x13, 0x43, 0x92, 0xd0, 0x0e, 0x40, 0x07, 0xe2, 0x53, 0x48, 0x78, 0xd9, 0xb2, 0x42, 0xe1, 0x0d, 0x76, 0x20}},
      {{0xf6, 0xc6, 0x84, 0x0b, 0x9c, 0xf1, 0x45, 0xbb, 0x2d, 0xcc, 0xf8, 0x6e, 0x94, 0x0b, 0xe0, 0xfc, 0x09, 0x8e, 0x32, 0xe3, 0x10, 0x99, 0xd5, 0x6f, 0x7f, 0xe0, 0x87, 0xbd, 0x5d, 0xeb, 0x50, 0x94}},
      {{0x28, 0x83, 0x1a, 0x33, 0x40, 0x07, 0x0e, 0xb1, 0xdb, 0x87, 0xc1, 0x2e, 0x05, 0x98, 0x0d, 0x5f, 0x33, 0xe9, 0xef, 0x90, 0xf8, 0x3a, 0x48, 0x17, 0xc9, 0xf4, 0xa0, 0xa3, 0x32, 0x27, 0xe1, 0x97}},
      {{0x87, 0x63, 0x22, 0x73, 0xd6, 0x29, 0xcc, 0xb7, 0xe1, 0xed, 0x1a, 0x76, 0x8f, 0xa2, 0xeb, 0xd5, 0x17, 0x60, 0xf3, 0x2e, 0x1c, 0x0b, 0x86, 0x7a, 0x5d, 0x36, 0x8d, 0x52, 0x71, 0x05, 0x5c, 0x6e}},
      {{0x5c, 0x7b, 0x29, 0x42, 0x43, 0x47, 0x96, 0x4d, 0x04, 0x27, 0x55, 0x17, 0xc5, 0xae, 0x14, 0xb6, 0xb5, 0xea, 0x27, 0x98, 0xb5, 0x73, 0xfc, 0x94, 0xe6, 0xe4, 0x4a, 0x53, 0x21, 0x60, 0x0c, 0xfb}},
      {{0xe6, 0x94, 0x50, 0x42, 0xd7, 0x8b, 0xc2, 0xc3, 0xbd, 0x6e, 0xc5, 0x8c, 0x51, 0x1a, 0x9f, 0xe8, 0x59, 0xc0, 0xad, 0x63, 0xfd, 0xe4, 0x94, 0xf5, 0x03, 0x9e, 0x0e, 0x82, 0x32, 0x61, 0x2b, 0xd5}},
      {{0x36, 0xd5, 0x69, 0x07, 0xe2, 0xec, 0x74, 0x5d, 0xb6, 0xe5, 0x4f, 0x0b, 0x2e, 0x1b, 0x23, 0x00, 0xab, 0xcb, 0x42, 0x2e, 0x71, 0x2d, 0xa5, 0x88, 0xa4, 0x0d, 0x3f, 0x1e, 0xbb, 0xbe, 0x02, 0xf6}},
      {{0x34, 0xdb, 0x6e, 0xe4, 0xd0, 0x60, 0x8e, 0x5f, 0x78, 0x36, 0x50, 0x49, 0x5a, 0x3b, 0x2f, 0x52, 0x73, 0xc5, 0x13, 0x4e, 0x52, 0x84, 0xe4, 0xfd, 0xf9, 0x66, 0x27, 0xbb, 0x16, 0xe3, 0x1e, 0x6b}},
      {{0x8e, 0x76, 0x59, 0xfb, 0x45, 0xa3, 0x78, 0x7d, 0x67, 0x4a, 0xe8, 0x67, 0x31, 0xfa, 0xa2, 0x53, 0x8e, 0xc0, 0xfd, 0xf4, 0x42, 0xab, 0x26, 0xe9, 0xc7, 0x91, 0xfa, 0xda, 0x08, 0x94, 0x67, 0xe9}},
      {{0x30, 0x06, 0xcf, 0x19, 0x8b, 0x24, 0xf3, 0x1b, 0xb4, 0xc7, 0xe6, 0x34, 0x60, 0x00, 0xab, 0xc7, 0x01, 0xe8, 0x27, 0xcf, 0xbb, 0x5d, 0xf5, 0x2d, 0xcf, 0xa4, 0x2e, 0x9c, 0xa9, 0xff, 0x08, 0x02}},
      {{0xf5, 0xfd, 0x40, 0x3c, 0xb6, 0xe8, 0xbe, 0x21, 0x47, 0x2e, 0x37, 0x7f, 0xfd, 0x80, 0x5a, 0x8c, 0x60, 0x83, 0xea, 0x48, 0x03, 0xb8, 0x48, 0x53, 0x89, 0xcc, 0x3e, 0xbc, 0x21, 0x5f, 0x00, 0x2a}},
      {{0x37, 0x31, 0xb2, 0x60, 0xeb, 0x3f, 0x94, 0x82, 0xe4, 0x5f, 0x1c, 0x3f, 0x3b, 0x9d, 0xcf, 0x83, 0x4b, 0x75, 0xe6, 0xee, 0xf8, 0xc4, 0x0f, 0x46, 0x1e, 0xa2, 0x7e, 0x8b, 0x6e, 0xd9, 0x47, 0x3d}},
      {{0x9f, 0x9d, 0xab, 0x09, 0xc3, 0xf5, 0xe4, 0x28, 0x55, 0xc2, 0xde, 0x97, 0x1b, 0x65, 0x93, 0x28, 0xa2, 0xdb, 0xc4, 0x54, 0x84, 0x5f, 0x39, 0x6f, 0xfc, 0x05, 0x3f, 0x0b, 0xb1, 0x92, 0xf8, 0xc3}},
      {{0x5e, 0x05, 0x5d, 0x25, 0xf8, 0x5f, 0xdb, 0x98, 0xf2, 0x73, 0xe4, 0xaf, 0xe0, 0x84, 0x64, 0xc0, 0x03, 0xb7, 0x0f, 0x1e, 0xf0, 0x67, 0x7b, 0xb5, 0xe2, 0x57, 0x06, 0x40, 0x0b, 0xe6, 0x20, 0xa5}},
      {{0x86, 0x8b, 0xcf, 0x36, 0x79, 0xcb, 0x6b, 0x50, 0x0b, 0x94, 0x41, 0x8c, 0x0b, 0x89, 0x25, 0xf9, 0x86, 0x55, 0x30, 0x30, 0x3a, 0xe4, 0xe4, 0xb2, 0x62, 0x59, 0x18, 0x65, 0x66, 0x6a, 0x45, 0x90}},
      {{0xb3, 0xdb, 0x6b, 0xd3, 0x89, 0x7a, 0xfb, 0xd1, 0xdf, 0x3f, 0x96, 0x44, 0xab, 0x21, 0xc8, 0x05, 0x0e, 0x1f, 0x00, 0x38, 0xa5, 0x2f, 0x7c, 0xa9, 0x5a, 0xc0, 0xc3, 0xde, 0x75, 0x58, 0xcb, 0x7a}},
      {{0x81, 0x19, 0xb3, 0xa0, 0x59, 0xff, 0x2c, 0xac, 0x48, 0x3e, 0x69, 0xbc, 0xd4, 0x1d, 0x6d, 0x27, 0x14, 0x94, 0x47, 0x91, 0x42, 0x88, 0xbb, 0xea, 0xee, 0x34, 0x13, 0xe6, 0xdc, 0xc6, 0xd1, 0xeb}},
      {{0x10, 0xfc, 0x58, 0xf3, 0x5f, 0xc7, 0xfe, 0x7a, 0xe8, 0x75, 0x52, 0x4b, 0xb5, 0x85, 0x00, 0x03, 0x00, 0x5b, 0x7f, 0x97, 0x8c, 0x0c, 0x65, 0xe2, 0xa9, 0x65, 0x46, 0x4b, 0x6d, 0x00, 0x81, 0x9c}},
      {{0x5a, 0xcd, 0x94, 0xeb, 0x3c, 0x57, 0x83, 0x79, 0xc1, 0xea, 0x58, 0xa3, 0x43, 0xec, 0x4f, 0xcf, 0xf9, 0x62, 0x77, 0x6f, 0xe3, 0x55, 0x21, 0xe4, 0x75, 0xa0, 0xe0, 0x6d, 0x88, 0x7b, 0x2d, 0xb9}},
      {{0x33, 0xda, 0xf3, 0xa2, 0x14, 0xd6, 0xe0, 0xd4, 0x2d, 0x23, 0x00, 0xa7, 0xb4, 0x4b, 0x39, 0x29, 0x0d, 0xb8, 0x98, 0x9b, 0x42, 0x79, 0x74, 0xcd, 0x86, 0x5d, 0xb0, 0x11, 0x05, 0x5a, 0x29, 0x01}},
      {{0xcf, 0xc6, 0x57, 0x2f, 0x29, 0xaf, 0xd1, 0x64, 0xa4, 0x94, 0xe6, 0x4e, 0x6f, 0x1a, 0xeb, 0x82, 0x0c, 0x3e, 0x7d, 0xa3, 0x55, 0x14, 0x4e, 0x51, 0x24, 0xa3, 0x91, 0xd0, 0x6e, 0x9f, 0x95, 0xea}},
      {{0xd5, 0x31, 0x2a, 0x4b, 0x0e, 0xf6, 0x15, 0xa3, 0x31, 0xf6, 0x35, 0x2c, 0x2e, 0xd2, 0x1d, 0xac, 0x9e, 0x7c, 0x36, 0x39, 0x8b, 0x93, 0x9a, 0xec, 0x90, 0x1c, 0x25, 0x7f, 0x6c, 0xbc, 0x9e, 0x8e}},
      {{0x55, 0x1d, 0x67, 0xfe, 0xfc, 0x7b, 0x5b, 0x9f, 0x9f, 0xdb, 0xf6, 0xaf, 0x57, 0xc9, 0x6c, 0x8a, 0x74, 0xd7, 0xe4, 0x5a, 0x00, 0x20, 0x78, 0xa7, 0xb5, 0xba, 0x45, 0xc6, 0xfd, 0xe9, 0x3e, 0x33}},
      {{0xd5, 0x0a, 0xc7, 0xbd, 0x5c, 0xa5, 0x93, 0xc6, 0x56, 0x92, 0x8f, 0x38, 0x42, 0x80, 0x17, 0xfc, 0x7b, 0xa5, 0x02, 0x85, 0x4c, 0x43, 0xd8, 0x41, 0x49, 0x50, 0xe9, 0x6e, 0xcb, 0x40, 0x5d, 0xc3}},
      {{0x07, 0x73, 0xe1, 0x8e, 0xa1, 0xbe, 0x44, 0xfe, 0x1a, 0x97, 0xe2, 0x39, 0x57, 0x3c, 0xfa, 0xe3, 0xe4, 0xe9, 0x5e, 0xf9, 0xaa, 0x9f, 0xaa, 0xbe, 0xac, 0x12, 0x74, 0xd3, 0xad, 0x26, 0x16, 0x04}},
      {{0xe9, 0xaf, 0x0e, 0x7c, 0xa8, 0x93, 0x30, 0xd2, 0xb8, 0x61, 0x5d, 0x1b, 0x41, 0x37, 0xca, 0x61, 0x7e, 0x21, 0x29, 0x7f, 0x2f, 0x0d, 0xed, 0x8e, 0x31, 0xb7, 0xd2, 0xea, 0xd8, 0x71, 0x46, 0x60}},
      {{0x7b, 0x12, 0x45, 0x83, 0x09, 0x7f, 0x10, 0x29, 0xa0, 0xc7, 0x41, 0x91, 0xfe, 0x73, 0x78, 0xc9, 0x10, 0x5a, 0xcc, 0x70, 0x66, 0x95, 0xed, 0x14, 0x93, 0xbb, 0x76, 0x03, 0x42, 0x26, 0xa5, 0x7b}},
      {{0xec, 0x40, 0x05, 0x7b, 0x99, 0x54, 0x76, 0x65, 0x0b, 0x3d, 0xb9, 0x8e, 0x9d, 0xb7, 0x57, 0x38, 0xa8, 0xcd, 0x2f, 0x94, 0xd8, 0x63, 0xb9, 0x06, 0x15, 0x0c, 0x56, 0xaa, 0xc1, 0x9c, 0xaa, 0x6b}},
      {{0x01, 0xd9, 0xff, 0x72, 0x9e, 0xfd, 0x39, 0xd8, 0x37, 0x84, 0xc0, 0xfe, 0x59, 0xc4, 0xae, 0x81, 0xa6, 0x70, 0x34, 0xcb, 0x53, 0xc9, 0x43, 0xfb, 0x81, 0x8b, 0x9d, 0x8a, 0xe7, 0xfc, 0x33, 0xe5}},
      {{0x00, 0xdf, 0xb3, 0xc6, 0x96, 0x32, 0x8c, 0x76, 0x42, 0x45, 0x19, 0xa7, 0xbe, 0xfe, 0x8e, 0x0f, 0x6c, 0x76, 0xf9, 0x47, 0xb5, 0x27, 0x67, 0x91, 0x6d, 0x24, 0x82, 0x3f, 0x73, 0x5b, 0xaf, 0x2e}},
      {{0x46, 0x1b, 0x79, 0x9b, 0x4d, 0x9c, 0xee, 0xa8, 0xd5, 0x80, 0xdc, 0xb7, 0x6d, 0x11, 0x15, 0x0d, 0x53, 0x5e, 0x16, 0x39, 0xd1, 0x60, 0x03, 0xc3, 0xfb, 0x7e, 0x9d, 0x1f, 0xd1, 0x30, 0x83, 0xa8}},
      {{0xee, 0x03, 0x03, 0x94, 0x79, 0xe5, 0x22, 0x8f, 0xdc, 0x55, 0x1c, 0xbd, 0xe7, 0x07, 0x9d, 0x34, 0x12, 0xea, 0x18, 0x6a, 0x51, 0x7c, 0xcc, 0x63, 0xe4, 0x6e, 0x9f, 0xcc, 0xe4, 0xfe, 0x3a, 0x6c}},
      {{0xa8, 0xcf, 0xb5, 0x43, 0x52, 0x4e, 0x7f, 0x02, 0xb9, 0xf0, 0x45, 0xac, 0xd5, 0x43, 0xc2, 0x1c, 0x37, 0x3b, 0x4c, 0x9b, 0x98, 0xac, 0x20, 0xce, 0xc4, 0x17, 0xa6, 0xdd, 0xb5, 0x74, 0x4e, 0x94}},
      {{0x93, 0x2b, 0x79, 0x4b, 0xf8, 0x9c, 0x6e, 0xda, 0xf5, 0xd0, 0x65, 0x0c, 0x7c, 0x4b, 0xad, 0x92, 0x42, 0xb2, 0x56, 0x26, 0xe3, 0x7e, 0xad, 0x5a, 0xa7, 0x5e, 0xc8, 0xc6, 0x4e, 0x09, 0xdd, 0x4f}},
      {{0x16, 0xb1, 0x0c, 0x77, 0x9c, 0xe5, 0xcf, 0xef, 0x59, 0xc7, 0x71, 0x0d, 0x2e, 0x68, 0x44, 0x1e, 0xa6, 0xfa, 0xcb, 0x68, 0xe9, 0xb5, 0xf7, 0xd5, 0x33, 0xae, 0x0b, 0xb7, 0x8e, 0x28, 0xbf, 0x57}},
      {{0x0f, 0x77, 0xc7, 0x67, 0x43, 0xe7, 0x39, 0x6f, 0x99, 0x10, 0x13, 0x9f, 0x49, 0x37, 0xd8, 0x37, 0xae, 0x54, 0xe2, 0x10, 0x38, 0xac, 0x5c, 0x0b, 0x3f, 0xd6, 0xef, 0x17, 0x1a, 0x28, 0xa7, 0xe4}},
      {{0xd7, 0xe5, 0x74, 0xb7, 0xb9, 0x52, 0xf2, 0x93, 0xe8, 0x0d, 0xde, 0x90, 0x5e, 0xb5, 0x09, 0x37, 0x3f, 0x3f, 0x6c, 0xd1, 0x09, 0xa0, 0x22, 0x08, 0xb3, 0xc1, 0xe9, 0x24, 0x08, 0x0a, 0x20, 0xca}},
      {{0x45, 0x66, 0x6f, 0x8c, 0x38, 0x1e, 0x3d, 0xa6, 0x75, 0x56, 0x3f, 0xf8, 0xba, 0x23, 0xf8, 0x3b, 0xfa, 0xc3, 0x0c, 0x34, 0xab, 0xdd, 0xe6, 0xe5, 0xc0, 0x97, 0x5e, 0xf9, 0xfd, 0x70, 0x0c, 0xb9}},
      {{0xb2, 0x46, 0x12, 0xe4, 0x54, 0x60, 0x7e, 0xb1, 0xab, 0xa4, 0x47, 0xf8, 0x16, 0xd1, 0xa4, 0x55, 0x1e, 0xf9, 0x5f, 0xa7, 0x24, 0x7f, 0xb7, 0xc1, 0xf5, 0x03, 0x02, 0x0a, 0x71, 0x77, 0xf0, 0xdd}},
      {{0x7e, 0x20, 0x88, 0x61, 0x85, 0x6d, 0xa4, 0x2c, 0x8b, 0xb4, 0x6a, 0x75, 0x67, 0xf8, 0x12, 0x13, 0x62, 0xd9, 0xfb, 0x24, 0x96, 0xf1, 0x31, 0xa4, 0xaa, 0x90, 0x17, 0xcf, 0x36, 0x6c, 0xdf, 0xce}},
      {{0x5b, 0x64, 0x6b, 0xff, 0x6a, 0xd1, 0x10, 0x01, 0x65, 0x03, 0x7a, 0x05, 0x56, 0x01, 0xea, 0x02, 0x35, 0x8c, 0x0f, 0x41, 0x05, 0x0f, 0x9d, 0xfe, 0x3c, 0x95, 0xdc, 0xcb, 0xd3, 0x08, 0x7b, 0xe0}},
      {{0x74, 0x6d, 0x1d, 0xcc, 0xfe, 0xd2, 0xf0, 0xff, 0x1e, 0x13, 0xc5, 0x1e, 0x2d, 0x50, 0xd5, 0x32, 0x43, 0x75, 0xfb, 0xd5, 0xbf, 0x7c, 0xa8, 0x2a, 0x89, 0x31, 0x82, 0x8d, 0x80, 0x1d, 0x43, 0xab}},
      {{0xcb, 0x98, 0x11, 0x0d, 0x4a, 0x6b, 0xb9, 0x7d, 0x22, 0xfe, 0xad, 0xbc, 0x6c, 0x0d, 0x89, 0x30, 0xc5, 0xf8, 0xfc, 0x50, 0x8b, 0x2f, 0xc5, 0xb3, 0x53, 0x28, 0xd2, 0x6b, 0x88, 0xdb, 0x19, 0xae}},
      {{0x60, 0xb6, 0x26, 0xa0, 0x33, 0xb5, 0x5f, 0x27, 0xd7, 0x67, 0x6c, 0x40, 0x95, 0xea, 0xba, 0xbc, 0x7a, 0x2c, 0x7e, 0xde, 0x26, 0x24, 0xb4, 0x72, 0xe9, 0x7f, 0x64, 0xf9, 0x6b, 0x8c, 0xfc, 0x0e}},
      {{0xe5, 0xb5, 0x2b, 0xc9, 0x27, 0x46, 0x8d, 0xf7, 0x18, 0x93, 0xeb, 0x81, 0x97, 0xef, 0x82, 0x0c, 0xf7, 0x6c, 0xb0, 0xaa, 0xf6, 0xe8, 0xe4, 0xfe, 0x93, 0xad, 0x62, 0xd8, 0x03, 0x98, 0x31, 0x04}},
      {{0x05, 0x65, 0x41, 0xae, 0x5d, 0xa9, 0x96, 0x1b, 0xe2, 0xb0, 0xa5, 0xe8, 0x95, 0xe5, 0xc5, 0xba, 0x15, 0x3c, 0xbb, 0x62, 0xdd, 0x56, 0x1a, 0x42, 0x7b, 0xad, 0x0f, 0xfd, 0x41, 0x92, 0x31, 0x99}},
      {{0xf8, 0xfe, 0xf0, 0x5a, 0x3f, 0xa5, 0xc9, 0xf3, 0xeb, 0xa4, 0x16, 0x38, 0xb2, 0x47, 0xb7, 0x11, 0xa9, 0x9f, 0x96, 0x0f, 0xe7, 0x3a, 0xa2, 0xf9, 0x01, 0x36, 0xae, 0xb2, 0x03, 0x29, 0xb8, 0x88}}};
  
      //Debug printing for the above types
      //Actually use DP(value) and #define DBG
      void dp(key a);
      void dp(bool a);
      void dp(const char * a, int l);
      void dp(keyV a);
      void dp(keyM a);
      void dp(xmr_amount vali);
      void dp(int vali);
      void dp(bits amountb);
      void dp(const char * st);
  
      //various conversions
  
      //uint long long to 32 byte key
      void d2h(key & amounth, xmr_amount val);
      key d2h(xmr_amount val);
      //uint long long to int[64]
      void d2b(bits  amountb, xmr_amount val);
      //32 byte key to uint long long
      // if the key holds a value > 2^64
      // then the value in the first 8 bytes is returned
      xmr_amount h2d(const key &test);
      //32 byte key to int[64]
      void h2b(bits  amountb2, const key & test);
      //int[64] to 32 byte key
      void b2h(key  & amountdh, bits amountb2);
      //int[64] to uint long long
      xmr_amount b2d(bits amountb);
  
      bool is_rct_simple(int type);
      bool is_rct_bulletproof(int type);
      bool is_rct_borromean(int type);
  
      static inline const rct::key &pk2rct(const crypto::public_key &pk) { return (const rct::key&)pk; }
      static inline const rct::key &sk2rct(const crypto::secret_key &sk) { return (const rct::key&)sk; }
      static inline const rct::key &ki2rct(const crypto::key_image &ki) { return (const rct::key&)ki; }
      static inline const rct::key &hash2rct(const crypto::hash &h) { return (const rct::key&)h; }
      static inline const crypto::public_key &rct2pk(const rct::key &k) { return (const crypto::public_key&)k; }
      static inline const crypto::secret_key &rct2sk(const rct::key &k) { return (const crypto::secret_key&)k; }
      static inline const crypto::key_image &rct2ki(const rct::key &k) { return (const crypto::key_image&)k; }
      static inline const crypto::hash &rct2hash(const rct::key &k) { return (const crypto::hash&)k; }
      static inline bool operator==(const rct::key &k0, const crypto::public_key &k1) { return !crypto_verify_32(k0.bytes, (const unsigned char*)&k1); }
      static inline bool operator!=(const rct::key &k0, const crypto::public_key &k1) { return crypto_verify_32(k0.bytes, (const unsigned char*)&k1); }
  }
  
  
  namespace cryptonote {
      static inline bool operator==(const crypto::public_key &k0, const rct::key &k1) { return !crypto_verify_32((const unsigned char*)&k0, k1.bytes); }
      static inline bool operator!=(const crypto::public_key &k0, const rct::key &k1) { return crypto_verify_32((const unsigned char*)&k0, k1.bytes); }
      static inline bool operator==(const crypto::secret_key &k0, const rct::key &k1) { return !crypto_verify_32((const unsigned char*)&k0, k1.bytes); }
      static inline bool operator!=(const crypto::secret_key &k0, const rct::key &k1) { return crypto_verify_32((const unsigned char*)&k0, k1.bytes); }
  }
  
  namespace rct {
  inline std::ostream &operator <<(std::ostream &o, const rct::key &v) {
    epee::to_hex::formatted(o, epee::as_byte_span(v)); return o;
  }
  }
  
  
  namespace std
  {
    template<> struct hash<rct::key> { std::size_t operator()(const rct::key &k) const { return reinterpret_cast<const std::size_t&>(k); } };
  }
  
  BLOB_SERIALIZER(rct::key);
  BLOB_SERIALIZER(rct::key64);
  BLOB_SERIALIZER(rct::ctkey);
  BLOB_SERIALIZER(rct::multisig_kLRki);
  BLOB_SERIALIZER(rct::boroSig);
  
  VARIANT_TAG(debug_archive, rct::key, "rct::key");
  VARIANT_TAG(debug_archive, rct::key64, "rct::key64");
  VARIANT_TAG(debug_archive, rct::keyV, "rct::keyV");
  VARIANT_TAG(debug_archive, rct::keyM, "rct::keyM");
  VARIANT_TAG(debug_archive, rct::ctkey, "rct::ctkey");
  VARIANT_TAG(debug_archive, rct::ctkeyV, "rct::ctkeyV");
  VARIANT_TAG(debug_archive, rct::ctkeyM, "rct::ctkeyM");
  VARIANT_TAG(debug_archive, rct::ecdhTuple, "rct::ecdhTuple");
  VARIANT_TAG(debug_archive, rct::mgSig, "rct::mgSig");
  VARIANT_TAG(debug_archive, rct::rangeSig, "rct::rangeSig");
  VARIANT_TAG(debug_archive, rct::boroSig, "rct::boroSig");
  VARIANT_TAG(debug_archive, rct::rctSig, "rct::rctSig");
  VARIANT_TAG(debug_archive, rct::Bulletproof, "rct::bulletproof");
  VARIANT_TAG(debug_archive, rct::multisig_kLRki, "rct::multisig_kLRki");
  VARIANT_TAG(debug_archive, rct::multisig_out, "rct::multisig_out");
  
  VARIANT_TAG(binary_archive, rct::key, 0x90);
  VARIANT_TAG(binary_archive, rct::key64, 0x91);
  VARIANT_TAG(binary_archive, rct::keyV, 0x92);
  VARIANT_TAG(binary_archive, rct::keyM, 0x93);
  VARIANT_TAG(binary_archive, rct::ctkey, 0x94);
  VARIANT_TAG(binary_archive, rct::ctkeyV, 0x95);
  VARIANT_TAG(binary_archive, rct::ctkeyM, 0x96);
  VARIANT_TAG(binary_archive, rct::ecdhTuple, 0x97);
  VARIANT_TAG(binary_archive, rct::mgSig, 0x98);
  VARIANT_TAG(binary_archive, rct::rangeSig, 0x99);
  VARIANT_TAG(binary_archive, rct::boroSig, 0x9a);
  VARIANT_TAG(binary_archive, rct::rctSig, 0x9b);
  VARIANT_TAG(binary_archive, rct::Bulletproof, 0x9c);
  VARIANT_TAG(binary_archive, rct::multisig_kLRki, 0x9d);
  VARIANT_TAG(binary_archive, rct::multisig_out, 0x9e);
  
  VARIANT_TAG(json_archive, rct::key, "rct_key");
  VARIANT_TAG(json_archive, rct::key64, "rct_key64");
  VARIANT_TAG(json_archive, rct::keyV, "rct_keyV");
  VARIANT_TAG(json_archive, rct::keyM, "rct_keyM");
  VARIANT_TAG(json_archive, rct::ctkey, "rct_ctkey");
  VARIANT_TAG(json_archive, rct::ctkeyV, "rct_ctkeyV");
  VARIANT_TAG(json_archive, rct::ctkeyM, "rct_ctkeyM");
  VARIANT_TAG(json_archive, rct::ecdhTuple, "rct_ecdhTuple");
  VARIANT_TAG(json_archive, rct::mgSig, "rct_mgSig");
  VARIANT_TAG(json_archive, rct::rangeSig, "rct_rangeSig");
  VARIANT_TAG(json_archive, rct::boroSig, "rct_boroSig");
  VARIANT_TAG(json_archive, rct::rctSig, "rct_rctSig");
  VARIANT_TAG(json_archive, rct::Bulletproof, "rct_bulletproof");
  VARIANT_TAG(json_archive, rct::multisig_kLRki, "rct_multisig_kLR");
  VARIANT_TAG(json_archive, rct::multisig_out, "rct_multisig_out");
  
  #endif  /* RCTTYPES_H */
  