text: #include "merkle.h"
  #include "hash.h"
  #include "utilstrencodings.h"
  
  /*     WARNING! If you're reading this because you're learning about crypto
         and/or designing a new system that will use merkle trees, keep in mind
         that the following merkle tree algorithm has a serious flaw related to
         duplicate txids, resulting in a vulnerability (CVE-2012-2459).
  
         The reason is that if the number of hashes in the list at a given time
         is odd, the last one is duplicated before computing the next level (which
         is unusual in Merkle trees). This results in certain sequences of
         transactions leading to the same merkle root. For example, these two
         trees:
  
                      A               A
                    /  \            /   \
                  B     C         B       C
                 / \    |        / \     / \
                D   E   F       D   E   F   F
               / \ / \ / \     / \ / \ / \ / \
               1 2 3 4 5 6     1 2 3 4 5 6 5 6
  
         for transaction lists [1,2,3,4,5,6] and [1,2,3,4,5,6,5,6] (where 5 and
         6 are repeated) result in the same root hash A (because the hash of both
         of (F) and (F,F) is C).
  
         The vulnerability results from being able to send a block with such a
         transaction list, with the same merkle root, and the same block hash as
         the original without duplication, resulting in failed validation. If the
         receiving node proceeds to mark that block as permanently invalid
         however, it will fail to accept further unmodified (and thus potentially
         valid) versions of the same block. We defend against this by detecting
         the case where we would hash two identical hashes at the end of the list
         together, and treating that identically to the block having an invalid
         merkle root. Assuming no double-SHA256 collisions, this will detect all
         known ways of changing the transactions without affecting the merkle
         root.
  */
  
  /* This implements a constant-space merkle root/path calculator, limited to 2^32 leaves. */
  static void MerkleComputation(const std::vector<uint256>& leaves, uint256* proot, bool* pmutated, uint32_t branchpos, std::vector<uint256>* pbranch) {
      if (pbranch) pbranch->clear();
      if (leaves.size() == 0) {
          if (pmutated) *pmutated = false;
          if (proot) *proot = uint256();
          return;
      }
      bool mutated = false;
      // count is the number of leaves processed so far.
      uint32_t count = 0;
      // inner is an array of eagerly computed subtree hashes, indexed by tree
      // level (0 being the leaves).
      // For example, when count is 25 (11001 in binary), inner[4] is the hash of
      // the first 16 leaves, inner[3] of the next 8 leaves, and inner[0] equal to
      // the last leaf. The other inner entries are undefined.
      uint256 inner[32];
      // Which position in inner is a hash that depends on the matching leaf.
      int matchlevel = -1;
      // First process all leaves into 'inner' values.
      while (count < leaves.size()) {
          uint256 h = leaves[count];
          bool matchh = count == branchpos;
          count++;
          int level;
          // For each of the lower bits in count that are 0, do 1 step. Each
          // corresponds to an inner value that existed before processing the
          // current leaf, and each needs a hash to combine it.
          for (level = 0; !(count & (((uint32_t)1) << level)); level++) {
              if (pbranch) {
                  if (matchh) {
                      pbranch->push_back(inner[level]);
                  } else if (matchlevel == level) {
                      pbranch->push_back(h);
                      matchh = true;
                  }
              }
              mutated |= (inner[level] == h);
              CHash256().Write(inner[level].begin(), 32).Write(h.begin(), 32).Finalize(h.begin());
          }
          // Store the resulting hash at inner position level.
          inner[level] = h;
          if (matchh) {
              matchlevel = level;
          }
      }
      // Do a final 'sweep' over the rightmost branch of the tree to process
      // odd levels, and reduce everything to a single top value.
      // Level is the level (counted from the bottom) up to which we've sweeped.
      int level = 0;
      // As long as bit number level in count is zero, skip it. It means there
      // is nothing left at this level.
      while (!(count & (((uint32_t)1) << level))) {
          level++;
      }
      uint256 h = inner[level];
      bool matchh = matchlevel == level;
      while (count != (((uint32_t)1) << level)) {
          // If we reach this point, h is an inner value that is not the top.
          // We combine it with itself (Mashhadbit's special rule for odd levels in
          // the tree) to produce a higher level one.
          if (pbranch && matchh) {
              pbranch->push_back(h);
          }
          CHash256().Write(h.begin(), 32).Write(h.begin(), 32).Finalize(h.begin());
          // Increment count to the value it would have if two entries at this
          // level had existed.
          count += (((uint32_t)1) << level);
          level++;
          // And propagate the result upwards accordingly.
          while (!(count & (((uint32_t)1) << level))) {
              if (pbranch) {
                  if (matchh) {
                      pbranch->push_back(inner[level]);
                  } else if (matchlevel == level) {
                      pbranch->push_back(h);
                      matchh = true;
                  }
              }
              CHash256().Write(inner[level].begin(), 32).Write(h.begin(), 32).Finalize(h.begin());
              level++;
          }
      }
      // Return result.
      if (pmutated) *pmutated = mutated;
      if (proot) *proot = h;
  }
  
  uint256 ComputeMerkleRoot(const std::vector<uint256>& leaves, bool* mutated) {
      uint256 hash;
      MerkleComputation(leaves, &hash, mutated, -1, NULL);
      return hash;
  }
  
  std::vector<uint256> ComputeMerkleBranch(const std::vector<uint256>& leaves, uint32_t position) {
      std::vector<uint256> ret;
      MerkleComputation(leaves, NULL, NULL, position, &ret);
      return ret;
  }
  
  uint256 ComputeMerkleRootFromBranch(const uint256& leaf, const std::vector<uint256>& vMerkleBranch, uint32_t nIndex) {
      uint256 hash = leaf;
      for (std::vector<uint256>::const_iterator it = vMerkleBranch.begin(); it != vMerkleBranch.end(); ++it) {
          if (nIndex & 1) {
              hash = Hash(BEGIN(*it), END(*it), BEGIN(hash), END(hash));
          } else {
              hash = Hash(BEGIN(hash), END(hash), BEGIN(*it), END(*it));
          }
          nIndex >>= 1;
      }
      return hash;
  }
  
  uint256 BlockMerkleRoot(const CBlock& block, bool* mutated)
  {
      std::vector<uint256> leaves;
      leaves.resize(block.vtx.size());
      for (size_t s = 0; s < block.vtx.size(); s++) {
          leaves[s] = block.vtx[s].GetHash();
      }
      return ComputeMerkleRoot(leaves, mutated);
  }
  
  std::vector<uint256> BlockMerkleBranch(const CBlock& block, uint32_t position)
  {
      std::vector<uint256> leaves;
      leaves.resize(block.vtx.size());
      for (size_t s = 0; s < block.vtx.size(); s++) {
          leaves[s] = block.vtx[s].GetHash();
      }
      return ComputeMerkleBranch(leaves, position);
  }
  