比特币中的默克尔树Merkle

简介

Merkle Tree，通常也被称作Hash Tree，顾名思义，就是存储hash值的一棵树。Merkle树的叶子是数据块(例如，文件或者文件的集合)的hash值。非叶节点是其对应子节点串联字符串的hash。

比特币中对应的默克尔树

• 比特币中区块的定义结构
  

//
// Nodes collect new transactions into a block, hash them into a hash tree,
// and scan through nonce values to make the block's hash satisfy proof-of-work
// requirements.  When they solve the proof-of-work, they broadcast the block
// to everyone and the block is added to the block chain.  The first transaction
// in the block is a special one that creates a new coin owned by the creator
// of the block.
//
// Blocks are appended to blk0001.dat files on disk.  Their location on disk
// is indexed by CBlockIndex objects in memory.
//
class CBlock
{
public:
    // header
    int nVersion;
    uint256 hashPrevBlock;
    uint256 hashMerkleRoot;
    unsigned int nTime;
    unsigned int nBits; // 记录本区块难度
    unsigned int nNonce;

    // network and disk
    vector vtx;

    // memory only
    mutable vector vMerkleTree;

    // 对应的方法省略，后面用到会单独讲解
};

• 构建块中交易对应的默克尔树
  对应的代码如下：

uint256 CBlock::BuildMerkleTree() const
    {
        vMerkleTree.clear();
        foreach(const CTransaction& tx, vtx)
            vMerkleTree.push_back(tx.GetHash());
        int j = 0;
        for (int nSize = vtx.size(); nSize > 1; nSize = (nSize + 1) / 2)
        {
            for (int i = 0; i < nSize; i += 2)
            {
                int i2 = min(i+1, nSize-1);
                vMerkleTree.push_back(Hash(BEGIN(vMerkleTree[j+i]),  END(vMerkleTree[j+i]),
                                           BEGIN(vMerkleTree[j+i2]), END(vMerkleTree[j+i2])));
            }
            j += nSize;
        }
        return (vMerkleTree.empty() ? 0 : vMerkleTree.back());
    }

举一个例子，假设对应的block中有A,B,C,D四个交易记录（这些交易记录保存在block中的vector vtx）

则使用上述构建默克尔树的方法BuildMerkleTree，则使得block中对应的默克尔树结构体vector vMerkleTree如下图所示：


* 根据交易在块中的索引查询其对应的默克尔树分支

获取对应的默克尔树的分支在CBlock中对应的方法GetMerkleBranch代码如下：

    vector CBolck::GetMerkleBranch(int nIndex) const
    {
        if (vMerkleTree.empty())
            BuildMerkleTree();
        vector vMerkleBranch;
        int j = 0;
        for (int nSize = vtx.size(); nSize > 1; nSize = (nSize + 1) / 2)
        {
            int i = min(nIndex^1, nSize-1);
            vMerkleBranch.push_back(vMerkleTree[j+i]);
            nIndex >>= 1;
            j += nSize;
        }
        return vMerkleBranch;
    }

那么对应于上面的例子，如果我想得到在交易列表vtx中A对应的默克尔树分支，则对应函数GetMerkleBranch（0）对应的返回结果列表如下所示：

• 验证对应的交易是否在默克尔树中
  验证某个节点是否在默克尔树中，在CBlock中对应的方法代码如下：

 static uint256 CBlock::CheckMerkleBranch(uint256 hash, const vector& vMerkleBranch, int nIndex)
    {
        if (nIndex == -1)
            return 0;
        foreach(const uint256& otherside, vMerkleBranch)
        {
            if (nIndex & 1)
                hash = Hash(BEGIN(otherside), END(otherside), BEGIN(hash), END(hash));
            else
                hash = Hash(BEGIN(hash), END(hash), BEGIN(otherside), END(otherside));
            nIndex >>= 1;
        }
        return hash;
    }

验证CheckMerkleBranch方法返回的结果是否和CBlock中对应的默克尔树中对应根的值一样，即如下面代码所示：

if (CBlock::CheckMerkleBranch(GetHash(), vMerkleBranch, nIndex) != pBlock->hashMerkleRoot)
            return 0;

对应上面的例子对应的验证过程如下图所示：

比特币交易对应的数据结构

对应的代码如下：

//
// The basic transaction that is broadcasted on the network and contained in
// blocks.  A transaction can contain multiple inputs and outputs.
//
class CTransaction
{
public:
    int nVersion;
    vector vin;
    vector vout;
    int nLockTime;
// 方法省略
};
//
// A transaction with a merkle branch linking it to the block chain
//
class CMerkleTx : public CTransaction
{
public:
    uint256 hashBlock;
    vector vMerkleBranch;
    int nIndex;

    // memory only
    mutable bool fMerkleVerified;
// 方法省略
}；

从类图或代码中可以看到CMerkleTx 中有一个属性是vMerkleBranch，表示的是对应的每一个默克尔交易都对应一个默克尔树分支，因此对应默克尔交易可以很快的验证这个交易是否在某个CBlock中。