Bitcoin: 計算 Merkle Tree

文章來自簡書

在 計算Block Hash中，接觸到一個變數mrkl_root，即Merkle Tree, 默克爾樹.

                   A               A
                  /  \            /   \
                B     C         B       C
               / \    |        / \     / \
              D   E   F       D   E   F   G
             / \ / \ / \     / \ / \ / \ / \
             1 2 3 4 5 6     1 2 3 4 5 6 7 8

我們計算下 Height 100008的mrkl_root.

這個block只有2個tx:

de2c2e8628ab837ceff3de0217083d9d5feb71f758a5d083ada0b33a36e1b30e
89878bfd69fba52876e5217faec126fc6a20b1845865d4038c12f03200793f48

計算

import hashlib

def hash256(s):
  return hashlib.new('sha256', s).digest()

def dhash256(s):
  return hash256(hash256(s))

tx1="de2c2e8628ab837ceff3de0217083d9d5feb71f758a5d083ada0b33a36e1b30e".decode('hex')[::-1]
tx2="89878bfd69fba52876e5217faec126fc6a20b1845865d4038c12f03200793f48".decode('hex')[::-1]

mrkl_tree = dhash256(tx1+tx2)
result=mrkl_tree[::-1].encode('hex')

print result

result 是 7a059188283323a2ef0e02dd9f8ba1ac550f94646290d0a52a586e5426c956c5

而這個block的mrkl_root呢?

curl https://webbtc.com/block/000000000002dfb177c4acd494b3dd73b9abece24df11c62bb614a8c6c5665e2.json

mrkl_tree: [
"de2c2e8628ab837ceff3de0217083d9d5feb71f758a5d083ada0b33a36e1b30e",
"89878bfd69fba52876e5217faec126fc6a20b1845865d4038c12f03200793f48",
"7a059188283323a2ef0e02dd9f8ba1ac550f94646290d0a52a586e5426c956c5"
]

計算正確, 最需要注意的是大小端的資料轉換

如何做大小端資料轉換 , 請看 https://www.jianshu.com/p/7623cec7620a

一步步計算 merkle Tree

計算block高度 123456的merkle tree

import hashlib

def hash256(s):
  return hashlib.new('sha256', s).digest()

def dhash256(s):
  return hash256(hash256(s))

tx1="5b75086dafeede555fc8f9a810d8b10df57c46f9f176ccc3dd8d2fa20edd685b".decode('hex')[::-1]
tx2="e3d0425ab346dd5b76f44c222a4bb5d16640a4247050ef82462ab17e229c83b4".decode('hex')[::-1]
tx3="137d247eca8b99dee58e1e9232014183a5c5a9e338001a0109df32794cdcc92e".decode('hex')[::-1]
tx4="5fd167f7b8c417e59106ef5acfe181b09d71b8353a61a55a2f01aa266af5412d".decode('hex')[::-1]
tx5="60925f1948b71f429d514ead7ae7391e0edf965bf5a60331398dae24c6964774".decode('hex')[::-1]
tx6="d4d5fc1529487527e9873256934dfb1e4cdcb39f4c0509577ca19bfad6c5d28f".decode('hex')[::-1]
tx7="7b29d65e5018c56a33652085dbb13f2df39a1a9942bfe1f7e78e97919a6bdea2".decode('hex')[::-1]
tx8="0b89e120efd0a4674c127a76ff5f7590ca304e6a064fbc51adffbd7ce3a3deef".decode('hex')[::-1]
tx9="603f2044da9656084174cfb5812feaf510f862d3addcf70cacce3dc55dab446e".decode('hex')[::-1]
tx10="9a4ed892b43a4df916a7a1213b78e83cd83f5695f635d535c94b2b65ffb144d3".decode('hex')[::-1]
tx11="dda726e3dad9504dce5098dfab5064ecd4a7650bfe854bb2606da3152b60e427".decode('hex')[::-1]
tx12="e46ea8b4d68719b65ead930f07f1f3804cb3701014f8e6d76c4bdbc390893b94".decode('hex')[::-1]
tx13="864a102aeedf53dd9b2baab4eeb898c5083fde6141113e0606b664c41fe15e1f".decode('hex')[::-1]

mrkl_tree1 = dhash256(tx1+tx2)
mrkl_tree2 = dhash256(tx3+tx4)
mrkl_tree3 = dhash256(tx5+tx6)
mrkl_tree4 = dhash256(tx7+tx8)
mrkl_tree5 = dhash256(tx9+tx10)
mrkl_tree6 = dhash256(tx11+tx12)
mrkl_tree7 = dhash256(tx13+ tx13) #奇數要重複相加

mrkl_tree1_1 = dhash256(mrkl_tree1 + mrkl_tree2)
mrkl_tree2_2 = dhash256(mrkl_tree3 + mrkl_tree4)
mrkl_tree3_3 = dhash256(mrkl_tree5 + mrkl_tree6)
mrkl_tree4_4 = dhash256(mrkl_tree7 + mrkl_tree7)  #奇數個

mrkl_tree1_1_1 = dhash256(mrkl_tree1_1 + mrkl_tree2_2 )
mrkl_tree2_2_2 = dhash256(mrkl_tree3_3 + mrkl_tree4_4 )

result = dhash256(mrkl_tree1_1_1 + mrkl_tree2_2_2 )

print("0e60651a9934e8f0decd1c5fde39309e48fca0cd1c84a21ddfde95033762d86c", "ok")
print result[::-1].encode('hex')

通用程式碼

#coding: utf-8

import hashlib

def merkle(hashList):
    if len(hashList) == 1:
        return hashList[0]

    newHashList = []

    # Process pairs. For odd length, the last is skipped

    for i in range(0, len(hashList) - 1, 2):
        newHashList.append(dhash256(hashList[i], hashList[i + 1]))

    if len(hashList) % 2 == 1:  # odd, hash last item twice
        newHashList.append(dhash256(hashList[-1], hashList[-1]))
    return merkle(newHashList)

def dhash256(a, b): # a/b 大小端轉換後的資料
    # due to big-endian / little-endian nonsense
    concat = a + b
    temp = hashlib.sha256(concat).digest()
    h = hashlib.sha256(temp).digest()
    return h

#高度 123456
#https://btc.com/0000000000002917ed80650c6174aac8dfc46f5fe36480aaef682ff6cd83c3ca
txHashes = [
    '5b75086dafeede555fc8f9a810d8b10df57c46f9f176ccc3dd8d2fa20edd685b'.decode('hex')[::-1],
    'e3d0425ab346dd5b76f44c222a4bb5d16640a4247050ef82462ab17e229c83b4'.decode('hex')[::-1],
    '137d247eca8b99dee58e1e9232014183a5c5a9e338001a0109df32794cdcc92e'.decode('hex')[::-1],
    '5fd167f7b8c417e59106ef5acfe181b09d71b8353a61a55a2f01aa266af5412d'.decode('hex')[::-1],
    '60925f1948b71f429d514ead7ae7391e0edf965bf5a60331398dae24c6964774'.decode('hex')[::-1],
    'd4d5fc1529487527e9873256934dfb1e4cdcb39f4c0509577ca19bfad6c5d28f'.decode('hex')[::-1],
    '7b29d65e5018c56a33652085dbb13f2df39a1a9942bfe1f7e78e97919a6bdea2'.decode('hex')[::-1],
    '0b89e120efd0a4674c127a76ff5f7590ca304e6a064fbc51adffbd7ce3a3deef'.decode('hex')[::-1],
    '603f2044da9656084174cfb5812feaf510f862d3addcf70cacce3dc55dab446e'.decode('hex')[::-1],
    '9a4ed892b43a4df916a7a1213b78e83cd83f5695f635d535c94b2b65ffb144d3'.decode('hex')[::-1],
    'dda726e3dad9504dce5098dfab5064ecd4a7650bfe854bb2606da3152b60e427'.decode('hex')[::-1],
    'e46ea8b4d68719b65ead930f07f1f3804cb3701014f8e6d76c4bdbc390893b94'.decode('hex')[::-1],
    '864a102aeedf53dd9b2baab4eeb898c5083fde6141113e0606b664c41fe15e1f'.decode('hex')[::-1],
    ]

result = merkle(txHashes)
print(result[::-1].encode('hex'))

---

參考:
merkle-root-bitcoin-step-by-step
https://gist.github.com/shirriff/c9fb5d98e6da79d9a772
http://pythonfiddle.com/merkle-root-bitcoin/
http://www.cnblogs.com/fengzhiwu/p/5524324.html
https://en.wikipedia.org/wiki/Merkle_tree
http://bittorrent.org/beps/bep_0030.html