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myarbrough@oreilly.com 2014-11-25 13:22:47 -08:00
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@ -157,6 +157,10 @@ Merkle trees are used in bitcoin to summarize all the transactions in a block, p
When N data elements are hashed and summarized in a merkle tree, you can check to see if any one data element is included in the tree with at most +2*log~2~(N)+ calculations, making this a very efficient data structure. When N data elements are hashed and summarized in a merkle tree, you can check to see if any one data element is included in the tree with at most +2*log~2~(N)+ calculations, making this a very efficient data structure.
[[chain_of_blocks]]
.Blocks linked in a chain, by reference to the previous block header hash
image::images/msbt_0701.png[]
The merkle tree is constructed bottom-up. In the following example, we start with four transactions, A, B, C and D, which form the _leaves_ of the Merkle tree, as shown in <<simple_merkle>>. The transactions are not stored in the merkle tree; rather, their data is hashed and the resulting hash is stored in each leaf node as H~A~, H~B~, H~C~, and H~D~: The merkle tree is constructed bottom-up. In the following example, we start with four transactions, A, B, C and D, which form the _leaves_ of the Merkle tree, as shown in <<simple_merkle>>. The transactions are not stored in the merkle tree; rather, their data is hashed and the resulting hash is stored in each leaf node as H~A~, H~B~, H~C~, and H~D~:
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@ -171,10 +175,6 @@ H~AB~ = SHA256(SHA256(H~A~ + H~B~))
The process continues until there is only one node at the top, the node known as the Merkle root. That 32-byte hash is stored in the block header and summarizes all the data in all four transactions. The process continues until there is only one node at the top, the node known as the Merkle root. That 32-byte hash is stored in the block header and summarizes all the data in all four transactions.
[[chain_of_blocks]]
.Blocks linked in a chain, by reference to the previous block header hash
image::images/msbt_0701.png[]
[[simple_merkle]] [[simple_merkle]]
.Calculating the nodes in a merkle tree .Calculating the nodes in a merkle tree
image::images/msbt_0702.png["merkle_tree"] image::images/msbt_0702.png["merkle_tree"]