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@ -147,11 +147,11 @@ image::images/msbt_0701.png[scale="50"]
[[merkle_trees]]
=== Merkle Trees
((("blockchains","merkle trees and", id="ix_ch07-asciidoc1", range="startofrange")))((("merkle trees", id="ix_ch07-asciidoc2", range="startofrange")))Each block in the bitcoin blockchain contains a summary of all the transactions in the block, using a _merkle tree_.
((("block chains","merkle trees and", id="ix_ch07-asciidoc1", range="startofrange")))((("merkle trees", id="ix_ch07-asciidoc2", range="startofrange")))Each block in the bitcoin block chain contains a summary of all the transactions in the block, using a _merkle tree_.
A _merkle tree_, also known as a((("binary hash tree"))) _binary hash tree_, is a data structure used for efficiently summarizing and verifying the integrity of large sets of data. Merkle Trees are binary trees containing cryptographic hashes. The term "tree" is used in computer science to describe a branching data structure, but these trees are usually displayed upside down with the "root" at the top and the "leaves" at the bottom of a diagram, as you will see in the examples that follow.
A _merkle tree_, also known as a((("binary hash tree"))) _binary hash tree_, is a data structure used for efficiently summarizing and verifying the integrity of large sets of data. Merkle trees are binary trees containing cryptographic hashes. The term "tree" is used in computer science to describe a branching data structure, but these trees are usually displayed upside down with the "root" at the top and the "leaves" at the bottom of a diagram, as you will see in the examples that follow.
Merkle trees are used in bitcoin to summarize all the transactions in a block, producing an overall digital fingerprint of the entire set of transactions, providing a very efficient process to verify if a transaction is included in a block. A((("merkle trees","constructing"))) merkle tree is constructed by recursively hashing pairs of nodes until there is only one hash, called the _root_, or _merkle root_. The cryptographic hash algorithm used in bitcoin's merkle trees is SHA256 applied twice, also known as double-SHA256.
Merkle trees are used in bitcoin to summarize all the transactions in a block, producing an overall digital fingerprint of the entire set of transactions, providing a very efficient process to verify whether a transaction is included in a block. A((("Merkle trees","constructing"))) Merkle tree is constructed by recursively hashing pairs of nodes until there is only one hash, called the _root_, or _merkle root_. The cryptographic hash algorithm used in bitcoin's merkle trees is SHA256 applied twice, also known as double-SHA256.
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.