### More Examples

*“ Merkle trees allow secure verification of large data structures.”*

*“Bitcoin Merkle trees use a double SHA-256.”*

*“A row containing a single double-hash is the root of the Merkle tree.”*

### Definition(s) from the Web

- Merkle trees are binary trees of hashes. Merkle trees in bitcoin use a double SHA-256, the SHA-256 hash of the SHA-256 hash of something. If, when forming a row in the tree (other than the root of the tree), it would have an odd number of elements, the final double-hash is duplicated to ensure that the row has an even number of hashes. First form the bottom row of the tree with the ordered double-SHA-256 hashes of the byte streams of the transactions in the block. Then the row above it consists of half that number of hashes. Each entry is the double-SHA-256 of the 64-byte concatenation of the corresponding two hashes below it in the tree. This procedure repeats recursively until we reach a row consisting of just a single double-hash. This is the Merkle root of the tree. Source
- In cryptography and computer science, a hash tree or Merkle tree is a tree in which every leaf node is labelled with the cryptographic hash of a data block, and every non-leaf node is labelled with the cryptographic hash of the labels of its child nodes. Hash trees allow efficient and secure verification of the contents of large data structures. Hash trees are a generalization of hash lists and hash chains. Demonstrating that a leaf node is a part of a given binary hash tree requires computing a number of hashes proportional to the logarithm of the number of leaf nodes of the tree; this contrasts with hash lists, where the number is proportional to the number of leaf nodes itself. The concept of hash trees is named after Ralph Merkle, who patented it in 1979. Source