What is a hash tree, and how does it verify data?

A hash tree, also known as a Merkle tree, is a data structure used for efficiently verifying and handling data in computer systems.

A hash tree is a tree of hashes in which the leaves are hashes of data blocks in, for example, a file or set of files. Nodes further up in the tree are the hashes of their respective children. The 'root' or topmost hash is called the Merkle root. The beauty of this structure is that it allows for efficient and secure verification of the contents of large data structures. If a single detail changes in the input, it will cause a cascading effect, changing the parent hash, and ultimately the Merkle root.

To verify data using a hash tree, you would start by hashing each piece of data in the set to create the 'leaves' of the tree. Then, pair up these hashes and hash them together to create the next level of the tree. Continue this process until you reach the top of the tree, which will give you the Merkle root. This root can then be compared with a trusted root to verify the data. If the roots match, the data is verified. If not, the data has been tampered with or corrupted.

The advantage of using a hash tree is that it is very efficient. If you need to verify a large set of data, you don't need to re-hash the entire set. Instead, you only need to re-hash the branches of the tree that contain the changed data. This makes hash trees particularly useful in peer-to-peer systems and distributed networks, where efficiency is key.

In summary, a hash tree is a powerful tool in computer science for verifying and handling data. It uses the properties of hash functions to create a tree structure that can be used to efficiently verify whether data has been tampered with or corrupted.