Merkle tree

(data structure)

Definition: A tree (usually a binary tree) in which each internal node has a hash of all the information in the leaf nodes under it. Specifically, each internal node has a hash of the information in its children. Each leaf has a hash of the block of information it represents. All leaf nodes are at the same depth. All nodes are as far left as possible.

To add a block (leaf) to a full tree, a new root is created with the old root as its left child. Its right child is a degenerate tree (only left subtrees) all the way to the leaf level.

Also known as hash tree.

Generalization (I am a kind of ...)

Aggregate child (... is a part of or used in me.)
hash function.

See also Merkle_tree [Wikipedia].

Note: Usually the branching is two, making it a binary tree, but it can be a k-ary tree.

Merkle's paper describes a conceptually infinite (binary) tree with blocks (documents) at each internal node. To add a new block, use the next node in a level-order traversal. (A level-order traversal is the same order as a breadth-first search from the root.)

Given two copies of possibly-the-same information represented by Merkle trees, one can check whether the copies are the same by just comparing the hashes at the root. A single difference between the copies can be found by just comparing the hashes at internal nodes on a path to the different leaf. This is logarithmic in the number of leaves.

A complete tree has all nodes as far left as possible, too, but every level is filled.

Author: PEB

More information

Average space required and complexity for search, traversal, insert, delete, and synchronize.

Ralph C. Merkle, Method of providing digital signatures, U.S. Patent 4309569, filed 5 September 1979. PDF image available at Text version available at enter 4309569 and click Search.
Ralph C. Merkle, A Digital Signature Based on a Conventional Encryption Function, in C. Pomerance (ed) Advances in Cryptology — CRYPTO ’87. Lecture Notes in Computer Science 293:369-378, 1988. doi:10.1007/3-540-48184-2_32

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Entry modified 19 February 2019.
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Paul E. Black, "Merkle tree", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 19 February 2019. (accessed TODAY) Available from: