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(Summed) Merklized Binary Radix Tree library
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This Python3 library implements a form of Merklized Binary Prefix Tree called a "Merbinner Tree". Like a standard merkle tree a Merbinner Tree is a cryptographic data structure that securely and efficiently commits a set of items such that the existence of a given item in the set can be efficiently proven. Unlike a merkle tree these items are key:value pairs, forming a map/dictionary, allowing one to also efficently prove that a given key does not exist.

Items in a merbinner tree can be efficiently updated and removed, creating a new tree. Merbinner trees can also be pruned, resulting in a tree that can prove a subset of the operations the unpruned tree can prove.

Design Goals

  • Reasonable performance in space and time for both large and small number of items.

  • Simple implementation.

  • Deterministic: any key modification ordering should result in same tree.

  • Assume key and value are hashes - long key collisions essentially impossible.

  • Must be cryptographically secure and without collisions even in the face of an adversary.

Why not pure merkle binary prefix tree? Makes things simplier, but requires about an order of magnitude more hashes. (e.g. 20bit ~= 1million items vs 256bit)

Supported Operations



set key:value


remove key from tree


Return the key:value pair whose key is closest (rounding?) to a given key.


Merge two pruned trees together, resulting in a tree that can prove the superset of operations the two pruned trees supported.


Update one tree with another.

Postfix Key Compression

Compromise between a standard radix tree and a pure merkle binary prefix tree. When keys are hashes it's infeasible to find long collisions, limiting maximum proof size, good engineering. Also radix key compression becomes useless.

Types of Nodes

Empty Node

Contains: Nothing

Hashed: <0x00>

Signifies that this part of the tree has nothing in it.

Leaf Node

Contains: key and H(value)

Hashed: <H(value)> <0x01>

Inner Node

Contains: left and right child nodes

Hashed: {H(sums)} <0x02>

Pruned Inner Node

Contains: hash

Signifies that this part of the tree contains an inner node, however the contents have been pruned. We can't modify these contents, nor do we know what's in them.

Full Leaf Node

Contains: key and value

Unit Tests

python3 -m unittest discover -s merbinnertree

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