MMR
Merkle Mountain Range - efficient binary hash tree for appending new leaves while maintaining integrity.
A Merkle Mountain Range (MMR) is a binary hash tree data structure designed to allow efficient appending of new leaves while maintaining the integrity of the existing nodes. A MMR proof can be utilized to verify whether a specific item is included in the MMR root.
Key Features
Efficient Appending
Allows adding new leaves without rebuilding the entire tree
Integrity Preservation
Maintains integrity of existing nodes when adding new data
Inclusion Proofs
Provides cryptographic proofs for item inclusion verification
Binary Hash Tree
Based on binary tree structure with cryptographic hashing
How MMR Works
1. Mountain Structure
Organizes data as a series of perfect binary trees (mountains) of different heights
2. Append-Only
New items are added to the right, creating new mountains or merging existing ones
3. Proof Generation
Generates inclusion proofs by providing the path from leaf to root across mountains
Advantages over Standard Merkle Trees
- • No Rebalancing: Doesn't require rebuilding when adding new items
- • Efficient Updates: O(log n) complexity for appends
- • Historical Integrity: Previous states remain valid and verifiable
- • Scalable: Suitable for continuously growing datasets
Use Cases
Blockchain Applications
Efficient storage and verification of transaction histories
Audit Trails
Maintaining tamper-proof logs with efficient verification
Timestamping Services
Proving the existence of data at specific points in time
Role in RGB++
MMR structures may be used in RGB++ for efficient verification of Bitcoin block history and transaction inclusion proofs, providing a scalable way to maintain cryptographic commitments to the growing Bitcoin blockchain data.