Merkle Mountain Range (MMR)

A Merkle Mountain Range (MMR) is a data structure derived from the concept of a Merkle tree, designed to address certain limitations and provide improved efficiency and flexibility for maintaining and verifying a consistent log of data. Here's a detailed explanation of what an MMR is, how it differs from a Merkle tree, and why it is required:

• An MMR is a data structure that maintains a log of data elements in a tree-like fashion.
• In an MMR, each leaf node represents a distinct piece of data, and each node in the tree (including the leaves) is labeled with the hash of its child nodes, calculated using a hash function.
• MMRs are designed to efficiently handle the insertion of new data elements into the structure and provide a means to prove the existence of a specific data element within the tree.

Visual journey of adding elements

Notice that previous roots are not changing and new roots is only getting formed.

Key Characteristics and Differences from a Merkle Tree:

Efficient Data Insertion: MMRs excel in efficiently adding new data elements to the structure. When new data is appended, it creates a new subtree containing only the new element, and this operation can be done directly on-chain without the need to recalculate the entire tree. This is a significant improvement over traditional Merkle trees, which are computationally expensive to update on-chain.

Flexible Structure: MMRs are constructed to maintain the largest consistent single binary tree, which means that they may have multiple "peaks" or sister trees. This flexibility allows for better adaptation to evolving data sets.

Batching Peaks: To compute the root hash of the entire MMR, the peaks of the individual trees within the MMR must be batched together. This enables efficient verification of the overall MMR structure.

Verification of Existence: MMRs are especially useful for proving the existence of a specific data element within the structure. A verifier can provide a compact proof of inclusion, which can be verified using the MMR's root hash and the appropriate hashes at the necessary levels of the tree, without needing direct access to the entire MMR.

Why MMRs Are Required:

MMRs are required to overcome the limitations of traditional Merkle trees, particularly in scenarios where on-chain data updates are necessary. They provide an efficient and transparent way to maintain a consistent and secure record of data.
MMRs are valuable for use cases that involve non-interactive state proofs, allowing for the verification of data without the need for direct interaction with the data source. This is particularly important in blockchain and decentralized systems.
While MMRs can be more gas-expensive to verify on-chain compared to Merkle tree proofs, they offer a solution for managing growing data sets that cannot be practically handled with traditional Merkle trees. Off-chain verification methods, such as Zero-Knowledge Proofs (ZKPs), are often used to make large MMRs feasible for verification.
In summary, Merkle Mountain Ranges provide a versatile and efficient way to manage and verify data in a tree structure, making them essential for certain applications, especially in the context of blockchain and decentralized systems where data integrity and proof verification are crucial.