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crates.io docs.rs

Merkle Search Tree

This crate implements a Merkle Search Tree as described in the 2019 paper Merkle Search Trees: Efficient State-Based CRDTs in Open Networks by Alex Auvolat & François Taïani.1

When paired with CRDT-based value types, a Merkle Search Tree can act as an efficient anti-entropy primitive, allowing independent replicas to concurrently modify data within the tree with deterministic and eventual convergence across all peers.

See MerkleSearchTree documentation.

Use It

use merkle_search_tree::{MerkleSearchTree, diff::diff};

// Initialise a tree using the default configuration, appropriate for most uses.
let mut node_a = MerkleSearchTree::default();

// Upsert values into the tree.
// For the MST construct to be a CRDT itself, the values stored into the tree
// must also be CRDTs (or at least, have deterministic conflict resolution).
// Here the MST is used as an add-only set (a trivial CRDT) by using () as the
// key values.
node_a.upsert("bananas", &());
node_a.upsert("plátanos", &());

// Another node has differing keys.
let mut node_b = MerkleSearchTree::default();
node_b.upsert("donkey", &());

// The MST root hash can be used as an efficient consistency check (comparison
// is O(1) in space and time).
// In this case, both trees are inconsistent w.r.t each other, which is
// indicated by their differing root hashes.
assert_ne!(node_a.root_hash(), node_b.root_hash());

// Generate compact summaries of the MST content, suitable for transmission over
// the network, and use it to compute the diff between two trees.
let diff_range = diff(

// In this case, node B can obtain the missing/differing keys in node A by
// requesting keys within the computed diff range (inclusive):
assert_matches::assert_matches!(diff_range.as_slice(), [range] => {
    assert_eq!(range.start(), &"bananas");
    assert_eq!(range.end(), &"plátanos");


Operations against a Merkle Search Tree are fast, executing against millions/billions of keys per second:

Key CountInsert All KeysGenerate RootSerialiseDiff (consistent)Diff (inconsistent)
100 keys7µs3µs98ns152ns261ns
1,000 keys92µs39µs847ns577ns4µs
10,000 keys1356µs398µs10µs4µs36µs
100,000 keys17ms3ms112µs26µs287µs

The above measurements capture the single-threaded performance of operations against a tree containing varying numbers of keys on a M1 MacBook Pro.

  • Insert All Keys: insert the N keys listed for the row into an empty tree
  • Generate Root: regenerate the root hash of a modified tree
  • Serialise: encode the tree into a diff format for network communication
  • Diff (consistent): diff generation for identical trees (no differing ranges)
  • Diff (inconsistent): diff generation for a fully inconsistent tree

The benchmarks to generate these numbers are included in this repo (run cargo bench).


This crate is extensively tested using randomised fuzzing & property testing to validate correctness, and ensure no panics occur in release builds.

  1. Alex Auvolat, François Taïani. Merkle Search Trees: Efficient State-Based CRDTs in Open Networks. SRDS 2019 - 38th IEEE International Symposium on Reliable Distributed Systems, Oct 2019, Lyon, France. pp.1-10, ⟨10.1109/SRDS.2019.00032⟩. ⟨hal-02303490⟩ 


  • Tree difference calculation algorithm & associated types.
  • Hash function abstraction & digest types.
  • Trait & implementations for tree structure inspection.