Constructing and Verifying Merkle Trees using OP_CAT

Following our series #1, we demonstrate how to construct and verify Merkle trees using OP_CAT. In Bitcoin, Merkle trees are utilized as the data structure for verifying data, synchronization, and effectively linking the blockchain's transactions and blocks together.

This post was first published on Medium.

Following our series #1, we demonstrate how to construct and verify Merkle trees using OP_CAT.

In Bitcoin, Merkle trees are used as the data structure for verifying data, synchronizing the blockchain, and efficiently linking transactions and blocks together. The OP_CAT opcode, which allows for the concatenation of two stack variables, can be used with SHA256 hashes of public keys to streamline the Merkle tree verification process within Bitcoin Script. OP_CAT uniquely allows for the creation and opening of entries in Merkle trees, as the fundamental operation for building and verifying Merkle trees involves concatenating two values and then hashing them.

There are many applications for Merkle trees. Here are a few prominent examples:

Merkle proof

A Merkle proof is a cryptographic method used to verify that a particular transaction is included in a Merkle tree without having to download the entire blockchain. This is especially useful for lightweight clients and improving the efficiency of data verification.

Tree signature

A tree signature is a cryptographic method that improves the security and efficiency of digital signatures using tree structures, especially Merkle trees. This approach is used to generate a more compact and private proof that a message or set of messages has been signed by a particular key, compared to regular Multisig.

Zero-Knowledge Proof

STARK (Succinct Transparent Arguments of Knowledge) is a type of zero-knowledge proof system. STARKs are designed to allow a prover to prove the validity of a computation to a verifier without revealing any sensitive information about the computation itself. If OP_CAT were to be added to Bitcoin, it could potentially enable the implementation of a STARK verifier in Bitcoin Script, with work already underway on this. This would allow for secure and private transactions on the Bitcoin network. Compared to pairing-based proof systems like SNARK, STARK is considered to be more Bitcoin-friendly.

Implementation

The implementation of the Merkle tree using sCrypt is straightforward. The following code calculates the root hash of a merkle tree, given a leaf and its merkle path, typically used in verifying a merkle proof.

Full code is at https://github.com/sCrypt-Inc/scrypt-btc-merkle.

A single run results in the following transactions:

Check the transaction on Mempool

Check the transaction on Mempool

Script versions

There are alternative implementations in bare scripts, like the one below. One major benefit of using sCrypt for implementing merkle trees is its readability and maintainability. Scripts are often very difficult to read and work on.

OP_EXISTS

Plz tell me you had a compiler to generate that

— Jerry – Bitcoin Bay (@Lightswarm) March 1, 2024

Stay tuned for more OP_CAT use cases.

Watch: sCrypt Hackathon students realize there’s more to blockchain

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