Public key recovery for EC leaves in P2MR (BIP-360)

A Merkle tree's depth significantly influences the size of a witness in cryptographic protocols. For a depth-1 tree, the witness is approximately 100 bytes. However, every additional Merkle level increases the control block by 32 bytes, so a depth-2 tree results in a witness size of around 132 bytes. This increment makes the witness larger than that of a typical P2WPKH.

The overall space saving of 35 bytes compared to a standard EC leaf remains constant regardless of tree depth. Therefore, maintaining a shallow Merkle tree is crucial for achieving witness sizes that are comparable to P2WPKH. Deeper Merkle trees negate the efficiency advantage due to the increased size of the control block.