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

The exploration of utilizing the hash of the public key (pubkey) as opposed to the pubkey itself in the Schnorr challenge presents a significant observation with broader implications beyond its initial context. This technique could potentially enhance pubkey recovery processes, not only within Pay-to-Merkle-root (P2MR) transactions but also for taproot script paths. The possibility of implementing this method in future upgrades, such as through a new leaf version, is contingent on further evaluation of its benefits and drawbacks.

One notable complication arises from the impact on batch validation. Incorporating the pubkey hash might necessitate an adjustment in weight units due to the increased computational overhead, although this can be mitigated by opting to download pubkeys alongside blocks. This trade-off between CPU usage and bandwidth consumption offers flexibility depending on the verification practices at the node level, particularly for nodes that do not employ blocksonly mode and hence perform real-time transaction validation.

Further analysis reveals another intriguing aspect related to the outpoint, which serves as a commitment to the pubkey and appears on the input side of a transaction. This feature could be leveraged for pubkey recovery in scenarios involving taproot key path spends, assuming the implementation of a segwit v2 soft fork. Such advancements could pave the way for more efficient and secure cryptographic practices, although the practical applications of these observations still require thorough investigation and testing within the community.