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

In the exploration of advanced cryptographic techniques within blockchain technology, particularly focusing on Bitcoin's potential future upgrades, an interesting point arises regarding the use of outpoints as commitments to public keys. This concept could be innovatively applied in scenarios such as taproot key path spends if a segwit v2 soft fork is implemented. The idea suggests that by leveraging the outpoint—which is already available on the input side of a transaction—there may be an opportunity to recover public keys directly. This approach offers a theoretical workaround to some existing limitations by potentially eliminating the need to explicitly include the public key, thus subtly enhancing privacy and efficiency.

However, this method is not without its drawbacks, which are significant enough to warrant cautious consideration before any practical application is attempted. One major limitation is the inability to perform batch validation, a process crucial for ensuring the efficiency and scalability of transactions on the blockchain. Additionally, employing this technique would require breaking the abstraction around the signature scheme, which could introduce complexity and reduce the robustness of the system. These challenges highlight the need for a balanced approach to innovation in cryptographic practices, where the benefits must be carefully weighed against the potential risks and downsides.