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

The email details a comprehensive analysis of the security provided by various cryptocurrency transaction schemes under specific conditions. The schemes discussed include P2TRv2, P2TRH, P2MR, and P2QR, each with varying levels of security based on different transaction scenarios: post-deposit, after a Post-Quantum Cryptography (PQC) spend, and following an Elliptical Curve Cryptography (ECC) spend.

For P2TRv2, the scheme remains secure only if Elliptical Curve Cryptography was disabled or non-existent, indicating its vulnerability under standard conditions. The scheme P2TRH shows a moderate level of security, which holds unless there is address reuse, public key sharing, local-range CRQC threats, or collusion between CRQC and a hashrate majority. P2MR offers a similar level of security to P2TRH in standard scenarios but improves slightly when used exclusively under PQC conditions, equating it to the security level of P2QR. Meanwhile, P2QR presents the most robust protection, maintaining security across all tested conditions except when ECC spend occurs, where it fails entirely.

The sender expresses skepticism about the practical benefits of one of the more complex schemes, noting that while it maintains the same incentive profile as P2TRv2, the actual advantages are minimal—restricted primarily to scenarios without address reuse or public key sharing. This limited benefit raises questions about the real-world applicability of such a scheme for enhancing deposit-security without needing to disable ECC, despite its theoretical appeal. The sender's uncertainty highlights a fundamental concern regarding the balance between complexity and utility in developing secure transaction protocols in the evolving landscape of cryptocurrency technologies.