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

The email details a technical discussion regarding spend costs associated with different cryptographic paths, highlighting the overhead and signature requirements for each type. Specifically, all paths except P2PQ incur a consistent overhead of 32 bytes (B) for Post-Quantum Cryptography (PQC). Additionally, the ECC signature sizes vary with the smallest being 64B for P2TRv2 and P2TRH, while P2MR requires a larger size of 128B, and P2MR+PKR uses a 96B size. It is noted that non-batchable signatures due to public key recovery requirements are a significant consideration in these configurations.

Furthermore, the discussion considers the implications of increasing block sizes to accommodate the larger signatures required by quantum-resistant cryptographic methods. By introducing an extension block specifically for Post-Quantum (PQ) signature data, it suggests a potential reduction in overhead costs for ECC spends in scenarios like P2MR or P2MR+PKR. The proposal includes making the first 32B or 64B per input free, which might align the economic viability of ECC paths with more commonly used ones such as p2wpkh and p2tr. This solution aims to balance the need for enhanced security with the economic impacts of implementing these more robust cryptographic measures.