Post Quantum Signatures and Scaling Bitcoin

The discussion initiates with a focus on the potential for Bitcoin to adopt post-quantum (PQ) signature schemes, highlighting their computational efficiency and cost-effectiveness. Specifically, it is noted that PQ signatures, such as those from FALCON-512, are significantly cheaper to validate per byte compared to traditional schemes like edDSA. This cost efficiency, coupled with ongoing research suggesting these signatures' resistance to quantum computing attacks, presents a compelling case for their integration into Bitcoin, especially given the possibility of implementing discounts for their use.

A significant portion of the conversation then shifts towards addressing the challenges associated with transaction aggregation in a post-quantum context. The problem is illustrated through the scenario of handling double spends within aggregated transactions, where two sets of transactions, TA and TB, include mutually exclusive transactions due to double spending attempts. This issue, already present in current practices like coinjoins and mimblewimble aggregation, necessitates careful consideration to avoid unnecessary transaction drop-offs and potential abuse.

Two approaches are proposed to mitigate the risks associated with transaction aggregation. The first suggests that relay nodes share information about the Unspent Transaction Outputs (UTXOs) to be spent by their mempool's transactions before aggregation, aiming to detect and resolve double-spending attempts preemptively. The second approach recommends allowing an aggregator to non-interactively consolidate transactions if they are directly involved as a sender or receiver, thus reducing the likelihood of conflict and ensuring the integrity of transaction fees.

Finally, the conversation delves into the complexities of the relationship between miners, aggregators, and relay nodes concerning transaction fees. It is argued that the current incentive structure might lead to conflicts, where aggregators could potentially undercut miners by combining high and low fee transactions to create a more favorable fee structure for themselves. This scenario could diminish miners' profitability, particularly as block rewards decrease and transaction fees become a more significant income source. The discussion acknowledges this as an extension of existing tensions within Bitcoin's ecosystem but underscores the need for protocol-level interventions to prevent such conflicts, thereby ensuring a fair and efficient transaction processing landscape.