PQC output type discussion

The discussion on the adoption and evolution of Taproot in the context of Bitcoin transaction efficiency highlights several critical points. Firstly, the adoption of Taproot has been less extensive than anticipated over the past five years. This slow uptake is noted even during periods of mempool congestion, with limited support from providers for sending to Taproot addresses, let alone setting them as default.

Regarding the types of common payment paths, there are distinctions in their cost-effectiveness and implementation timelines. Single signature transactions using Taproot are slightly more expensive than p2wpkh due to larger outputs. For n-of-n multisig configurations, efficiency gains were not realized until the introduction of musig in recent updates across various platforms, with core updates and specifications for lightning only just being incorporated. However, for k-of-n multisig and more complex script-based transactions, such as those involving hash-path or timelock for HTLCs, there seems to be no significant cost advantage with Taproot at present.

In terms of fee reductions, potential impacts are explored, particularly for exchanges where transitioning to FROST key path signatures could reduce transaction fees significantly, up to 60% in some scenarios, contingent upon rising fee rates. The introduction of more complex codes for managing collisions in node anonymity also presents a trade-off between collision probability and reconstruction complexity.

Lastly, the consideration of future enhancements in blockchain technology, such as SHRINCS for optimizing computational costs related to witness data, suggests ongoing research and development efforts. The idea of expanding block sizes to accommodate new standards while managing data throughput efficiently proposes substantial changes to the underlying network protocols, potentially requiring new peer-to-peer messaging formats or constraints on transaction sizes to manage the load of post-quantum cryptographic signatures effectively.