ZK-gossip for lightning channel announcements

The discussion revolves around the continuous search for a practical and efficient proof scheme to enhance certain cryptographic operations, notably within the context of Bitcoin coding and possibly the Lightning Network. Over the years, there has been a quest to find a solution that improves upon the computational and verification times associated with these operations. Three years ago, the focus was on ring signatures, which despite their potential, failed to surpass the O(N) complexity for computation and verification processes. This historical context sets the stage for evaluating new developments in this domain.

A notable advancement in this area is the exploration of Curve Trees, which are presented as a significantly improved mechanism compared to ring signatures. These offer markedly reduced proving and verifying times, an essential factor for their consideration. Moreover, Curve Trees can be integrated into existing systems without introducing a vast array of new dependencies, as they are compatible with established cryptographic primitives like secp and secq curves, including bulletproof circuits. This compatibility is crucial for ensuring that the broader adoption within Bitcoin coding does not necessitate a complete overhaul of current cryptographic foundations.

However, the transition from theoretical advantages to practical application faces substantial challenges. The author mentions an experimental repository (aut-ct) dedicated to Curve Trees, acknowledging its status as more of a hobbyist project rather than a ready-to-deploy solution. The lack of widespread implementation and the absence of a "mature implementation space" highlights the early-stage nature of Curve Trees within the cryptographic community. Despite this, the mention of the FCMP++ project, which has undergone an audit, provides a glimpse into the efforts aimed at validating and potentially mainstreaming such novel concepts.

The conversation also touches upon zk-STARKs, another promising technology for achieving zero-knowledge proofs, indicating a broader landscape of innovation and exploration in cryptographic techniques. The dialogue reflects a critical examination of what criteria and technical specifications are necessary for these technologies to be considered viable for real-world applications, specifically within the Lightning Network's requirements for utxo ownership proofs.

In summary, while significant strides have been made towards identifying and developing more efficient cryptographic schemes like Curve Trees and zk-STARKs, the journey from theoretical innovation to practical utility involves navigating technical complexities, ensuring compatibility with existing systems, and fostering a collaborative effort towards maturation and eventual implementation.