[BIP proposal] Pay to Schnorr Key Hash (P2SKH)

The concept of finding a hash collision between Alice's script and Bob's script presents a fascinating yet computationally intensive challenge. The process involves generating a massive lookup table of Alice Script hashes, which then allows for the identification of a collision by comparing it against Bob Script hashes. This method requires about 2^81 operations, slightly more than the previously estimated 2^80, due to the specificity of the collision search rather than finding any collision. The task demands an enormous amount of storage, theoretically requiring around 2^45 terabytes, or approximately 100 trillion 1TB hard drives, highlighting the impracticality of such an endeavor with current technology.

However, the discussion introduces a potential solution through time-memory tradeoffs, suggesting that the problem is not entirely insurmountable. By applying these tradeoffs, as well as leveraging insights from the ColliderScript project, it's possible to reduce the requirements significantly. ColliderScript, which addresses similar challenges in creating covenants in Bitcoin via 160-bit hash collisions, provides valuable equations for optimizing this process. According to the calculations derived from ColliderScript’s approaches, the necessary resources could potentially be reduced to around 2^81 hash queries and 2^56 storage, equivalent to roughly 4096 1TB hard drives.

The financial aspect of generating such a hash collision also receives attention. If one were to use ASICs (Application-Specific Integrated Circuits) for this task, the electricity costs alone would range from $100,000 to $2 million per collision. This estimation suggests that while still expensive, the cost is considerably lower than what might be expected for similar operations in other contexts, like those outlined in ColliderScript. This discrepancy in cost arises from the different parameters and considerations specific to each case, underscoring the unique challenges and efficiencies present in this particular cryptographic endeavor.

For further reading and a deeper understanding of the technical underpinnings and mathematical formulas involved in hash collision efforts within the realm of Bitcoin and cryptographic research, the ColliderScript paper offers detailed insights. Interested parties can explore the document, particularly appendix E and F, which are directly relevant to the discussed hash collision problem, at ColliderScript: Covenants in Bitcoin via 160-bit hash collisions.