Optimal Threshold Signatures in Bitcoin

The discussion revolves around the statistical analysis of multisignature and threshold systems, highlighting a curiosity about the independence of probabilities (p(\tau)) and (q(\tau)). The sender expresses interest in previous literature on this subject, implying that such analyses might not be novel but are still of significant interest. There is an acknowledgment of a specific paper that deals with the topic at hand, suggesting that the question of whether (p(\tau)) and (q(\tau)) are truly independent has been considered academically.

Further into the conversation, the sender questions the assumption that (p(\tau)) and (q(\tau)) are independent, providing a rationale that these probabilities may inherently be related due to their definitions within the context of security systems. Specifically, (p(\tau)) is associated with the likelihood of an authorized user accessing their own system, while (q(\tau)) pertains to the probability of an external party gaining unauthorized access. This distinction raises concerns about the simplification of considering these probabilities as independent without taking into account potential underlying connections, particularly in how they relate to user behavior and the formalization of "someone else" within threshold systems. The dialogue suggests a deeper examination of these probabilities' interdependence, challenging the initial assumption and pointing towards a nuanced understanding of security dynamics in multisignature and threshold frameworks.