Complete security analysis for certified randomness

Derive a complete security analysis for the certified-randomness protocol based on planted IQP circuits, including security against polynomial-space classical provers with a time budget comparable to the verifier’s simulation time and appropriate preservation of the XEB success parameters.

Background

The paper sketches a certified-randomness application but notes that a full analysis must handle both efficient quantum adversaries and exponential-time classical adversaries constrained by polynomial space. In particular, deriving the needed classical hardness guarantee from the exponential XEB and planted-independent-space conjectures requires a reduction that preserves acceptance and failure probabilities while respecting the time and space bounds.