Negligible-distance simulation of ideal and real adversaries

Construct real and ideal PRF adversaries whose response distributions have negligible statistical distance, thereby eliminating the need for the query-boundedness assumption in the meta-reduction argument.

Background

The proof introduces an ideal adversary that can query the PRG extensively and a real adversary that attempts to simulate the ideal adversary using only the PRG query-answer pairs observed by the reduction. The authors can show only an inverse-polynomial statistical gap between the two adversaries, with the polynomial depending on both the reduction’s number of calls and the adversary’s number of function queries.

Because controlling this dependence requires the reduction’s interaction bound to be fixed independently of the adversary’s query complexity, the proof assumes query-bounded reductions. A negligible-distance simulation would remove that dependence and would make the query-boundedness assumption unnecessary.