A Convex Analysis Approach to Computational Entropy

TL;DR

This paper applies convex optimization techniques to analyze computational entropy, exploring derandomization, differences across circuit classes, and simplified characterizations to deepen understanding of security measures.

Contribution

It introduces a convex analysis framework to study computational entropy, providing new insights into derandomization, class differences, and simplified characterizations.

Findings

Derandomization of computational entropy is possible under certain conditions.

Significant differences in entropy exist between unbounded and efficient adversaries.

New convex-based characterizations of computational entropy are proposed.

Abstract

This paper studies the notion of computational entropy. Using techniques from convex optimization, we investigate the following problems: (a) Can we derandomize the computational entropy? More precisely, for the computational entropy, what is the real difference in security defined using the three important classes of circuits: deterministic boolean, deterministic real valued, or (the most powerful) randomized ones? (b) How large the difference in the computational entropy for an unbounded versus efficient adversary can be? (c) Can we obtain useful, simpler characterizations for the computational entropy?