# Unifying computational entropies via Kullback-Leibler divergence

## TL;DR

This paper introduces a new notion called hardness in relative entropy that unifies different forms of computational entropy, providing a clearer understanding and simpler proofs of their relationships with one-way functions.

## Contribution

It defines hardness in relative entropy, unifies multiple entropy notions, and offers a modular proof connecting one-way functions to various entropy forms.

## Key findings

- Hardness in relative entropy is satisfied by all one-way functions.
- It implies both next-block pseudoentropy and inaccessible entropy.
- Provides a simpler proof that one-way functions imply next-block inaccessible entropy.

## Abstract

We introduce hardness in relative entropy, a new notion of hardness for search problems which on the one hand is satisfied by all one-way functions and on the other hand implies both next-block pseudoentropy and inaccessible entropy, two forms of computational entropy used in recent constructions of pseudorandom generators and statistically hiding commitment schemes, respectively. Thus, hardness in relative entropy unifies the latter two notions of computational entropy and sheds light on the apparent "duality" between them. Additionally, it yields a more modular and illuminating proof that one-way functions imply next-block inaccessible entropy, similar in structure to the proof that one-way functions imply next-block pseudoentropy (Vadhan and Zheng, STOC '12).