Cryptology ePrint Archive: Report 2019/264

Unifying computational entropies via Kullback-Leibler divergence

Rohit Agrawal and Yi-Hsiu Chen and Thibaut Horel and Salil Vadhan

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).

Category / Keywords: foundations / one-way functions, pseudo-randomness, bit commitment, information theory, pseudoentropy, inaccessible entropy

Original Publication (with minor differences): IACR-CRYPTO-2019

Date: received 4 Mar 2019, last revised 20 Aug 2019

Contact author: thorel at seas harvard edu

Available format(s): PDF | BibTeX Citation

Version: 20190820:182926 (All versions of this report)

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