Unifying computational entropies via Kullback-Leibler divergence

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

Paper 2019/264

Unifying computational entropies via Kullback-Leibler divergence

Rohit Agrawal, Yi-Hsiu Chen, 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).

Metadata

Available format(s): PDF
Category: Foundations
Publication info: A minor revision of an IACR publication in CRYPTO 2019
DOI: 10.1007/978-3-030-26951-7_28
Keywords: one-way functions pseudo-randomness bit commitment information theory pseudoentropy inaccessible entropy
Contact author(s): thorel @ seas harvard edu
History: 2019-08-20: revised; 2019-03-06: received; See all versions
Short URL: https://ia.cr/2019/264
License: CC BY

BibTeX

@misc{cryptoeprint:2019/264,
      author = {Rohit Agrawal and Yi-Hsiu Chen and Thibaut Horel and Salil Vadhan},
      title = {Unifying computational entropies via Kullback-Leibler divergence},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/264},
      year = {2019},
      doi = {10.1007/978-3-030-26951-7_28},
      url = {https://eprint.iacr.org/2019/264}
}