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Unifying Computational Entropies via Kullback–Leibler Divergence

  • Rohit AgrawalEmail author
  • Yi-Hsiu ChenEmail author
  • Thibaut HorelEmail author
  • Salil Vadhan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11693)

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).

Keywords

One-way function Pseudorandom generator Pseudoentropy Computational entropy Inaccessible entropy Statistically hiding commitment Next-bit pseudoentropy 

Notes

Acknowledgements

We thank Muthuramakrishnan Venkitasubramaniam for an inspiring conversation which sparked this work.

Supplementary material

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.John A. Paulson School of Engineering and Applied SciencesHarvard UniversityCambridgeUSA

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