An Information-Theoretic Proof of the Streaming Switching Lemma for Symmetric Encryption

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Abstract

Motivated by a fundamental paradigm in cryptography, we consider a recent variant of the classic problem of bounding the distinguishing advantage between a random function and a random permutation. Specifically, we consider the problem of deciding whether a sequence of q values was sampled uniformly with or without replacement from [N], where the decision is made by a streaming algorithm restricted to using at most s bits of internal memory. In this work, the distinguishing advantage of such an algorithm is measured by the KL divergence between the distributions of its output as induced under the two cases. We show that for any s = Ω(logN) the distinguishing advantage is upper bounded by O(q · s/N), and even by O(q·s/N logN) when q N1 - ϵ for any constant ϵ > 0 where it is nearly tight with respect to the KL divergence.

Original languageAmerican English
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages858-863
Number of pages6
ISBN (Electronic)9781728164328
DOIs
StatePublished - Jun 2020
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: 21 Jul 202026 Jul 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2020-June

Conference

Conference2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/TerritoryUnited States
CityLos Angeles
Period21/07/2026/07/20

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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