On the Streaming Indistinguishability of a Random Permutation and a Random Function

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Abstract

An adversary with S bits of memory obtains a stream of Q elements that are uniformly drawn from the set {1,2,...,N}, either with or without replacement. This corresponds to sampling Q elements using either a random function or a random permutation. The adversary’s goal is to distinguish between these two cases. This problem was first considered by Jaeger and Tessaro (EUROCRYPT 2019), which proved that the adversary’s advantage is upper bounded by √Q · S/N. Jaeger and Tessaro used this bound as a streaming switching lemma which allowed proving that known time-memory tradeoff attacks on several modes of operation (such as counter-mode) are optimal up to a factor of O(log N) if Q · S ≈ N. However, the bound’s proof assumed an unproven combinatorial conjecture. Moreover, if Q · S << N there is a gap between the upper bound of √Q · S/N and the Q · S/N advantage obtained by known attacks. In this paper, we prove a tight upper bound (up to poly-logarithmic factors) of O(log Q · Q · S/N) on the adversary’s advantage in the streaming distinguishing problem. The proof does not require a conjecture and is based on a hybrid argument that gives rise to a reduction from the unique-disjointness communication complexity problem to streaming.

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsAnne Canteaut, Yuval Ishai
PublisherSpringer
Pages433-460
Number of pages28
ISBN (Print)9783030457235
DOIs
StatePublished - 1 Jan 2020
Event39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 - Zagreb, Croatia
Duration: 10 May 202014 May 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12106 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020
Country/TerritoryCroatia
CityZagreb
Period10/05/2014/05/20

Keywords

  • Communication complexity
  • Mode of operation
  • Provable security
  • Streaming algorithm
  • Switching lemma
  • Time-memory tradeoff

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