License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2017.39
URN: urn:nbn:de:0030-drops-74738
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7473/
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Pietrzak, Krzysztof ; Skorski, Maciej

Non-Uniform Attacks Against Pseudoentropy

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LIPIcs-ICALP-2017-39.pdf (0.6 MB)

Abstract

De, Trevisan and Tulsiani [CRYPTO 2010] show that every distribution over n-bit strings which has constant statistical distance to uniform (e.g., the output of a pseudorandom generator mapping n-1 to n bit strings), can be distinguished from the uniform distribution with advantage epsilon by a circuit of size O( 2^n epsilon^2).

We generalize this result, showing that a distribution which has less than k bits of min-entropy, can be distinguished from any distribution with k bits of delta-smooth min-entropy with advantage epsilon by a circuit of size O(2^k epsilon^2/delta^2). As a special case, this implies that any distribution with support at most 2^k (e.g., the output of a pseudoentropy generator mapping k to n bit strings) can be distinguished from any given distribution with min-entropy k+1 with advantage epsilon by a circuit of size O(2^k epsilon^2).

Our result thus shows that pseudoentropy distributions face basically the same non-uniform attacks as pseudorandom distributions.

BibTeX - Entry

@InProceedings{pietrzak_et_al:LIPIcs:2017:7473,
  author =	{Krzysztof Pietrzak and Maciej Skorski},
  title =	{{Non-Uniform Attacks Against Pseudoentropy}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{39:1--39:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7473},
  URN =		{urn:nbn:de:0030-drops-74738},
  doi =		{10.4230/LIPIcs.ICALP.2017.39},
  annote =	{Keywords: pseudoentropy, non-uniform attacks}
}

Keywords: pseudoentropy, non-uniform attacks
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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