Non uniform attacks against pseudoentropy
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Corresponding author has ISTA affiliation
Department
Series Title
LIPIcs
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.
Publishing Year
Date Published
2017-07-01
Publisher
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Volume
80
Article Number
39
Conference
ICALP: Automata, Languages and Programming
Conference Location
Warsaw, Poland
Conference Date
2017-07-10 – 2017-07-14
ISSN
IST-REx-ID
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2018-12-12
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