Proving hard-core predicates using list decoding

A. Akavia, S. Goldwasser, S. Safra

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We introduce a unifying framework for proving that predicate P is hard-core for a one-way function f, and apply it to a broad family of functions and predicates, reproving old results in an entirely different way as well as showing new hard-core predicates for well known one-way function candidates. Our framework extends the list-coding method of Goldreich and Levin for showing hard-core predicates. Namely, a predicate will correspond to some error correcting code, predicting a predicate will correspond to access to a corrupted codeword, and the task of inverting one-way functions will correspond to the task of list decoding a corrupted codeword. A characteristic of the error correcting codes which emerge and are addressed by our framework is that codewords can be approximated by a small number of heavy coefficients in their Fourier representation. Moreover, as long as corrupted words are close enough to legal codewords, they will share a heavy Fourier coefficient. We list decodes, by devising a learning algorithm applied to corrupted codewords for learning heavy Fourier coefficients. For codes defined over {0, 1}n domain, a learning algorithm by Kushilevitz and Mansour already exists. For codes defined over ZN, which are the codes which emerge for predicates based on number theoretic one-way functions such as the RSA and Exponentiation modulo primes, we develop a new learning algorithm. This latter algorithm may be of independent interest outside the realm of hard-core predicates.

Original languageEnglish
Title of host publicationProceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003
PublisherIEEE Computer Society
Pages146-157
Number of pages12
ISBN (Electronic)0769520405
DOIs
StatePublished - 2003
Externally publishedYes
Event44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003 - Cambridge, United States
Duration: 11 Oct 200314 Oct 2003

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2003-January
ISSN (Print)0272-5428

Conference

Conference44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003
Country/TerritoryUnited States
CityCambridge
Period11/10/0314/10/03

Bibliographical note

Publisher Copyright:
© 2003 IEEE.

Keywords

  • Computer science
  • Decoding

ASJC Scopus subject areas

  • Computer Science (all)

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