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Proving Hard-Core Predicates Using List Decoding

10 years 8 months ago
Proving Hard-Core Predicates Using List Decoding
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-decoding 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 code word, and the task of inverting one-way functions will correspond to the task of list decoding a corrupted code word. A characteristic of the error correcting codes which emerge and are addressed by our framework, is that code words 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 code words, they will share a heavy Fourier coefficient. We list dec...
Adi Akavia, Shafi Goldwasser, Shmuel Safra
Added 04 Jul 2010
Updated 04 Jul 2010
Type Conference
Year 2003
Where FOCS
Authors Adi Akavia, Shafi Goldwasser, Shmuel Safra
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