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...

• Type: Conference
• Year: 2003
• Where: FOCS
• Authors: Adi Akavia, Shafi Goldwasser, Shmuel Safra
• Keywords: Code Words, FOCS 2003, Hard-core Predicates, One-way Functions, Theoretical Computer Science