Hard-core predicate and list decoding

Abstract

 A hard-core predicate P of a one-way function f is a predicate of the
input of f which is not leaked by f.  There are many classical results
regarding hard-core predicates of the most common cryptographically
useful one-way functions such as RSA, discrete exponentiation or the
Rabin function. A classical result by Goldreich and Levin states that
every one-way function has a hard-core predicate.

At FOCS 2003, Akavia, Goldwasser and Safra gave a coding theoretic
interpretation of Goldreich and Levin's result and an elegant list
decoding methodology to prove that a predicate is a hard-core of a
one-way function. Additionally, they showed how to use the methodology
to  get a simpler proof of many classical works on hard-core predicates,
although their result did not apply to important results like the one
that says that the bits in the middle of RSA, Rabin or the discrete
exponentiation problem are hard-core (Håstad and Näslund, 1996).

In this talk I will explain this connection between list decoding and
hard-core predicates of Akavia et al. I will also explain how, in joint
work with Paz Morillo, we extended their results to the middle bits of
these functions.  The talk is aimed at a general public interested in
theoretical computer science  (not necessarily cryptographically savvy).