Multisymbol majority vote and hard core

Abstract

This paper describes a weak sense majority-vote technique for a k -symbol function g ( z ) as follows. If a probabilistic polynomial time algorithm A exists such that Pr [A(z) = g(z)] ⩾ 1 k+ ε , then s≜2 k−1 − 1 probabilistic polynomial time algorithms { A ̂ ,…, A ̂ s } exist such that for ∀ z ϵ {0, …, k − 1} ∗ , there exists A ̂ i ϵ { A ̂ 1 ,…, A ̂ s } such that Pr[ A ̂ i (z) = g(z) ] ⩾ 1 − ¦ z ¦ −c , where c is a constant. We apply our technique to obtain a hard core of k -symbol one-way functions.