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 + , then s 4 = 2 k 1 1 probabilistic polynomial time algorithms f ^ A 1 ; : : : ; ^ A s g exist such that for 8z 2 f0; : : : ; k 1g , there exists ^ A i 2 f ^ A 1 ; : : : ; ^ A s g such that Pr[ ^ A i (z) = g(z)] 1...

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 pred...

For various well-known proofs of knowledge, we address the problem of how much information a cheating polynomial-time veriier can learn about individual bits of the prover's secret key. Speciically, under the widely believed assumption that the Schnorr identiication protocol is witness hiding, no polynomial-time veriier can distinguish the O(log k) most signiicant bits of the prover's secret ke...

We prove that a general family of hard core predicates requires circuits of depth (l-o(l)) ~ or super-polynomial size to be realized. This lower bound is essentially tight, l~or constant depth circuits, an exponential lower bound on the size is obtained. Assuming the existence of one-way functions, we explicitly construct a one-way function f(x) such that for any circuit c from a family of circ...

We study a 12-parameter stochastic process involving particles with two-site interaction and hardcore repulsion on a d-dimensional lattice. In this model, which includes the asymmetric exclusion process, contact processes and other processes, the stochastic variables are particle occupation numbers taking values n~x = 0, 1. We show that on a 10-parameter submanifold the k-point equaltime correl...

We developed a self-consistent screened-Korringa± Kohn± Rostoker (KKR) method in an ab initio tight-binding formulation. The reduction in numerical e€ ort in comparison with that required for the standard KKR method is achieved by the choice of a suitable reference system. Following the idea of Zeller et al. (1995, Phys. Rev. B, 52, 8807), reference systems with repulsive mu n-tin potentials o...