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We ask whether an Identity Based Encryption (IBE) system can be built from simpler public-key primitives. We show that there is no black-box construction of IBE from Trapdoor Permutations (TDP) or even from Chosen Ci-phertext Secure Public Key Encryption (CCA-PKE). These black-box separation results are based on an essential property of IBE, namely that an… (More)

We give an explicit construction of a pseudorandom generator for read-once formulas whose inputs can be read in arbitrary order. For formulas in n inputs and arbitrary gates of fan-in at most d = O(n/ log n), the pseudorandom generator uses (1 − Ω(1))n bits of randomness and produces an output that looks 2 −Ω(n)-pseudorandom to all such formulas. Our… (More)

This paper consists of two conceptually related but independent parts. In the first part we initiate the study of k-SAT instances of bounded diameter. The diameter of an ordered CNF formula is defined as the maximum difference between the index of the first and the last occurrence of a variable. We investigate the relation between the diameter of a formula… (More)

The standard approach for constructing a large-stretch pseudo-random generator given a one-way permutation or given a smaller-stretch pseudo-random generator involves repeatedly composing the given primitive with itself. In this paper, we consider whether this approach is necessary , that is, whether there are constructions that do not involve composition.… (More)

Alekhnovich and Razborov (2002) presented an algorithm that solves SAT on instances φ of size n and tree-width TW(φ), using time and space bounded by 2 O(TW(φ)) n O(1). Although several follow-up works appeared over the last decade, the first open question of Alekhnovich and Razborov remained essentially unresolved: Can one check satisfiability of formulas… (More)

The starting point of this work is the basic question of whether there exists a formal and meaningful way to limit the computational power that a time bounded randomized Turing Machine can employ on its randomness. We attack this question using a fascinating connection between space and time bounded machines given by Cook [Coo71]: a Turing Machine S running… (More)

We characterize the complexity of SAT instances with path-decompositions of width w(n). Although pathwidth is the most restrictive among the studied width-parameterizations of SAT, the most time-efficient algorithms known for such SAT instances run in time 2 Ω(w(n)) , even when the path-decomposition is given in the input. We wish to better understand the… (More)