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A major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists, since expander graphs, the protagonists of our story, come up in numerous and often surprising contexts in both fields. But, perhaps, we should start with a few words about graphs in general. They are, of course, one of the(More)
Informally, an <i>obfuscator</i> <i>O</i> is an (efficient, probabilistic) &#8220;compiler&#8221; that takes as input a program (or circuit) <i>P</i> and produces a new program <i>O</i>(<i>P</i>) that has the same functionality as <i>P</i> yet is &#8220;unintelligible&#8221; in some sense. Obfuscators, if they exist, would have a wide variety of(More)
The simulation paradigm is central to cryptography. A simulator is an algorithm that tries to simulate the interaction of the adversary with an honest party, without knowing the private input of this honest party. Almost all known simulators use the adversary's algorithm as a black-box. We present the first constructions of non-black-box simulators. Using(More)
The contingency table is a work horse of official statistics, the format of reported data for the US Census, Bureau of Labor Statistics, and the Internal Revenue Service. In many settings such as these privacy is not only ethically mandated, but frequently legally as well. Consequently there is an extensive and diverse literature dedicated to the problems(More)
Subexponential time approximation algorithms are presented for the U<scp>nique</scp> G<scp>ames</scp> and S<scp>mall</scp>-S<scp>et</scp> E<scp>xpansion</scp> problems. Specifically, for some absolute constant <i>c</i>, the following two algorithms are presented. (1) An exp(<i>kn</i><sup>&epsi;</sup>)-time algorithm that, given as input a <i>k</i>-alphabet(More)
We show a new way to round vector solutions of semidefinite programming (SDP) hierarchies into integral solutions, based on a connection between these hierarchies and the spectrum of the input graph. We demonstrate the utility of our method by providing a new SDP-hierarchy based algorithm for constraint satisfaction problems with 2-variable constraints(More)
Resettably-sound proofs and arguments maintain sound-ness even when the prover can reset the verifier to use the same random coins in repeated executions of the protocol. We show that resettably-sound zero-knowledge arguments for AEÈ exist if collision-free hash functions exist. In contrast , resettably-sound zero-knowledge proofs are possible only for(More)