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- Sanjeev Arora, Boaz Barak
- 2009

Not to be reproduced or distributed without the authors' permission This is an Internet draft. Some chapters are more finished than others. References and attributions are very preliminary and we apologize in advance for any omissions (but hope you will nevertheless point them out to us).

- Shlomo Hoory, Nathan Linial, Avi Wigderson, Ran Gilad-Bachrach, Danny Harnik, Boaz Barak +15 others
- 2006

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)

- Boaz Barak, Oded Goldreich, Russell Impagliazzo, Steven Rudich, Amit Sahai, Salil P. Vadhan +1 other
- CRYPTO
- 2001

Informally, an <i>obfuscator</i> <i>O</i> is an (efficient, probabilistic) “compiler” 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 “unintelligible” in some sense. Obfuscators, if they exist, would have a wide variety of… (More)

- Boaz Barak
- FOCS
- 2001

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>ε</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)

We put forward a new type of computationally-sound proof systems, called universal-arguments, which are related but diierent from both CS-proofs (as deened by Micali) and arguments (as deened by Brassard, Chaum and Crepeau). In particular, we adopt the instance-based prover-eeciency paradigm of CS-proofs, but follow the computational-soundness condition of… (More)

We describe new ways to simulate 2-party communication protocols to get protocols with potentially smaller communication. We show that every communication protocol that communicates C bits and reveals I bits of information about the inputs to the participating parties can be simulated by a new protocol involving at most ~O(√CI) bits of communication.… (More)