Boaz Barak
Microsoft
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Featured researches published by Boaz Barak.
international conference on cluster computing | 2001
Boaz Barak
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 adversarys algorithm as a black-box. We present the first constructions of non-black-box simulators. Using these new non-black-box techniques, we obtain several results that were previously proven to be impossible to obtain using black-box simulators. Specifically, assuming the existence of collision resistent hash functions, we construct a new zero-knowledge argument system for NP that satisfies the following properties: 1. This system has a constant number of rounds with negligible soundness error. 2. It remains zero knowledge even when composed concurrently n times, where n is the security parameter. Simultaneously obtaining 1 and 2 has been recently proven to be impossible to achieve using black-box simulators. 3. It is an Arthur-Merlin (public coins) protocol. Simultaneously obtaining 1 and 3 was known to be impossible to achieve with a black-box simulator. 4. It has a simulator that runs in strict polynomial time, rather than in expected polynomial time. All previously known constant-round, negligible-error zero-knowledge arguments utilized expected polynomial-time simulators.
theory and application of cryptographic techniques | 2014
Boaz Barak; Sanjam Garg; Yael Tauman Kalai; Omer Paneth; Amit Sahai
Recently, Garg, Gentry, Halevi, Raykova, Sahai, and Waters (FOCS 2013) constructed a general-purpose obfuscating compiler for NC1 circuits. We describe a simplified variant of this compiler, and prove that it is a virtual black box obfuscator in a generic multilinear map model. This improves on Brakerski and Rothblum (eprint 2013) who gave such a result under a strengthening of the Exponential Time Hypothesis. We remove this assumption, and thus resolve an open question of Garg et al. As shown by Garg et al., a compiler for NC1 circuits can be bootstrapped to a compiler for all polynomial-sized circuits under the learning with errors (LWE) hardness assumption.
Journal of the ACM | 2015
Sanjeev Arora; Boaz Barak; David Steurer
We give a sub exponential time approximation algorithm for the \textsc{Unique Games} problem. The algorithms run in time that is exponential in an arbitrarily small polynomial of the input size,
SIAM Journal on Computing | 2008
Boaz Barak; Oded Goldreich
n^{\epsilon}
SIAM Journal on Computing | 2013
Boaz Barak; Mark Braverman; Xi Chen; Anup Rao
. The approximation guarantee depends on~
foundations of computer science | 2002
Boaz Barak
\epsilon
symposium on the theory of computing | 2005
Boaz Barak; Guy Kindler; Ronen Shaltiel; Benny Sudakov; Avi Wigderson
, but not on the alphabet size or the number of variables. We also obtain a sub exponential algorithms with improved approximations for \textsc{Small-Set Expansion} and \textsc{Multicut}. For \textsc{Max Cut}, \textsc{Sparsest Cut}, and \textsc{Vertex Cover}, we give sub exponential algorithms with improved approximations on some interesting subclasses of instances. Khots Unique Games Conjecture (UGC) states that it is NP-hard to achieve approximation guarantees such as ours for the \textsc{Unique Games}. While our results stop short of refuting the UGC, they do suggest that \textsc{Unique Games} is significantly easier than NP-hard problems such as \textsc{Max 3Sat}, \textsc{Max 3Lin}, \textsc{Label Cover} and more, that are believed not to have a sub exponential algorithm achieving a non-trivial approximation ratio. The main component in our algorithms is a new result on graph decomposition that may have other applications. Namely we show that for every
randomization and approximation techniques in computer science | 2003
Boaz Barak; Ronen Shaltiel; Avi Wigderson
\epsilon>0
symposium on the theory of computing | 2010
Boaz Barak; Mark Braverman; Xi Chen; Anup Rao
and every regular
international conference on cluster computing | 2001
Boaz Barak; Oded Goldreich; Shafi Goldwasser; Yehuda Lindell
n