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Electronic Colloquium on Computational Complexity

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All reports by Author Erez Petrank:

TR04-085 | 3rd October 2004
Erez Petrank, Guy Rothblum

Selection from Structured Data Sets

A large body of work studies the complexity of selecting the
$j$-th largest element in an arbitrary set of $n$ elements (a.k.a.
the select$(j)$ operation). In this work, we study the
complexity of select in data that is partially structured by
an initial preprocessing stage and in a data structure ... more >>>

TR02-045 | 8th July 2002
Daniele Micciancio, Erez Petrank

Efficient and Concurrent Zero-Knowledge from any public coin HVZK protocol

We show how to efficiently transform any public coin honest verifier
zero knowledge proof system into a proof system that is concurrent
zero-knowledge with respect to any (possibly cheating) verifier via
black box simulation. By efficient we mean that our transformation
incurs only an additive overhead, ... more >>>

TR01-050 | 24th June 2001
Ran Canetti, Joe Kilian, Erez Petrank, Alon Rosen

Black-Box Concurrent Zero-Knowledge Requires $\tilde\Omega(\log n)$ Rounds

We show that any concurrent zero-knowledge protocol for a non-trivial
language (i.e., for a language outside $\BPP$), whose security is proven
via black-box simulation, must use at least $\tilde\Omega(\log n)$
rounds of interaction. This result achieves a substantial improvement
over previous lower bounds, and is the first bound to rule ... more >>>

TR98-032 | 10th June 1998
Mihir Bellare, Oded Goldreich, Erez Petrank

Uniform Generation of NP-witnesses using an NP-oracle.

A Uniform Generation procedure for $NP$ is an
algorithm which given any input in a fixed NP-language, outputs a uniformly
distributed NP-witness for membership of the input in the language.
We present a Uniform Generation procedure for $NP$ that runs in probabilistic
polynomial-time with an NP-oracle. This improves upon ... more >>>

TR95-038 | 2nd July 1995
Joe Kilian, Erez Petrank

An Efficient Non-Interactive Zero-Knowledge Proof System for NP with General Assumptions

We consider noninteractive zero-knowledge proofs in the shared random
string model proposed by Blum, Feldman and Micali \cite{bfm}. Until
recently there was a sizable polynomial gap between the most
efficient noninteractive proofs for {\sf NP} based on general
complexity assumptions \cite{fls} versus those based on specific
algebraic assumptions \cite{Da}. ... more >>>

TR94-007 | 12th December 1994
Oded Goldreich, Rafail Ostrovsky, Erez Petrank

Computational Complexity and Knowledge Complexity

We study the computational complexity of languages which have
interactive proofs of logarithmic knowledge complexity. We show that
all such languages can be recognized in ${\cal BPP}^{\cal NP}$. Prior
to this work, for languages with greater-than-zero knowledge
complexity (and specifically, even for knowledge complexity 1) only
trivial computational complexity bounds ... more >>>

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