A $(q,k,t)$-design matrix is an m x n matrix whose pattern of zeros/non-zeros satisfies the following design-like condition: each row has at most $q$ non-zeros, each column has at least $k$ non-zeros and the supports of every two columns intersect in at most t rows. We prove that the rank ... more >>>

We present new explicit constructions of *deterministic* randomness extractors, dispersers and related objects. We say that a
distribution $X$ on binary strings of length $n$ is a
$\delta$-source if $X$ assigns probability at most $2^{-\delta n}$
to any string of length $n$. For every $\delta>0$ we construct the
following poly($n$)-time ... more >>>

We study the question of whether the value of mathematical programs such as
linear and semidefinite programming hierarchies on a graph $G$, is preserved
when taking a small random subgraph $G'$ of $G$. We show that the value of the
Goemans-Williamson (1995) semidefinite program (SDP) for \maxcut of $G'$ is
more >>>

Does computing n copies of a function require n times the computational effort? In this work, we

give the first non-trivial answer to this question for the model of randomized communication

complexity.

We show that:

1. Computing n copies of a function requires sqrt{n} times the communication.

2. ... more >>>

We give two applications of Nisan--Wigderson-type ("non-cryptographic") pseudorandom generators in cryptography. Specifically, assuming the existence of an appropriate NW-type generator, we construct:

A one-message witness-indistinguishable proof system for every language in NP, based on any trapdoor permutation. This proof system does not assume a shared random string or any setup ... more >>>

We construct a secure protocol for any multi-party functionality
that remains secure (under a relaxed definition of security) when
executed concurrently with multiple copies of itself and other
protocols. We stress that we do *not* use any assumptions on
existence of trusted parties, common reference string, honest
majority or synchronicity ... more >>>

We show new lower bounds and impossibility results for general (possibly <i>non-black-box</i>) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions:
<ol>
<li> There does not exist a two-round zero-knowledge <i>proof</i> system with perfect completeness for an NP-complete language. The previous impossibility result for two-round zero ... more >>>

The notion of efficient computation is usually identified in cryptography and complexity with probabilistic polynomial time. However, until recently, in order to obtain \emph{constant-round} zero-knowledge proofs and proofs of knowledge, one had to allow simulators and knowledge-extractors to run in time which is only polynomial {\em on the average} (i.e., ... more >>>

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

Informally, an <i>obfuscator</i> <b>O</b> is an (efficient, probabilistic)
"compiler" that takes as input a program (or circuit) <b>P</b> and
produces a new program <b>O(P)</b> that has the same functionality as <b>P</b>
yet is "unintelligible" in some sense. Obfuscators, if they exist,
would have a wide variety of cryptographic ... more >>>