We address the following problem: how to execute any algorithm P, for an unbounded number of executions, in the presence of an adversary who observes partial information on the internal state of the computation during executions. The security guarantee is that the adversary learns nothing, beyond P's input/output behavior.

This ... more >>>

We investigate the complexity of the following computational problem:

Polynomial Entropy Approximation (PEA):
Given a low-degree polynomial mapping
$p : F^n\rightarrow F^m$, where $F$ is a finite field, approximate the output entropy
$H(p(U_n))$, where $U_n$ is the uniform distribution on $F^n$ and $H$ may be any of several entropy measures.

Starting with Kilian (STOC `92), several works have shown how to use probabilistically checkable proofs (PCPs) and cryptographic primitives such as collision-resistant hashing to construct very efficient argument systems (a.k.a. computationally sound proofs), for example with polylogarithmic communication complexity. Ishai et al. (CCC `07) raised the question of whether PCPs ... more >>>

We study the complexity of locally list-decoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that computing majority over $\Theta(1/\eps)$ bits is essentially equivalent to locally list-decoding binary codes from relative distance $1/2-\eps$ with list size $\poly(1/\eps)$. That is, a local-decoder ... more >>>

Program checking, program self-correcting and program self-testing
were pioneered by [Blum and Kannan] and [Blum, Luby and Rubinfeld] in
the mid eighties as a new way to gain confidence in software, by
considering program correctness on an input by input basis rather than
full program verification. Work in ... more >>>

Suppose you want to store a large file on a remote and unreliable server. You would like to verify that your file has not been corrupted, so you store a small private (randomized)``fingerprint'' of the file on your own computer. This is the setting for the well-studied authentication problem, and ... more >>>

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 >>>