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Electronic Colloquium on Computational Complexity

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All reports by Author Yuval Ishai:

TR20-083 | 30th May 2020
Eli Ben-Sasson, Dan Carmon, Yuval Ishai, Swastik Kopparty, Shubhangi Saraf

Proximity Gaps for Reed-Solomon Codes

A collection of sets displays a proximity gap with respect to some property if for every set in the collection, either (i) all members are $\delta$-close to the property in relative Hamming distance or (ii) only a tiny fraction of members are $\delta$-close to the property. In particular, no set ... more >>>

TR17-008 | 14th January 2017
Benny Applebaum, Naama Haramaty, Yuval Ishai, Eyal Kushilevitz, Vinod Vaikuntanathan

Low-Complexity Cryptographic Hash Functions

Cryptographic hash functions are efficiently computable functions that shrink a long input into a shorter output while achieving some of the useful security properties of a random function. The most common type of such hash functions is {\em collision resistant} hash functions (CRH), which prevent an efficient attacker from finding ... more >>>

TR15-182 | 13th November 2015
Andrej Bogdanov, Yuval Ishai, Emanuele Viola, Christopher Williamson

Bounded Indistinguishability and the Complexity of Recovering Secrets

Revisions: 1

We say that a function $f\colon \Sigma^n \to \{0, 1\}$ is $\epsilon$-fooled by $k$-wise indistinguishability if $f$ cannot distinguish with advantage $\epsilon$ between any two distributions $\mu$ and $\nu$ over $\Sigma^n$ whose projections to any $k$ symbols are identical. We study the class of functions $f$ that are fooled by ... more >>>

TR15-094 | 10th June 2015
Eli Ben-Sasson, iddo Ben-Tov, Ivan Bjerre Damgard, Yuval Ishai, Noga Ron-Zewi

On Public Key Encryption from Noisy Codewords

Several well-known public key encryption schemes, including those of Alekhnovich (FOCS 2003), Regev (STOC 2005), and Gentry, Peikert and Vaikuntanathan (STOC 2008), rely on the conjectured intractability of inverting noisy linear encodings. These schemes are limited in that they either require the underlying field to grow with the security parameter, ... more >>>

TR15-045 | 1st April 2015
Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

Minimizing Locality of One-Way Functions via Semi-Private Randomized Encodings

Revisions: 1

A one-way function is $d$-local if each of its outputs depends on at most $d$ input bits. In (Applebaum, Ishai, and Kushilevitz, FOCS 2004) it was shown that, under relatively mild assumptions, there exist $4$-local one-way functions (OWFs). This result is not far from optimal as it is not hard ... more >>>

TR13-143 | 19th October 2013
Yuval Ishai, Eyal Kushilevitz, Xin Li, Rafail Ostrovsky, Manoj Prabhakaran, Amit Sahai, David Zuckerman

Robust Pseudorandom Generators

Revisions: 1

Let $G:\{0,1\}^n\to\{0,1\}^m$ be a pseudorandom generator. We say that a circuit implementation of $G$ is $(k,q)$-robust if for every set $S$ of at most $k$ wires anywhere in the circuit, there is a set $T$ of at most $q|S|$ outputs, such that conditioned on the values of $S$ and $T$ ... more >>>

TR13-107 | 7th August 2013
Gil Cohen, Ivan Bjerre Damgard, Yuval Ishai, Jonas Kolker, Peter Bro Miltersen, Ran Raz, Ron Rothblum

Efficient Multiparty Protocols via Log-Depth Threshold Formulae

We put forward a new approach for the design of efficient multiparty protocols:

1. Design a protocol for a small number of parties (say, 3 or 4) which achieves
security against a single corrupted party. Such protocols are typically easy
to construct as they may employ techniques that do not ... more >>>

TR12-058 | 5th May 2012
Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

How to Garble Arithmetic Circuits

Revisions: 1

Yao's garbled circuit construction transforms a boolean circuit $C:\{0,1\}^n\to\{0,1\}^m$
into a ``garbled circuit'' $\hat{C}$ along with $n$ pairs of $k$-bit keys, one for each
input bit, such that $\hat{C}$ together with the $n$ keys
corresponding to an input $x$ reveal $C(x)$ and no additional information about $x$.
The garbled circuit ... more >>>

TR10-020 | 19th February 2010
Vipul Goyal, Yuval Ishai, Mohammad Mahmoody, Amit Sahai

Interactive Locking, Zero-Knowledge PCPs, and Unconditional Cryptography

Motivated by the question of basing cryptographic protocols on stateless tamper-proof hardware tokens, we revisit the question of unconditional two-prover zero-knowledge proofs for $NP$. We show that such protocols exist in the {\em interactive PCP} model of Kalai and Raz (ICALP '08), where one of the provers is replaced by ... more >>>

TR01-015 | 9th February 2001
Amos Beimel, Yuval Ishai

Information-Theoretic Private Information Retrieval: A Unified Construction

A Private Information Retrieval (PIR) protocol enables a user to
retrieve a data item from a database while hiding the identity of the
item being retrieved. In a $t$-private, $k$-server PIR protocol the
database is replicated among $k$ servers, and the user's privacy is
protected from any collusion of up ... more >>>

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