All reports by Author Ilan Komargodski:

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TR24-014
| 28th January 2024
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Elette Boyle, Ilan Komargodski, Neekon Vafa#### Memory Checking Requires Logarithmic Overhead

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TR23-195
| 6th December 2023
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Shai Evra, Shay Gadot, Ohad Klein, Ilan Komargodski#### Verifying Groups in Linear Time

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TR19-113
| 5th September 2019
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Tomer Grossman, Ilan Komargodski, Moni Naor#### Instance Complexity and Unlabeled Certificates in the Decision Tree Model

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TR18-140
| 11th August 2018
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Ilan Komargodski, Ran Raz, Yael Tauman Kalai#### A Lower Bound for Adaptively-Secure Collective Coin-Flipping Protocols

Revisions: 1

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TR17-060
| 9th April 2017
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Boaz Barak, Zvika Brakerski, Ilan Komargodski, Pravesh Kothari#### Limits on Low-Degree Pseudorandom Generators (Or: Sum-of-Squares Meets Program Obfuscation)

Revisions: 1

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TR17-015
| 4th February 2017
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Ilan Komargodski, Moni Naor, Eylon Yogev#### White-Box vs. Black-Box Complexity of Search Problems: Ramsey and Graph Property Testing

Revisions: 2

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TR16-131
| 21st August 2016
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Andrej Bogdanov, Siyao Guo, Ilan Komargodski#### Threshold Secret Sharing Requires a Linear Size Alphabet

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TR16-023
| 23rd February 2016
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Ilan Komargodski, Moni Naor, Eylon Yogev#### How to Share a Secret, Infinitely

Revisions: 4

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TR15-092
| 31st May 2015
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Yael Tauman Kalai, Ilan Komargodski#### Compressing Communication in Distributed Protocols

Revisions: 2

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TR15-064
| 19th April 2015
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Ilan Komargodski, Pravesh Kothari, Madhu Sudan#### Communication with Contextual Uncertainty

Revisions: 1

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TR15-026
| 21st February 2015
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Siyao Guo, Ilan Komargodski#### Negation-Limited Formulas

Revisions: 1

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TR14-025
| 25th February 2014
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Oded Goldreich, Tom Gur, Ilan Komargodski#### Strong Locally Testable Codes with Relaxed Local Decoders

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TR13-058
| 5th April 2013
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Ilan Komargodski, Ran Raz, Avishay Tal#### Improved Average-Case Lower Bounds for DeMorgan Formula Size

Revisions: 2

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TR12-182
| 24th December 2012
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Itay Berman, Iftach Haitner, Ilan Komargodski, Moni Naor#### Hardness Preserving Reductions via Cuckoo Hashing

Revisions: 2

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TR12-174
| 12th December 2012
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Anat Ganor, Ilan Komargodski, Ran Raz#### The Spectrum of Small DeMorgan Formulas

Revisions: 1

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TR12-062
| 17th May 2012
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Ilan Komargodski, Ran Raz#### Average-Case Lower Bounds for Formula Size

Revisions: 2

Elette Boyle, Ilan Komargodski, Neekon Vafa

We study the complexity of memory checkers with computational security and prove the first general tight lower bound.

Memory checkers, first introduced over 30 years ago by Blum, Evans, Gemmel, Kannan, and Naor (FOCS '91, Algorithmica '94), allow a user to store and maintain a large memory on a remote ... more >>>

Shai Evra, Shay Gadot, Ohad Klein, Ilan Komargodski

We consider the following problem: Given an $n \times n$ multiplication table, decide whether it is a Cayley multiplication table of a group. Among deterministic algorithms for this problem, the best known algorithm is implied by F. W. Light's associativity test (1949) and has running time of $O(n^2 \log n)$. ... more >>>

Tomer Grossman, Ilan Komargodski, Moni Naor

Instance complexity is a measure of goodness of an algorithm in which the performance of one algorithm is compared to others per input. This is in sharp contrast to worst-case and average-case complexity measures, where the performance is compared either on the worst input or on an average one, ... more >>>

Ilan Komargodski, Ran Raz, Yael Tauman Kalai

In 1985, Ben-Or and Linial (Advances in Computing Research '89) introduced the collective coin-flipping problem, where $n$ parties communicate via a single broadcast channel and wish to generate a common random bit in the presence of adaptive Byzantine corruptions. In this model, the adversary can decide to corrupt a party ... more >>>

Boaz Barak, Zvika Brakerski, Ilan Komargodski, Pravesh Kothari

We prove that for every function $G\colon\{0,1\}^n \rightarrow \mathbb{R}^m$, if every output of $G$ is a polynomial (over $\mathbb{R}$) of degree at most $d$ of at most $s$ monomials and $m > \widetilde{O}(sn^{\lceil d/2 \rceil})$, then there is a polynomial time algorithm that can distinguish a vector of the form ... more >>>

Ilan Komargodski, Moni Naor, Eylon Yogev

Ramsey theory assures us that in any graph there is a clique or independent set of a certain size, roughly logarithmic in the graph size. But how difficult is it to find the clique or independent set? If the graph is given explicitly, then it is possible to do so ... more >>>

Andrej Bogdanov, Siyao Guo, Ilan Komargodski

We prove that for every $n$ and $1 < t < n$ any $t$-out-of-$n$ threshold secret sharing scheme for one-bit secrets requires share size $\log(t + 1)$. Our bound is tight when $t = n - 1$ and $n$ is a prime power. In 1990 Kilian and Nisan proved ... more >>>

Ilan Komargodski, Moni Naor, Eylon Yogev

Secret sharing schemes allow a dealer to distribute a secret piece of information among several parties so that any qualified subset of parties can reconstruct the secret, while every unqualified subset of parties learns nothing about the secret. The collection of qualified subsets is called an access structure. The best ... more >>>

Yael Tauman Kalai, Ilan Komargodski

We show how to compress communication in distributed protocols in which parties do not have private inputs. More specifically, we present a generic method for converting any protocol in which parties do not have private inputs, into another protocol where each message is "short" while preserving the same number of ... more >>>

Ilan Komargodski, Pravesh Kothari, Madhu Sudan

We introduce a simple model illustrating the role of context in communication and the challenge posed by uncertainty of knowledge of context. We consider a variant of distributional communication complexity where Alice gets some information $x$ and Bob gets $y$, where $(x,y)$ is drawn from a known distribution, and Bob ... more >>>

Siyao Guo, Ilan Komargodski

Understanding the power of negation gates is crucial to bridge the exponential gap between monotone and non-monotone computation. We focus on the model of formulas over the De Morgan basis and consider it in a negation-limited setting.

We prove that every formula that contains $t$ negation gates can be shrunk ... more >>>

Oded Goldreich, Tom Gur, Ilan Komargodski

Locally testable codes (LTCs) are error-correcting codes

that admit very efficient codeword tests. An LTC is said to

be strong if it has a proximity-oblivious tester;

that is, a tester that makes only a constant number of queries

and reject non-codewords with probability that depends solely

on their distance from ...
more >>>

Ilan Komargodski, Ran Raz, Avishay Tal

We give a function $h:\{0,1\}^n\to\{0,1\}$ such that every deMorgan formula of size $n^{3-o(1)}/r^2$ agrees with $h$ on at most a fraction of $\frac{1}{2}+2^{-\Omega(r)}$ of the inputs. This improves the previous average-case lower bound of Komargodski and Raz (STOC, 2013).

Our technical contributions include a theorem that shows that the ``expected ... more >>>

Itay Berman, Iftach Haitner, Ilan Komargodski, Moni Naor

A common method for increasing the usability and uplifting the security of pseudorandom function families (PRFs) is to ``hash" the inputs into a smaller domain before applying the PRF. This approach, known as ``Levin's trick", is used to achieve ``PRF domain extension" (using a short, e.g., fixed, input length PRF ... more >>>

Anat Ganor, Ilan Komargodski, Ran Raz

We show a connection between the deMorgan formula size of a Boolean function and the noise stability of the function. Using this connection, we show that the Fourier spectrum of any balanced Boolean function computed by a deMorgan formula of size $s$ is concentrated on coefficients of degree up to ... more >>>

Ilan Komargodski, Ran Raz

We give an explicit function $h:\{0,1\}^n\to\{0,1\}$ such that any deMorgan formula of size $O(n^{2.499})$ agrees with $h$ on at most $\frac{1}{2} + \epsilon$ fraction of the inputs, where $\epsilon$ is exponentially small (i.e. $\epsilon = 2^{-n^{\Omega(1)}}$). Previous lower bounds for formula size were obtained for exact computation.

The same ... more >>>