All reports by Author Eshan Chattopadhyay:

__
TR19-145
| 31st October 2019
__

Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, Shachar Lovett, David Zuckerman#### XOR Lemmas for Resilient Functions Against Polynomials

__
TR18-100
| 18th May 2018
__

Eshan Chattopadhyay, Anindya De, Rocco Servedio#### Simple and efficient pseudorandom generators from Gaussian processes

Revisions: 1

__
TR18-070
| 13th April 2018
__

Eshan Chattopadhyay, Xin Li#### Non-Malleable Extractors and Codes in the Interleaved Split-State Model and More

Revisions: 2

__
TR18-015
| 25th January 2018
__

Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, Shachar Lovett#### Pseudorandom Generators from Polarizing Random Walks

Revisions: 1
,
Comments: 1

__
TR17-171
| 6th November 2017
__

Eshan Chattopadhyay, Pooya Hatami, Omer Reingold, Avishay Tal#### Improved Pseudorandomness for Unordered Branching Programs through Local Monotonicity

Revisions: 1

__
TR17-027
| 16th February 2017
__

Avraham Ben-Aroya, Eshan Chattopadhyay, Dean Doron, Xin Li, Amnon Ta-Shma#### A reduction from efficient non-malleable extractors to low-error two-source extractors with arbitrary constant rate

Revisions: 1

__
TR16-180
| 15th November 2016
__

Eshan Chattopadhyay, Xin Li#### Non-Malleable Codes and Extractors for Small-Depth Circuits, and Affine Functions

__
TR16-036
| 13th March 2016
__

Eshan Chattopadhyay, Xin Li#### Explicit Non-Malleable Extractors, Multi-Source Extractors and Almost Optimal Privacy Amplification Protocols

Revisions: 3

__
TR15-178
| 10th November 2015
__

Eshan Chattopadhyay, Xin Li#### Extractors for Sumset Sources

__
TR15-151
| 14th September 2015
__

Eshan Chattopadhyay, David Zuckerman#### New Extractors for Interleaved Sources

Revisions: 1

__
TR15-119
| 23rd July 2015
__

Eshan Chattopadhyay, David Zuckerman#### Explicit Two-Source Extractors and Resilient Functions

Revisions: 5

__
TR15-075
| 29th April 2015
__

Eshan Chattopadhyay, Vipul Goyal, Xin Li#### Non-Malleable Extractors and Codes, with their Many Tampered Extensions

Revisions: 1

__
TR14-102
| 4th August 2014
__

Eshan Chattopadhyay, David Zuckerman#### Non-Malleable Codes Against Constant Split-State Tampering

__
TR12-127
| 3rd October 2012
__

Eshan Chattopadhyay, Adam Klivans, Pravesh Kothari#### An Explicit VC-Theorem for Low-Degree Polynomials

Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, Shachar Lovett, David Zuckerman

A major challenge in complexity theory is to explicitly construct functions that have small correlation with low-degree polynomials over $F_2$. We introduce a new technique to prove such correlation bounds with $F_2$ polynomials. Using this technique, we bound the correlation of an XOR of Majorities with constant degree polynomials. In ... more >>>

Eshan Chattopadhyay, Anindya De, Rocco Servedio

We show that a very simple pseudorandom generator fools intersections of $k$ linear threshold functions (LTFs) and arbitrary functions of $k$ LTFs over $n$-dimensional Gaussian space.

The two analyses of our PRG (for intersections versus arbitrary functions of LTFs) are quite different from each other and from previous analyses of ... more >>>

Eshan Chattopadhyay, Xin Li

We present explicit constructions of non-malleable codes with respect to the following tampering classes. (i) Linear functions composed with split-state adversaries: In this model, the codeword is first tampered by a split-state adversary, and then the whole tampered codeword is further tampered by a linear function. (ii) Interleaved split-state adversary: ... more >>>

Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, Shachar Lovett

We propose a new framework for constructing pseudorandom generators for $n$-variate Boolean functions. It is based on two new notions. First, we introduce fractional pseudorandom generators, which are pseudorandom distributions taking values in $[-1,1]^n$. Next, we use a fractional pseudorandom generator as steps of a random walk in $[-1,1]^n$ that ... more >>>

Eshan Chattopadhyay, Pooya Hatami, Omer Reingold, Avishay Tal

We present an explicit pseudorandom generator with seed length $\tilde{O}((\log n)^{w+1})$ for read-once, oblivious, width $w$ branching programs that can read their input bits in any order. This improves upon the work of Impaggliazzo, Meka and Zuckerman (FOCS'12) where they required seed length $n^{1/2+o(1)}$.

A central ingredient in our work ... more >>>

Avraham Ben-Aroya, Eshan Chattopadhyay, Dean Doron, Xin Li, Amnon Ta-Shma

We show a reduction from the existence of explicit t-non-malleable

extractors with a small seed length, to the construction of explicit

two-source extractors with small error for sources with arbitrarily

small constant rate. Previously, such a reduction was known either

when one source had entropy rate above half [Raz05] or ...
more >>>

Eshan Chattopadhyay, Xin Li

Non-malleable codes were introduced by Dziembowski, Pietrzak and Wichs as an elegant relaxation of error correcting codes, where the motivation is to handle more general forms of tampering while still providing meaningful guarantees. This has led to many elegant constructions and applications in cryptography. However, most works so far only ... more >>>

Eshan Chattopadhyay, Xin Li

We make progress in the following three problems: 1. Constructing optimal seeded non-malleable extractors; 2. Constructing optimal privacy amplification protocols with an active adversary, for any possible security parameter; 3. Constructing extractors for independent weak random sources, when the min-entropy is extremely small (i.e., near logarithmic).

For the first ... more >>>

Eshan Chattopadhyay, Xin Li

We propose a new model of weak random sources which we call sumset sources. A sumset source $\mathbf{X}$ is the sum of $C$ independent sources $\mathbf{X}_1,\ldots,\mathbf{X}_C$, where each $\mathbf{X}_i$ is an $n$-bit source with min-entropy $k$. We show that extractors for this class of sources can be used to give ... more >>>

Eshan Chattopadhyay, David Zuckerman

We study how to extract randomness from a $C$-interleaved source, that is, a source comprised of $C$ independent sources whose bits or symbols are interleaved. We describe a simple approach for constructing such extractors that yields:

(1) For some $\delta>0, c > 0$,

explicit extractors for $2$-interleaved sources on $\{ ...
more >>>

Eshan Chattopadhyay, David Zuckerman

We explicitly construct an extractor for two independent sources on $n$ bits, each with min-entropy at least $\log^C n$ for a large enough constant $C$. Our extractor outputs one bit and has error $n^{-\Omega(1)}$. The best previous extractor, by Bourgain [B2], required each source to have min-entropy $.499n$.

A key ... more >>>

Eshan Chattopadhyay, Vipul Goyal, Xin Li

Randomness extractors and error correcting codes are fundamental objects in computer science. Recently, there have been several natural generalizations of these objects, in the context and study of tamper resilient cryptography. These are \emph{seeded non-malleable extractors}, introduced by Dodis and Wichs \cite{DW09}; \emph{seedless non-malleable extractors}, introduced by Cheraghchi and Guruswami ... more >>>

Eshan Chattopadhyay, David Zuckerman

Non-malleable codes were introduced by Dziembowski, Pietrzak and Wichs \cite{DPW10} as an elegant generalization of the classical notions of error detection, where the corruption of a codeword is viewed as a tampering function acting on it. Informally, a non-malleable code with respect to a family of tampering functions $\mathcal{F}$ consists ... more >>>

Eshan Chattopadhyay, Adam Klivans, Pravesh Kothari

Let $X \subseteq \mathbb{R}^{n}$ and let ${\mathcal C}$ be a class of functions mapping $\mathbb{R}^{n} \rightarrow \{-1,1\}.$ The famous VC-Theorem states that a random subset $S$ of $X$ of size $O(\frac{d}{\epsilon^{2}} \log \frac{d}{\epsilon})$, where $d$ is the VC-Dimension of ${\mathcal C}$, is (with constant probability) an $\epsilon$-approximation for ${\mathcal C}$ ... more >>>