Theoretical CS Reading Group

The reading group meets once a week usually, Monday 1:30-2:30pm to discuss a particular paper or topic.

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Theory Seminar.

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Spring 2017

Friday, 20th January 2017 — Vladimir Braverman, Stephen R. Chestnut, Nikita Ivkin, David P. Woodruff
Beating CountSketch for Heavy Hitters in Insertion Streams
Presenter: Samson Zhou

Monday, 23rd January 2017
Locally Decodable Codes
Presenter: GV

Tuesday, 31st January 2017 — Theory Seminar - Prof. Jeremiah Blocki, Purdue University
Towards Human Computable Passwords

Click to view Abstract

An interesting challenge for the cryptography community is to design authentication protocols that are so simple that a human can execute them without relying on a fully trusted computer. We propose several candidate authentication protocols for a setting in which the human user can only receive assistance from a semi-trusted computer---a computer that stores information and performs computations correctly but does not provide confidentiality. Our schemes use a semi-trusted computer to store and display public challenges $C_i\in[n]^k$. The human user memorizes a random secret mapping $\sigma:[n]\rightarrow \mathbb{Z}_d$ and authenticates by computing responses $f(\sigma(C_i))$ to a sequence of public challenges where $f:\mathbb{Z}_d^k\rightarrow \mathbb{Z}_d$ is a function that is easy for the human to evaluate. We prove that any statistical adversary needs to sample $m=\tilde{\Omega}\paren{n^{s(f)}}$ challenge-response pairs to recover $\sigma$, for a security parameter $s(f)$ that depends on two key properties of $f$. Our lower bound generalizes recent results of Feldman et al. \cite{feldman2013complexity} who proved analogous results for the special case $d=2$. To obtain our results, we apply the general hypercontractivity theorem \cite{o2007analysis} to lower bound the {\em statistical dimension } of the distribution over challenge-response pairs induced by $f$ and $\sigma$. Our {\em statistical dimension} lower bounds apply to arbitrary functions $f:\mathbb{Z}_d^k\rightarrow \mathbb{Z}_d$ (not just to functions that are easy for a human to evaluate). As an application, we propose a family of human computable password functions $f_{k_1,k_2}$ in which the user needs to perform $2k_1+2k_2+1$ primitive operations (e.g., adding two digits or remembering a secret value $\sigma(i)$), and we show that $s(f) = \min\{k_1+1, (k_2+1)/2\}$. For these schemes, we prove that forging passwords is equivalent to recovering the secret mapping. Thus, our human computable password schemes can maintain strong security guarantees even after an adversary has observed the user login to many different accounts. Joint work with Manuel Blum, Anupam Datta, Santosh Vempala.

Monday, 6th February 2017
Certifying Algorithms
Presenter: Nima Darivandpour

Thursday, 9th February 2017 — Theory Seminar - Samson Zhou, Purdue University
Streaming for Aibohphobes: Longest Near-Palindrome under Hamming Distance

Click to view Abstract

Palindromes are strings which read the same backwards and forwards, such as "racecar". Given a metric and an integer d>0, a d-near-palindrome is a string of distance at most d from its reverse. This talk will cover the problem of identifying the longest d-near-palindrome in data streams under the Hamming distance. The problem is relevant to the analysis of DNA databases, and to the task of repairing recursive structures in documents such as XML and JSON. We present the first streaming algorithm for the longest d-near-palindrome problem, which returns a d-near-palindrome whose length is within a multiplicative (1+c)-factor of the longest d-near-palindrome, for "small" d. We present additional streaming algorithms which return a d-near-palindrome whose length is within an additive sqrt(n)-factor of the longest d-near-palindrome in one-pass, as well as the longest length d-near-palindrome in two passes. Finally, we provide lower bounds for the space necessary to approximate the longest d-near-palindrome. Joint work with Elena Grigorescu and Erfan Sadeqi Azer.

Wednesday, 15th February 2017
Holant problems and Holographic transformations
Presenter: Minshen Zhu

Wednesday, 22nd February 2017 — Theory Seminar - Hai Nguyen, Purdue University
Secure Computation based on Leaky Correlations: High Resilience Setting

Wednesday, 1st March 2017 — Guruswami et. al.
On Profit-Maximization Envy-Free Pricing
Presenter: Young-San Lin

Wednesday, 8th March 2017
An Introduction to Sum of Squares
Presenter: Negin Karisani

Wednesday, 29th March 2017TCS+ Talk - Noah Stephens-Davidowitz, NYU
A Reverse Minkowski Theorem

Thursday, 6th April 2017
Dependent Random Choice
Presenters: Akash Kumar

Wednesday, 19th April 2017 — Theory Seminar - Andrej Bogdanov, CUHK
On the complexity and efficiency of secret sharing schemes

Click to view Abstract

A secret sharing scheme is a mechanism for dividing up a secret among several parties so that unqualified subsets of the parties do not learn any information about the secret, while qualified subsets can recover the secret. Such schemes were introduced by Shamir and Blakley in 1979 and have become an indispensable component in the architecture of secure communication and computation protocols. This talk will address the following foundational aspects of secret sharing and reconstruction: 1. Most secret sharing schemes are based on codes or polynomials. Is the use of linear algebra a necessity in this context or merely a convenience? What are "non-algebraic" schemes good for? What would be the consequences of the non-existence of such schemes? 2. In known secret sharing schemes, the shares are sometimes substantially larger than the secret. Is this loss in information efficiency a necessary price to pay for security? Our methods (from joint works with Siyao Guo, Yuval Ishai, Ilan Komargodski, Emanuele Viola, and Christopher Williamson) expose new connections between secret sharing, approximation theory, and game theory. Bio: Andrej Bogdanov is associate professor of Computer Science and co-director of the Institute of Theoretical Computer Science and Communications at the Chinese University of Hong Kong. He obtained his B.Sc. and M.Eng. degrees from MIT and his Ph.D. from UC Berkeley. He has worked as a postdoctoral researcher at the Institute for Advanced Study in Princeton, at DIMACS (Rutgers University), and at ITCS (Tsinghua University), and as a visiting professor at the Tokyo Institute of Technology. He is currently a long-term participant in the pseudorandomness program at the UC Berkeley Simons Institute for the Theory of Computing. His research interests are in computational complexity and the foundations of cryptography.

Wednesday, 26th April 2017TCS+ Talk - Santosh Vempala, Georgia Tech
Sampling Polytopes: from Euclid to Riemann