EATCS General Assembly 2013
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Information Theory Methods in Communication Complexity
INFORMATION THEORY METHODS IN COMMUNICATION COMPLEXITY BY NIKOLAOS LEONARDOS A dissertation submitted to the Graduate School—New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Computer Science Written under the direction of Michael Saks and approved by New Brunswick, New Jersey JANUARY, 2012 ABSTRACT OF THE DISSERTATION Information theory methods in communication complexity by Nikolaos Leonardos Dissertation Director: Michael Saks This dissertation is concerned with the application of notions and methods from the field of information theory to the field of communication complexity. It con- sists of two main parts. In the first part of the dissertation, we prove lower bounds on the random- ized two-party communication complexity of functions that arise from read-once boolean formulae. A read-once boolean formula is a formula in propositional logic with the property that every variable appears exactly once. Such a formula can be represented by a tree, where the leaves correspond to variables, and the in- ternal nodes are labeled by binary connectives. Under certain assumptions, this representation is unique. Thus, one can define the depth of a formula as the depth of the tree that represents it. The complexity of the evaluation of general read-once formulae has attracted interest mainly in the decision tree model. In the communication complexity model many interesting results deal with specific read-once formulae, such as disjointness and tribes. In this dissertation we use information theory methods to prove lower bounds that hold for any read-once ii formula. -
The Multiplicative Weights Update Method: a Meta Algorithm and Applications
The Multiplicative Weights Update Method: a Meta Algorithm and Applications Sanjeev Arora∗ Elad Hazan Satyen Kale Abstract Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analysis are usually very similar and rely on an exponential potential function. We present a simple meta algorithm that unifies these disparate algorithms and drives them as simple instantiations of the meta algo- rithm. 1 Introduction Algorithms in varied fields work as follows: a distribution is maintained on a certain set, and at each step the probability assigned to i is multi- plied or divided by (1 + C(i)) where C(i) is some kind of “payoff” for element i. (Rescaling may be needed to ensure that the new values form a distribution.) Some examples include: the Ada Boost algorithm in ma- chine learning [FS97]; algorithms for game playing studied in economics (see below), the Plotkin-Shmoys-Tardos algorithm for packing and covering LPs [PST91], and its improvements in the case of flow problems by Young, Garg-Konneman, and Fleischer [You95, GK98, Fle00]; Impagliazzo’s proof of the Yao XOR lemma [Imp95], etc. The analysis of the running time uses a potential function argument and the final running time is proportional to 1/2. It has been clear to most researchers that these results are very similar, see for instance, Khandekar’s PhD thesis [Kha04]. Here we point out that these are all instances of the same (more general) algorithm. This meta ∗This project supported by David and Lucile Packard Fellowship and NSF grant CCR- 0205594. -
On SZK and PP
Electronic Colloquium on Computational Complexity, Revision 2 of Report No. 140 (2016) On SZK and PP Adam Bouland1, Lijie Chen2, Dhiraj Holden1, Justin Thaler3, and Prashant Nalini Vasudevan1 1CSAIL, Massachusetts Institute of Technology, Cambridge, MA USA 2IIIS, Tsinghua University, Beijing, China 3Georgetown University, Washington, DC USA Abstract In both query and communication complexity, we give separations between the class NISZK, con- taining those problems with non-interactive statistical zero knowledge proof systems, and the class UPP, containing those problems with randomized algorithms with unbounded error. These results significantly improve on earlier query separations of Vereschagin [Ver95] and Aaronson [Aar12] and earlier commu- nication complexity separations of Klauck [Kla11] and Razborov and Sherstov [RS10]. In addition, our results imply an oracle relative to which the class NISZK 6⊆ PP. This answers an open question of Wa- trous from 2002 [Aar]. The technical core of our result is a stronger hardness amplification theorem for approximate degree, which roughly says that composing the gapped-majority function with any function of high approximate degree yields a function with high threshold degree. Using our techniques, we also give oracles relative to which the following two separations hold: perfect zero knowledge (PZK) is not contained in its complement (coPZK), and SZK (indeed, even NISZK) is not contained in PZK (indeed, even HVPZK). Along the way, we show that HVPZK is contained in PP in a relativizing manner. We prove a number of implications of these results, which may be of independent interest outside of structural complexity. Specifically, our oracle separation implies that certain parameters of the Polariza- tion Lemma of Sahai and Vadhan [SV03] cannot be much improved in a black-box manner. -
Garbled Protocols and Two-Round MPC from Bilinear Maps
58th Annual IEEE Symposium on Foundations of Computer Science Garbled Protocols and Two-Round MPC from Bilinear Maps Sanjam Garg Akshayaram Srinivasan Dept. of Computer Science Dept. of Computer Science University of California, Berkeley University of California, Berkeley Berkeley, USA Berkeley, USA Email: [email protected] Email: [email protected] Abstract—In this paper, we initiate the study of garbled (OT) protocol [57], [2], [51], [40] gives an easy solution to protocols — a generalization of Yao’s garbled circuits construc- the problem of (semi-honest) two-round secure computation tion to distributed protocols. More specifically, in a garbled in the two-party setting. However, the same problem for protocol construction, each party can independently generate a garbled protocol component along with pairs of input the multiparty setting turns out to be much harder. Beaver, labels. Additionally, it generates an encoding of its input. The Micali and Rogaway [7] show that garbled circuits can be evaluation procedure takes as input the set of all garbled used to realize a constant round multi-party computation protocol components and the labels corresponding to the input protocol. However, unlike the two-party case, this protocol encodings of all parties and outputs the entire transcript of the is not two rounds. distributed protocol. We provide constructions for garbling arbitrary protocols A. Garbled Protocols based on standard computational assumptions on bilinear maps (in the common random string model). Next, using In this paper, we introduce a generalization of Yao’s garbled protocols we obtain a general compiler that compresses construction from circuits to distributed protocols. We next any arbitrary round multiparty secure computation protocol elaborate on (i) what it means to garble a protocol, (ii) why into a two-round UC secure protocol. -
Onyx: New Encryption and Signature Schemes with Multivariate Public Key in Degree 3
Onyx: New Encryption and Signature Schemes with Multivariate Public Key in Degree 3 Gilles Macario-Rat1 and Jacques Patarin2 1 Orange, Orange Gardens, 46 avenue de la R´epublique,F-92320 Ch^atillon,France [email protected] 2 Versailles Laboratory of Mathematics, UVSQ, CNRS, University of Paris-Saclay [email protected] Abstract. In this paper, we present a new secret trapdoor function for the design of multivariate schemes that we call \Onyx", suitable for en- cryption and signature. It has been inspired by the schemes presented in [19,20]. From this idea, we present some efficient encryption and signa- ture multivariate schemes with explicit parameters that resist all known attacks. In particular they resist the two main (and often very power- ful) attacks in this area: the Gr¨obner attacks (to compute a solution of the system derived from the public key) and the MinRank attacks (to recover the secret key). Specific attacks due to the properties of the function and its differential are also addressed in this paper. The \Onyx" schemes have public key equations of degree 3. Despite this, the size of the public key may still be reasonable since we can use larger fields and smaller extension degrees. Onyx signatures can be as short as the \birth- day paradox" allows, i.e. twice the security level, or even shorter thanks to the Feistel-Patarin construction, like many other signatures schemes based on multivariate equations. Keywords: public-key cryptography, post-quantum multivariate cryptography, UOV, HFE, Gr¨obnerbasis, MinRank problem, differential attacks. 1 Introduction Many schemes in Multivariate cryptography have been broken. -
January 2011 Prizes and Awards
January 2011 Prizes and Awards 4:25 P.M., Friday, January 7, 2011 PROGRAM SUMMARY OF AWARDS OPENING REMARKS FOR AMS George E. Andrews, President BÔCHER MEMORIAL PRIZE: ASAF NAOR, GUNTHER UHLMANN American Mathematical Society FRANK NELSON COLE PRIZE IN NUMBER THEORY: CHANDRASHEKHAR KHARE AND DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY JEAN-PIERRE WINTENBERGER TEACHING OF MATHEMATICS LEVI L. CONANT PRIZE: DAVID VOGAN Mathematical Association of America JOSEPH L. DOOB PRIZE: PETER KRONHEIMER AND TOMASZ MROWKA EULER BOOK PRIZE LEONARD EISENBUD PRIZE FOR MATHEMATICS AND PHYSICS: HERBERT SPOHN Mathematical Association of America RUTH LYTTLE SATTER PRIZE IN MATHEMATICS: AMIE WILKINSON DAVID P. R OBBINS PRIZE LEROY P. S TEELE PRIZE FOR LIFETIME ACHIEVEMENT: JOHN WILLARD MILNOR Mathematical Association of America LEROY P. S TEELE PRIZE FOR MATHEMATICAL EXPOSITION: HENRYK IWANIEC BÔCHER MEMORIAL PRIZE LEROY P. S TEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH: INGRID DAUBECHIES American Mathematical Society FOR AMS-MAA-SIAM LEVI L. CONANT PRIZE American Mathematical Society FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY AN UNDERGRADUATE STUDENT: MARIA MONKS LEONARD EISENBUD PRIZE FOR MATHEMATICS AND OR PHYSICS F AWM American Mathematical Society LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION: PATRICIA CAMPBELL RUTH LYTTLE SATTER PRIZE IN MATHEMATICS M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS: American Mathematical Society RHONDA HUGHES ALICE T. S CHAFER PRIZE FOR EXCELLENCE IN MATHEMATICS BY AN UNDERGRADUATE WOMAN: LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION SHERRY GONG Association for Women in Mathematics ALICE T. S CHAFER PRIZE FOR EXCELLENCE IN MATHEMATICS BY AN UNDERGRADUATE WOMAN FOR JPBM Association for Women in Mathematics COMMUNICATIONS AWARD: NICOLAS FALACCI AND CHERYL HEUTON M. -
ACM SIGLOG News 1 October 2015, Vol
Volume 2, Number 4 Published by the Association for Computing Machinery Special Interest Group on Logic and Computation October 2015 SIGLOG news TABLE OF CONTENTS General Information 1 From the Editor Andrzej Murawski 2 Chair's Letter Prakash Panangaden Technical Columns 3 Automata Mikołaj Bojańczyk 16 Verication Neha Rungta Announcements 26 Gödel Prize - Call for Nominations 28 SIGLOG Monthly 175 SIGLOG NEWS Published by the ACM Special Interest Group on Logic and Computation SIGLOG Executive Committee Chair Prakash Panangaden McGill University Vice-Chair Luke Ong University of Oxford Treasurer Natarajan Shankar SRI International Secretary Alexandra Silva Radboud University Nijmegen Catuscia Palamidessi INRIA and LIX, Ecole´ Polytechnique EACSL President Anuj Dawar University of Cambridge EATCS President Luca Aceto Reykjavik University ACM ToCL E-in-C Dale Miller INRIA and LIX, Ecole´ Polytechnique Andrzej Murawski University of Warwick Veronique´ Cortier CNRS and LORIA, Nancy ADVISORY BOARD Mart´ın Abadi Google and UC Santa Cruz Phokion Kolaitis University of California, Santa Cruz Dexter Kozen Cornell University Gordon Plotkin University of Edinburgh Moshe Vardi Rice University COLUMN EDITORS Automata Mikołaj Bojanczyk´ University of Warsaw Complexity Neil Immerman University of Massachusetts Amherst Security and Privacy Matteo Maffei CISPA, Saarland University Semantics Mike Mislove Tulane University Verification Neha Rungta SGT Inc. and NASA Ames Notice to Contributing Authors to SIG Newsletters By submitting your article for distribution -
A Revisionist History of Algorithmic Game Theory
A Revisionist History of Algorithmic Game Theory Moshe Y. Vardi Rice University Theoretical Computer Science: Vols. A and B van Leeuwen, 1990: Handbook of Theoretical Computer Science Volume A: algorithms and complexity • Volume B: formal models and semantics (“logic”) • E.W. Dijkstra, EWD Note 611: “On the fact that the Atlantic Ocean has two sides” North-American TCS (FOCS&STOC): Volume A. • European TCS (ICALP): Volumes A&B • A Key Theme in FOCS/STOC: Algorithmic Game Theory – algorithm design for strategic environments 1 Birth of AGT: The ”Official” Version NEW YORK, May 16, 2012 – ACM’s Special Interest Group on Algorithms and Computation Theory (SIGACT) together with the European Association for Theoretical Computer Science (EATCS) will recognize three groups of researchers for their contributions to understanding how selfish behavior by users and service providers impacts the behavior of the Internet and other complex computational systems. The papers were presented by Elias Koutsoupias and Christos Papadimitriou, Tim Roughgarden and Eva Tardos, and Noam Nisan and Amir Ronen. They will receive the 2012 Godel¨ Prize, sponsored jointly by SIGACT and EATCS for outstanding papers in theoretical computer science at the International Colloquium on Automata, Languages and Programming (ICALP), July 9–13, in Warwick, UK. 2 Three seminal papers Koutsoupias&Papadimitriou, STACS 1999: Worst- • case Equilibira – introduced the “price of anarchy” concept, a measure of the extent to which competition approximates cooperation, quantifying how much utility is lost due to selfish behaviors on the Internet, which operates without a system designer or monitor striving to achieve the “social optimum.” Roughgarden & Tardos, FOCS 2000: How Bad is • Selfish Routing? – studied the power and depth of the “price of anarchy” concept as it applies to routing traffic in large-scale communications networks to optimize the performance of a congested network. -
The Gödel Prize 2020 - Call for Nominatonn
The Gödel Prize 2020 - Call for Nominatonn Deadline: February 15, 2020 The Gödel Prize for outntanding papern in the area of theoretial iomputer niienie in nponnored jointly by the European Annoiiaton for Theoretial Computer Siienie (EATCS) and the Annoiiaton for Computng Maihinery, Speiial Innterent Group on Algorithmn and Computaton Theory (AC M SInGACT) The award in prenented annually, with the prenentaton taaing plaie alternately at the Innternatonal Colloquium on Automata, Languagen, and Programming (InCALP) and the AC M Symponium on Theory of Computng (STOC) The 28th Gödel Prize will be awarded at the 47th Innternatonal Colloquium on Automata, Languagen, and Programming to be held during 8-12 July, 2020 in Beijing The Prize in named in honour of Kurt Gödel in reiogniton of hin major iontributonn to mathematial logii and of hin interent, diniovered in a leter he wrote to John von Neumann nhortly before von Neumann’n death, in what han beiome the famoun “P vernun NP” quenton The Prize iniluden an award of USD 5,000 Award Committee: The 2020 Award Commitee ionnintn of Samnon Abramnay (Univernity of Oxford), Anuj Dawar (Chair, Univernity of Cambridge), Joan Feigenbaum (Yale Univernity), Robert Krauthgamer (Weizmann Innnttute), Daniel Spielman (Yale Univernity) and David Zuiaerman (Univernity of Texan, Auntn) Eligibility: The 2020 Prize rulen are given below and they nupernede any diferent interpretaton of the generii rule to be found on webniten of both SInGACT and EATCS Any renearih paper or nerien of papern by a ningle author or by -
On the Utility of Fine-Grained Complexity Theory
On The Utility of Fine-Grained Complexity Theory Manuel Sabin Electrical Engineering and Computer Sciences University of California at Berkeley Technical Report No. UCB/EECS-2020-165 http://www2.eecs.berkeley.edu/Pubs/TechRpts/2020/EECS-2020-165.html August 14, 2020 Copyright © 2020, by the author(s). All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. On The Utility of Fine-Grained Complexity Theory by Manuel Sabin (they/them) A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Computer Science in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Shafi Goldwasser, Chair Associate Professor Prasad Raghavendra Assistant Professor Nikhil Srivastava Summer 2020 On The Utility of Fine-Grained Complexity Theory Copyright 2020 by Manuel Sabin (they/them) 1 Abstract On The Utility of Fine-Grained Complexity Theory by Manuel Sabin (they/them) Doctor of Philosophy in Computer Science University of California, Berkeley Professor Shafi Goldwasser, Chair The nascent field of Fine-Grained Complexity Theory has emerged and grown rapidly in the past decade. By studying \Hardness within P" and the connections of problems computable in, say, n2 time versus n3 time, this field addresses the practical efficiency of problems. -
On Differentially Private Graph Sparsification and Applications
On Differentially Private Graph Sparsification and Applications Raman Arora Jalaj Upadhyay Johns Hopkins University Rutgers University [email protected] [email protected] Abstract In this paper, we study private sparsification of graphs. In particular, we give an algorithm that given an input graph, returns a sparse graph which approximates the spectrum of the input graph while ensuring differential privacy. This allows one to solve many graph problems privately yet efficiently and accurately. This is exemplified with application of the proposed meta-algorithm to graph algorithms for privately answering cut-queries, as well as practical algorithms for computing MAX-CUT and SPARSEST-CUT with better accuracy than previously known. We also give an efficient private algorithm to learn Laplacian eigenmap on a graph. 1 Introduction Data from social and communication networks have become a rich source to gain useful insights into the social, behavioral, and information sciences. Such data is naturally modeled as observations on a graph, and encodes rich, fine-grained, and structured information. At the same time, due to the seamless nature of data acquisition, often collected through personal devices, the individual information content in network data is often highly sensitive. This raises valid privacy concerns pertaining the analysis and release of such data. We address these concerns in this paper by presenting a novel algorithm that can be used to publish a succinct differentially private representation of network data with minimal degradation in accuracy for various graph related tasks. There are several notions of differential privacy one can consider in the setting described above. Depending on privacy requirements, one can consider edge level privacy that renders two graphs that differ in a single edge as in-distinguishable based on the algorithm’s output; this is the setting studied in many recent works [9, 19, 25, 54]. -
SETH-Based Lower Bounds for Subset Sum and Bicriteria Path
SETH-Based Lower Bounds for Subset Sum and Bicriteria Path Amir Abboud1, Karl Bringmann2, Danny Hermelin3, and Dvir Shabtay3 1 Department of Computer Science, Stanford University, CA, USA [email protected] 2 Max Planck Institute for Informatics, Saarland Informatics Campus, Germany [email protected] 3 Department of Industrial Engineering and Management, Ben-Gurion University, Israel [email protected], [email protected] Abstract. Subset Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. An important open problem in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset Sum on dense instances, proving that Bellman’s 1962 pseudo-polynomial O∗(T )-time algorithm for Subset Sum on n numbers and target T − cannot be improved to time T 1 ε · 2o(n) for any ε> 0, unless the Strong Exponential Time Hypothesis (SETH) fails. As a corollary, we prove a “Direct-OR” theorem for Subset Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of N − given instances of Subset Sum is a YES instance requires time (NT )1 o(1). As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset Sum: On graphs with m edges and edge lengths bounded by L, we show that the O(Lm) pseudo- polynomial time algorithm by Joksch from 1966 cannot be improved to O˜(L + m), in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017).