FOCS 2005 Program SUNDAY October 23, 2005
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Reproducibility and Pseudo-Determinism in Log-Space
Reproducibility and Pseudo-determinism in Log-Space by Ofer Grossman S.B., Massachusetts Institute of Technology (2017) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 c Massachusetts Institute of Technology 2020. All rights reserved. Author...................................................................... Department of Electrical Engineering and Computer Science May 15, 2020 Certified by.................................................................. Shafi Goldwasser RSA Professor of Electrical Engineering and Computer Science Thesis Supervisor Accepted by................................................................. Leslie A. Kolodziejski Professor of Electrical Engineering and Computer Science Chair, Department Committee on Graduate Students 2 Reproducibility and Pseudo-determinism in Log-Space by Ofer Grossman Submitted to the Department of Electrical Engineering and Computer Science on May 15, 2020, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract Acuriouspropertyofrandomizedlog-spacesearchalgorithmsisthattheiroutputsareoften longer than their workspace. This leads to the question: how can we reproduce the results of a randomized log space computation without storing the output or randomness verbatim? Running the algorithm again with new -
Concurrent Non-Malleable Zero Knowledge Proofs
Concurrent Non-Malleable Zero Knowledge Proofs Huijia Lin?, Rafael Pass??, Wei-Lung Dustin Tseng???, and Muthuramakrishnan Venkitasubramaniam Cornell University, {huijia,rafael,wdtseng,vmuthu}@cs.cornell.edu Abstract. Concurrent non-malleable zero-knowledge (NMZK) consid- ers the concurrent execution of zero-knowledge protocols in a setting where the attacker can simultaneously corrupt multiple provers and ver- ifiers. Barak, Prabhakaran and Sahai (FOCS’06) recently provided the first construction of a concurrent NMZK protocol without any set-up assumptions. Their protocol, however, is only computationally sound (a.k.a., a concurrent NMZK argument). In this work we present the first construction of a concurrent NMZK proof without any set-up assump- tions. Our protocol requires poly(n) rounds assuming one-way functions, or O~(log n) rounds assuming collision-resistant hash functions. As an additional contribution, we improve the round complexity of con- current NMZK arguments based on one-way functions (from poly(n) to O~(log n)), and achieve a near linear (instead of cubic) security reduc- tions. Taken together, our results close the gap between concurrent ZK protocols and concurrent NMZK protocols (in terms of feasibility, round complexity, hardness assumptions, and tightness of the security reduc- tion). 1 Introduction Zero-knowledge (ZK) interactive proofs [GMR89] are fundamental constructs that allow the Prover to convince the Verifier of the validity of a mathematical statement x 2 L, while providing zero additional knowledge to the Verifier. Con- current ZK, first introduced and achieved by Dwork, Naor and Sahai [DNS04], considers the execution of zero-knowledge protocols in an asynchronous and con- current setting. -
Property Testing on Boolean Functions Thesis Proposal
Property testing on boolean functions Thesis proposal Eric Blais Computer Science Department Carnegie Mellon University Pittsburgh, PA [email protected] May 20, 2010 Abstract Property testing deals with the following general question: given query access to some combinatorial object, what properties of the ob- ject can one test with only a small number of queries? In this thesis, we will study property testing on boolean functions. Specifically, we will focus on two basic questions in the field: Can we characterize the set of properties on boolean functions that can be tested with a constant number of queries? And can we determine the exact number of queries needed to test some fundamental properties of boolean functions? 1 Contents 1 Introduction 3 2 Definitions and notation 4 2.1 Boolean functions . 4 2.2 Property testing . 5 3 Characterization of testable properties 5 3.1 Related work . 6 3.2 Testing function isomorphism . 7 3.3 Completed work on testing function isomorphism . 7 3.4 Proposed research . 8 4 Exact query complexity bounds 10 4.1 Related work . 10 4.2 Completed work on testing juntas . 11 4.3 Proposed research . 11 5 Other proposed research 12 5.1 Alternative models of property testing . 13 5.2 Application of property testing ideas to other domains . 14 6 Suggested timeline 14 2 1 Introduction This thesis is primarily concerned with the study of boolean functions. Boolean functions play a central role in many areas of computer science: complexity theory [44], machine learning [19], coding theory [43], cryptog- raphy [18], circuit design [34], data structures [30], and combinatorics [16]. -
Privacy Loss in Apple's Implementation of Differential
Privacy Loss in Apple’s Implementation of Differential Privacy on MacOS 10.12 Jun Tang Aleksandra Korolova Xiaolong Bai University of Southern California University of Southern California Tsinghua University [email protected] [email protected] [email protected] Xueqiang Wang Xiaofeng Wang Indiana University Indiana University [email protected] [email protected] ABSTRACT 1 INTRODUCTION In June 2016, Apple made a bold announcement that it will deploy Differential privacy [7] has been widely recognized as the lead- local differential privacy for some of their user data collection in ing statistical data privacy definition by the academic commu- order to ensure privacy of user data, even from Apple [21, 23]. nity [6, 11]. Thus, as one of the first large-scale commercial de- The details of Apple’s approach remained sparse. Although several ployments of differential privacy (preceded only by Google’s RAP- patents [17–19] have since appeared hinting at the algorithms that POR [10]), Apple’s deployment is of significant interest to privacy may be used to achieve differential privacy, they did not include theoreticians and practitioners alike. Furthermore, since Apple may a precise explanation of the approach taken to privacy parameter be perceived as competing on privacy with other consumer com- choice. Such choice and the overall approach to privacy budget use panies, understanding the actual privacy protections afforded by and management are key questions for understanding the privacy the deployment of differential privacy in its desktop and mobile protections provided by any deployment of differential privacy. OSes may be of interest to consumers and consumer advocate In this work, through a combination of experiments, static and groups [16]. -
Hierarchical Clustering with Global Objectives: Approximation Algorithms and Hardness Results
HIERARCHICAL CLUSTERING WITH GLOBAL OBJECTIVES: APPROXIMATION ALGORITHMS AND HARDNESS RESULTS ADISSERTATION SUBMITTED TO THE DEPARTMENT OF COMPUTER SCIENCE AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Evangelos Chatziafratis June 2020 © 2020 by Evangelos Chatziafratis. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/bb164pj1759 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Tim Roughgarden, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Moses Charikar, Co-Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Li-Yang Tan I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Gregory Valiant Approved for the Stanford University Committee on Graduate Studies. Stacey F. Bent, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. -
Magic Adversaries Versus Individual Reduction: Science Wins Either Way ?
Magic Adversaries Versus Individual Reduction: Science Wins Either Way ? Yi Deng1;2 1 SKLOIS, Institute of Information Engineering, CAS, Beijing, P.R.China 2 State Key Laboratory of Cryptology, P. O. Box 5159, Beijing ,100878,China [email protected] Abstract. We prove that, assuming there exists an injective one-way function f, at least one of the following statements is true: – (Infinitely-often) Non-uniform public-key encryption and key agreement exist; – The Feige-Shamir protocol instantiated with f is distributional concurrent zero knowledge for a large class of distributions over any OR NP-relations with small distinguishability gap. The questions of whether we can achieve these goals are known to be subject to black-box lim- itations. Our win-win result also establishes an unexpected connection between the complexity of public-key encryption and the round-complexity of concurrent zero knowledge. As the main technical contribution, we introduce a dissection procedure for concurrent ad- versaries, which enables us to transform a magic concurrent adversary that breaks the distribu- tional concurrent zero knowledge of the Feige-Shamir protocol into non-black-box construc- tions of (infinitely-often) public-key encryption and key agreement. This dissection of complex algorithms gives insight into the fundamental gap between the known universal security reductions/simulations, in which a single reduction algorithm or simu- lator works for all adversaries, and the natural security definitions (that are sufficient for almost all cryptographic primitives/protocols), which switch the order of qualifiers and only require that for every adversary there exists an individual reduction or simulator. 1 Introduction The seminal work of Impagliazzo and Rudich [IR89] provides a methodology for studying the lim- itations of black-box reductions. -
Secure Multi-Party Computation in Practice
SECURE MULTI-PARTY COMPUTATION IN PRACTICE Marcella Christine Hastings A DISSERTATION in Computer and Information Science Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2021 Supervisor of Dissertation Nadia Heninger Adjunct Associate Professor, University of Pennsylvania Associate Professor, University of California, San Diego Graduate Group Chairperson Mayur Naik Professor and Computer and Information Science Graduate Group Chair Dissertation Committee Brett Hemenway Falk, Research Assistant Professor Stephan A. Zdancewic, Professor Sebastian Angel, Raj and Neera Singh Term Assistant Professor abhi shelat, Associate Professor at Khoury College of Computer Sciences, Northeastern University ACKNOWLEDGMENT This dissertation would have been much less pleasant to produce without the presence of many people in my life. I would like to thank my advisor and my dissertation committee for their helpful advice, direction, and long-distance phone calls over the past six years. I would like to thank my fellow PhD students at the University of Pennsylvania, especially the ever-changing but consistently lovely office mates in the Distributed Systems Laboratory and my cohort. Our shared tea-time, cookies, disappointments, and achievements provided an essential community that brought me great joy during my time at Penn. I would like to thank the mentors and colleagues who hosted me at the Security and Privacy Lab at the University of Washington in 2018, the Software & Application Innovation Lab at Boston University in 2019, and the Cryptography and Privacy Research group at Microsoft Research in 2020. My career and happiness greatly benefited from spending these summers exploring fresh research directions and rediscovering the world outside my own work. -
2021 Leroy P. Steele Prizes
FROM THE AMS SECRETARY 2021 Leroy P. Steele Prizes The 2021 Leroy P. Steele Prizes were presented at the Annual Meeting of the AMS, held virtually January 6–9, 2021. Noga Alon and Joel Spencer received the Steele Prize for Mathematical Exposition. Murray Gerstenhaber was awarded the Prize for Seminal Contribution to Research. Spencer Bloch was honored with the Prize for Lifetime Achievement. Citation for Mathematical Biographical Sketch: Noga Alon Exposition: Noga Alon Noga Alon is a Professor of Mathematics at Princeton and Joel Spencer University and a Professor Emeritus of Mathematics and The 2021 Steele Prize for Math- Computer Science at Tel Aviv University, Israel. He received ematical Exposition is awarded his PhD in Mathematics at the Hebrew University of Jeru- to Noga Alon and Joel Spencer salem in 1983 and had visiting and part-time positions in for the book The Probabilistic various research institutes, including the Massachusetts Method, published by Wiley Institute of Technology, Harvard University, the Institute and Sons, Inc., in 1992. for Advanced Study in Princeton, IBM Almaden Research Now in its fourth edition, Center, Bell Laboratories, Bellcore, and Microsoft Research The Probabilistic Method is an (Redmond and Israel). He joined Tel Aviv University in invaluable toolbox for both 1985, served as the head of the School of Mathematical Noga Alon the beginner and the experi- Sciences in 1999–2001, and moved to Princeton in 2018. enced researcher in discrete He supervised more than twenty PhD students. He serves probability. It brings together on the editorial boards of more than a dozen international through one unifying perspec- technical journals and has given invited lectures in numer- tive a head-spinning variety of ous conferences, including plenary addresses in the 1996 results and methods, linked to European Congress of Mathematics and in the 2002 Inter- applications in graph theory, national Congress of Mathematicians. -
Constraint Clustering and Parity Games
Constrained Clustering Problems and Parity Games Clemens Rösner geboren in Ulm Dissertation zur Erlangung des Doktorgrades (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn Bonn 2019 1. Gutachter: Prof. Dr. Heiko Röglin 2. Gutachterin: Prof. Dr. Anne Driemel Tag der mündlichen Prüfung: 05. September 2019 Erscheinungsjahr: 2019 Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn Abstract Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. We study several clustering objectives. We begin with studying the Euclidean k-center problem. The k-center problem is a classical combinatorial optimization problem which asks to select k centers and assign each input point in a set P to one of the centers, such that the maximum distance of any input point to its assigned center is minimized. The Euclidean k-center problem assumes that the input set P is a subset of a Euclidean space and that each location in the Euclidean space can be chosen as a center. We focus on the special case with k = 1, the smallest enclosing ball problem: given a set of points in m-dimensional Euclidean space, find the smallest sphere enclosing all the points. We combine known results about convex optimization with structural properties of the smallest enclosing ball to create a new algorithm. We show that on instances with rational coefficients our new algorithm computes the exact center of the optimal solutions and has a worst-case run time that is polynomial in the size of the input. -
The Complexity of Nash Equilibria by Constantinos Daskalakis Diploma
The Complexity of Nash Equilibria by Constantinos Daskalakis Diploma (National Technical University of Athens) 2004 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 Christos H. Papadimitriou, Chair Professor Alistair J. Sinclair Professor Satish Rao Professor Ilan Adler Fall 2008 The dissertation of Constantinos Daskalakis is approved: Chair Date Date Date Date University of California, Berkeley Fall 2008 The Complexity of Nash Equilibria Copyright 2008 by Constantinos Daskalakis Abstract The Complexity of Nash Equilibria by Constantinos Daskalakis Doctor of Philosophy in Computer Science University of California, Berkeley Professor Christos H. Papadimitriou, Chair The Internet owes much of its complexity to the large number of entities that run it and use it. These entities have different and potentially conflicting interests, so their interactions are strategic in nature. Therefore, to understand these interactions, concepts from Economics and, most importantly, Game Theory are necessary. An important such concept is the notion of Nash equilibrium, which provides us with a rigorous way of predicting the behavior of strategic agents in situations of conflict. But the credibility of the Nash equilibrium as a framework for behavior-prediction depends on whether such equilibria are efficiently computable. After all, why should we expect a group of rational agents to behave in a fashion that requires exponential time to be computed? Motivated by this question, we study the computational complexity of the Nash equilibrium. We show that computing a Nash equilibrium is an intractable problem. -
Mathematisches Forschungsinstitut Oberwolfach Complexity Theory
Mathematisches Forschungsinstitut Oberwolfach Report No. 54/2015 DOI: 10.4171/OWR/2015/54 Complexity Theory Organised by Peter B¨urgisser, Berlin Oded Goldreich, Rehovot Madhu Sudan, Cambridge MA Salil Vadhan, Cambridge MA 15 November – 21 November 2015 Abstract. Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseu- dorandomness and randomness extraction. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinato- rial number theory, probability theory, representation theory, and the theory of error-correcting codes. Mathematics Subject Classification (2010): 68-06, 68Q01, 68Q10, 68Q15, 68Q17, 68Q25, 94B05, 94B35. Introduction by the Organisers The workshop Complexity Theory was organized by Peter B¨urgisser (TU Berlin), Oded Goldreich (Weizmann Institute), Madhu Sudan (Harvard), and Salil Vadhan (Harvard). The workshop was held on November 15th–21st 2015, and attended by approximately 50 participants spanning a wide range of interests within the field of Computational Complexity. The plenary program, attended by all participants, featured fifteen long lectures and five short (8-minute) reports by students and postdocs. In addition, intensive interaction took place in smaller groups. The Oberwolfach Meeting on Complexity Theory is marked by a long tradition and a continuous transformation. Originally starting with a focus on algebraic and Boolean complexity, the meeting has continuously evolved to cover a wide variety 3050 Oberwolfach Report 54/2015 of areas, most of which were not even in existence at the time of the first meeting (in 1972). -
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