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Going Beyond Dual Execution: MPC for Functions with Efficient Verification
Going Beyond Dual Execution: MPC for Functions with Efficient Verification Carmit Hazay abhi shelat ∗ Bar-Ilan University Northeastern Universityy Muthuramakrishnan Venkitasubramaniamz University of Rochester Abstract The dual execution paradigm of Mohassel and Franklin (PKC’06) and Huang, Katz and Evans (IEEE ’12) shows how to achieve the notion of 1-bit leakage security at roughly twice the cost of semi-honest security for the special case of two-party secure computation. To date, there are no multi-party compu- tation (MPC) protocols that offer such a strong trade-off between security and semi-honest performance. Our main result is to address this shortcoming by designing 1-bit leakage protocols for the multi- party setting, albeit for a special class of functions. We say that function f (x, y) is efficiently verifiable by g if the running time of g is always smaller than f and g(x, y, z) = 1 if and only if f (x, y) = z. In the two-party setting, we first improve dual execution by observing that the “second execution” can be an evaluation of g instead of f , and that by definition, the evaluation of g is asymptotically more efficient. Our main MPC result is to construct a 1-bit leakage protocol for such functions from any passive protocol for f that is secure up to additive errors and any active protocol for g. An important result by Genkin et al. (STOC ’14) shows how the classic protocols by Goldreich et al. (STOC ’87) and Ben-Or et al. (STOC ’88) naturally support this property, which allows to instantiate our compiler with two-party and multi-party protocols. -
Adaptive Garbled RAM from Laconic Oblivious Transfer
Adaptive Garbled RAM from Laconic Oblivious Transfer Sanjam Garg?1, Rafail Ostrovsky??2, and Akshayaram Srinivasan1 1 University of California, Berkeley fsanjamg,[email protected] 2 UCLA [email protected] Abstract. We give a construction of an adaptive garbled RAM scheme. In the adaptive setting, a client first garbles a \large" persistent database which is stored on a server. Next, the client can provide garbling of mul- tiple adaptively and adversarially chosen RAM programs that execute and modify the stored database arbitrarily. The garbled database and the garbled program should reveal nothing more than the running time and the output of the computation. Furthermore, the sizes of the garbled database and the garbled program grow only linearly in the size of the database and the running time of the executed program respectively (up to poly logarithmic factors). The security of our construction is based on the assumption that laconic oblivious transfer (Cho et al., CRYPTO 2017) exists. Previously, such adaptive garbled RAM constructions were only known using indistinguishability obfuscation or in random oracle model. As an additional application, we note that this work yields the first constant round secure computation protocol for persistent RAM pro- grams in the malicious setting from standard assumptions. Prior works did not support persistence in the malicious setting. 1 Introduction Over the years, garbling methods [Yao86,LP09,AIK04,BHR12b,App17] have been extremely influential and have engendered an enormous number of applications ? Research supported in part from DARPA/ARL SAFEWARE Award W911NF15C0210, AFOSR Award FA9550-15-1-0274, AFOSR YIP Award, DARPA and SPAWAR under contract N66001-15-C-4065, a Hellman Award and research grants by the Okawa Foundation, Visa Inc., and Center for Long-Term Cybersecurity (CLTC, UC Berkeley). -
FOCS 2005 Program SUNDAY October 23, 2005
FOCS 2005 Program SUNDAY October 23, 2005 Talks in Grand Ballroom, 17th floor Session 1: 8:50am – 10:10am Chair: Eva´ Tardos 8:50 Agnostically Learning Halfspaces Adam Kalai, Adam Klivans, Yishay Mansour and Rocco Servedio 9:10 Noise stability of functions with low influences: invari- ance and optimality The 46th Annual IEEE Symposium on Elchanan Mossel, Ryan O’Donnell and Krzysztof Foundations of Computer Science Oleszkiewicz October 22-25, 2005 Omni William Penn Hotel, 9:30 Every decision tree has an influential variable Pittsburgh, PA Ryan O’Donnell, Michael Saks, Oded Schramm and Rocco Servedio Sponsored by the IEEE Computer Society Technical Committee on Mathematical Foundations of Computing 9:50 Lower Bounds for the Noisy Broadcast Problem In cooperation with ACM SIGACT Navin Goyal, Guy Kindler and Michael Saks Break 10:10am – 10:30am FOCS ’05 gratefully acknowledges financial support from Microsoft Research, Yahoo! Research, and the CMU Aladdin center Session 2: 10:30am – 12:10pm Chair: Satish Rao SATURDAY October 22, 2005 10:30 The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics Tutorials held at CMU University Center into `1 [Best paper award] Reception at Omni William Penn Hotel, Monongahela Room, Subhash Khot and Nisheeth Vishnoi 17th floor 10:50 The Closest Substring problem with small distances Tutorial 1: 1:30pm – 3:30pm Daniel Marx (McConomy Auditorium) Chair: Irit Dinur 11:10 Fitting tree metrics: Hierarchical clustering and Phy- logeny Subhash Khot Nir Ailon and Moses Charikar On the Unique Games Conjecture 11:30 Metric Embeddings with Relaxed Guarantees Break 3:30pm – 4:00pm Ittai Abraham, Yair Bartal, T-H. -
László Lovász Avi Wigderson De L’Université Eötvös Loránd À De L’Institute for Advanced Study De Budapest, En Hongrie Et À Princeton, Aux États-Unis
2021 L’Académie des sciences et des lettres de Norvège a décidé de décerner le prix Abel 2021 à László Lovász Avi Wigderson de l’université Eötvös Loránd à de l’Institute for Advanced Study de Budapest, en Hongrie et à Princeton, aux États-Unis, « pour leurs contributions fondamentales à l’informatique théorique et aux mathématiques discrètes, et pour leur rôle de premier plan dans leur transformation en domaines centraux des mathématiques contemporaines ». L’informatique théorique est l’étude de la puissance croissante sur plusieurs autres sciences, ce et des limites du calcul. Elle trouve son origine qui permet de faire de nouvelles découvertes dans les travaux fondateurs de Kurt Gödel, Alonzo en « chaussant des lunettes d’informaticien ». Church, Alan Turing et John von Neumann, qui ont Les structures discrètes telles que les graphes, conduit au développement de véritables ordinateurs les chaînes de caractères et les permutations physiques. L’informatique théorique comprend deux sont au cœur de l’informatique théorique, et les sous-disciplines complémentaires : l’algorithmique mathématiques discrètes et l’informatique théorique qui développe des méthodes efficaces pour une ont naturellement été des domaines étroitement multitude de problèmes de calcul ; et la complexité, liés. Certes, ces deux domaines ont énormément qui montre les limites inhérentes à l’efficacité des bénéficié des champs de recherche plus traditionnels algorithmes. La notion d’algorithmes en temps des mathématiques, mais on constate également polynomial mise en avant dans les années 1960 par une influence croissante dans le sens inverse. Alan Cobham, Jack Edmonds et d’autres, ainsi que Les applications, concepts et techniques de la célèbre conjecture P≠NP de Stephen Cook, Leonid l’informatique théorique ont généré de nouveaux Levin et Richard Karp ont eu un fort impact sur le défis, ouvert de nouvelles directions de recherche domaine et sur les travaux de Lovász et Wigderson. -
The Flajolet-Martin Sketch Itself Preserves Differential Privacy: Private Counting with Minimal Space
The Flajolet-Martin Sketch Itself Preserves Differential Privacy: Private Counting with Minimal Space Adam Smith Shuang Song Abhradeep Thakurta Boston University Google Research, Brain Team Google Research, Brain Team [email protected] [email protected] [email protected] Abstract We revisit the problem of counting the number of distinct elements F0(D) in a data stream D, over a domain [u]. We propose an ("; δ)-differentially private algorithm that approximates F0(D) within a factor of (1 ± γ), and with additive error of p O( ln(1/δ)="), using space O(ln(ln(u)/γ)/γ2). We improve on the prior work at least quadratically and up to exponentially, in terms of both space and additive p error. Our additive error guarantee is optimal up to a factor of O( ln(1/δ)), n ln(u) 1 o and the space bound is optimal up to a factor of O min ln γ ; γ2 . We assume the existence of an ideal uniform random hash function, and ignore the space required to store it. We later relax this requirement by assuming pseudo- random functions and appealing to a computational variant of differential privacy, SIM-CDP. Our algorithm is built on top of the celebrated Flajolet-Martin (FM) sketch. We show that FM-sketch is differentially private as is, as long as there are p ≈ ln(1/δ)=(εγ) distinct elements in the data set. Along the way, we prove a structural result showing that the maximum of k i.i.d. random variables is statisti- cally close (in the sense of "-differential privacy) to the maximum of (k + 1) i.i.d. -
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]. -
A Decade of Lattice Cryptography
Full text available at: http://dx.doi.org/10.1561/0400000074 A Decade of Lattice Cryptography Chris Peikert Computer Science and Engineering University of Michigan, United States Boston — Delft Full text available at: http://dx.doi.org/10.1561/0400000074 Foundations and Trends R in Theoretical Computer Science Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 United States Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is C. Peikert. A Decade of Lattice Cryptography. Foundations and Trends R in Theoretical Computer Science, vol. 10, no. 4, pp. 283–424, 2014. R This Foundations and Trends issue was typeset in LATEX using a class file designed by Neal Parikh. Printed on acid-free paper. ISBN: 978-1-68083-113-9 c 2016 C. Peikert All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for in- ternal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The ‘services’ for users can be found on the internet at: www.copyright.com For those organizations that have been granted a photocopy license, a separate system of payment has been arranged. -
The Best Nurturers in Computer Science Research
The Best Nurturers in Computer Science Research Bharath Kumar M. Y. N. Srikant IISc-CSA-TR-2004-10 http://archive.csa.iisc.ernet.in/TR/2004/10/ Computer Science and Automation Indian Institute of Science, India October 2004 The Best Nurturers in Computer Science Research Bharath Kumar M.∗ Y. N. Srikant† Abstract The paper presents a heuristic for mining nurturers in temporally organized collaboration networks: people who facilitate the growth and success of the young ones. Specifically, this heuristic is applied to the computer science bibliographic data to find the best nurturers in computer science research. The measure of success is parameterized, and the paper demonstrates experiments and results with publication count and citations as success metrics. Rather than just the nurturer’s success, the heuristic captures the influence he has had in the indepen- dent success of the relatively young in the network. These results can hence be a useful resource to graduate students and post-doctoral can- didates. The heuristic is extended to accurately yield ranked nurturers inside a particular time period. Interestingly, there is a recognizable deviation between the rankings of the most successful researchers and the best nurturers, which although is obvious from a social perspective has not been statistically demonstrated. Keywords: Social Network Analysis, Bibliometrics, Temporal Data Mining. 1 Introduction Consider a student Arjun, who has finished his under-graduate degree in Computer Science, and is seeking a PhD degree followed by a successful career in Computer Science research. How does he choose his research advisor? He has the following options with him: 1. Look up the rankings of various universities [1], and apply to any “rea- sonably good” professor in any of the top universities. -
Constraint Based Dimension Correlation and Distance
Preface The papers in this volume were presented at the Fourteenth Annual IEEE Conference on Computational Complexity held from May 4-6, 1999 in Atlanta, Georgia, in conjunction with the Federated Computing Research Conference. This conference was sponsored by the IEEE Computer Society Technical Committee on Mathematical Foundations of Computing, in cooperation with the ACM SIGACT (The special interest group on Algorithms and Complexity Theory) and EATCS (The European Association for Theoretical Computer Science). The call for papers sought original research papers in all areas of computational complexity. A total of 70 papers were submitted for consideration of which 28 papers were accepted for the conference and for inclusion in these proceedings. Six of these papers were accepted to a joint STOC/Complexity session. For these papers the full conference paper appears in the STOC proceedings and a one-page summary appears in these proceedings. The program committee invited two distinguished researchers in computational complexity - Avi Wigderson and Jin-Yi Cai - to present invited talks. These proceedings contain survey articles based on their talks. The program committee thanks Pradyut Shah and Marcus Schaefer for their organizational and computer help, Steve Tate and the SIGACT Electronic Publishing Board for the use and help of the electronic submissions server, Peter Shor and Mike Saks for the electronic conference meeting software and Danielle Martin of the IEEE for editing this volume. The committee would also like to thank the following people for their help in reviewing the papers: E. Allender, V. Arvind, M. Ajtai, A. Ambainis, G. Barequet, S. Baumer, A. Berthiaume, S. -
Interactions of Computational Complexity Theory and Mathematics
Interactions of Computational Complexity Theory and Mathematics Avi Wigderson October 22, 2017 Abstract [This paper is a (self contained) chapter in a new book on computational complexity theory, called Mathematics and Computation, whose draft is available at https://www.math.ias.edu/avi/book]. We survey some concrete interaction areas between computational complexity theory and different fields of mathematics. We hope to demonstrate here that hardly any area of modern mathematics is untouched by the computational connection (which in some cases is completely natural and in others may seem quite surprising). In my view, the breadth, depth, beauty and novelty of these connections is inspiring, and speaks to a great potential of future interactions (which indeed, are quickly expanding). We aim for variety. We give short, simple descriptions (without proofs or much technical detail) of ideas, motivations, results and connections; this will hopefully entice the reader to dig deeper. Each vignette focuses only on a single topic within a large mathematical filed. We cover the following: • Number Theory: Primality testing • Combinatorial Geometry: Point-line incidences • Operator Theory: The Kadison-Singer problem • Metric Geometry: Distortion of embeddings • Group Theory: Generation and random generation • Statistical Physics: Monte-Carlo Markov chains • Analysis and Probability: Noise stability • Lattice Theory: Short vectors • Invariant Theory: Actions on matrix tuples 1 1 introduction The Theory of Computation (ToC) lays out the mathematical foundations of computer science. I am often asked if ToC is a branch of Mathematics, or of Computer Science. The answer is easy: it is clearly both (and in fact, much more). Ever since Turing's 1936 definition of the Turing machine, we have had a formal mathematical model of computation that enables the rigorous mathematical study of computational tasks, algorithms to solve them, and the resources these require. -
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Cambridge University Press 978-0-521-87282-9 - Algorithmic Game Theory Edited by Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani Copyright Information More information Algorithmic Game Theory Edited by Noam Nisan Hebrew University of Jerusalem Tim Roughgarden Stanford University Eva´ Tardos Cornell University Vijay V. Vazirani Georgia Institute of Technology © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-87282-9 - Algorithmic Game Theory Edited by Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani Copyright Information More information cambridge university press Cambridge, New York,Melbourne, Madrid, Cape Town, Singapore, Sao˜ Paulo, Delhi Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9780521872829 C Noam Nisan, Tim Roughgarden, Eva´ Tardos, Vijay V. Vazirani 2007 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2007 Printed in the United States of America A catalog record for this book is available from the British Library. Library of Congress Cataloging in Publication Data Algorithmic game theory / edited by Noam Nisan ...[et al.]; foreword by Christos Papadimitriou. p. cm. Includes index. ISBN-13: 978-0-521-87282-9 (hardback) ISBN-10: 0-521-87282-0 (hardback) 1. Game theory. 2. Algorithms. I. Nisan, Noam. II. Title. QA269.A43 2007 519.3–dc22 2007014231 ISBN 978-0-521-87282-9 hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLS for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate. -
Securely Obfuscating Re-Encryption
Securely Obfuscating Re-Encryption Susan Hohenberger¤ Guy N. Rothblumy abhi shelatz Vinod Vaikuntanathanx December 1, 2008 Abstract We present a positive obfuscation result for a traditional cryptographic functionality. This posi- tive result stands in contrast to well-known impossibility results [3] for general obfuscation and recent impossibility and improbability [13] results for obfuscation of many cryptographic functionalities. Whereas other positive obfuscation results in the standard model apply to very simple point func- tions, our obfuscation result applies to the signi¯cantly more complex and widely-used re-encryption functionality. This functionality takes a ciphertext for message m encrypted under Alice's public key and transforms it into a ciphertext for the same message m under Bob's public key. To overcome impossibility results and to make our results meaningful for cryptographic functionalities, our scheme satis¯es a de¯nition of obfuscation which incorporates more security-aware provisions. ¤Johns Hopkins University, [email protected]. Research partially performed at IBM Zurich Research Laboratory, Switzer- land. yMIT CSAIL, [email protected]. Research supported by NSF grant CNS-0430450 and NSF grant CFF-0635297. zUniversity of Virginia, [email protected]. Research performed at IBM Zurich Research Laboratory, Switzerland. xMIT CSAIL, [email protected] 1 1 Introduction A recent line of research in theoretical cryptography aims to understand whether it is possible to obfuscate programs so that a program's code becomes unintelligible while its functionality remains unchanged. A general method for obfuscating programs would lead to the solution of many open problems in cryptography. Unfortunately, Barak, Goldreich, Impagliazzo, Rudich, Sahai, Vadhan and Yang [3] show that for many notions of obfuscation, a general program obfuscator does not exist|i.e., they exhibit a class of circuits which cannot be obfuscated.