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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 -
Efficient Algorithms with Asymmetric Read and Write Costs
Efficient Algorithms with Asymmetric Read and Write Costs Guy E. Blelloch1, Jeremy T. Fineman2, Phillip B. Gibbons1, Yan Gu1, and Julian Shun3 1 Carnegie Mellon University 2 Georgetown University 3 University of California, Berkeley Abstract In several emerging technologies for computer memory (main memory), the cost of reading is significantly cheaper than the cost of writing. Such asymmetry in memory costs poses a fun- damentally different model from the RAM for algorithm design. In this paper we study lower and upper bounds for various problems under such asymmetric read and write costs. We con- sider both the case in which all but O(1) memory has asymmetric cost, and the case of a small cache of symmetric memory. We model both cases using the (M, ω)-ARAM, in which there is a small (symmetric) memory of size M and a large unbounded (asymmetric) memory, both random access, and where reading from the large memory has unit cost, but writing has cost ω 1. For FFT and sorting networks we show a lower bound cost of Ω(ωn logωM n), which indicates that it is not possible to achieve asymptotic improvements with cheaper reads when ω is bounded by a polynomial in M. Moreover, there is an asymptotic gap (of min(ω, log n)/ log(ωM)) between the cost of sorting networks and comparison sorting in the model. This contrasts with the RAM, and most other models, in which the asymptotic costs are the same. We also show a lower bound for computations on an n × n diamond DAG of Ω(ωn2/M) cost, which indicates no asymptotic improvement is achievable with fast reads. -
Fault-Tolerant Distributed Computing in Full-Information Networks
Fault-Tolerant Distributed Computing in Full-Information Networks Shafi Goldwasser∗ Elan Pavlov Vinod Vaikuntanathan∗ CSAIL, MIT MIT CSAIL, MIT Cambridge MA, USA Cambridge MA, USA Cambridge MA, USA December 15, 2006 Abstract In this paper, we use random-selection protocols in the full-information model to solve classical problems in distributed computing. Our main results are the following: • An O(log n)-round randomized Byzantine Agreement (BA) protocol in a synchronous full-information n network tolerating t < 3+ faulty players (for any constant > 0). As such, our protocol is asymp- totically optimal in terms of fault-tolerance. • An O(1)-round randomized BA protocol in a synchronous full-information network tolerating t = n O( (log n)1.58 ) faulty players. • A compiler that converts any randomized protocol Πin designed to tolerate t fail-stop faults, where the n source of randomness of Πin is an SV-source, into a protocol Πout that tolerates min(t, 3 ) Byzantine ∗ faults. If the round-complexity of Πin is r, that of Πout is O(r log n). Central to our results is the development of a new tool, “audited protocols”. Informally “auditing” is a transformation that converts any protocol that assumes built-in broadcast channels into one that achieves a slightly weaker guarantee, without assuming broadcast channels. We regard this as a tool of independent interest, which could potentially find applications in the design of simple and modular randomized distributed algorithms. ∗Supported by NSF grants CNS-0430450 and CCF0514167. 1 1 Introduction The problem of how n players, some of who may be faulty, can make a common random selection in a set, has received much attention. -
Computational Learning Theory: New Models and Algorithms
Computational Learning Theory: New Models and Algorithms by Robert Hal Sloan S.M. EECS, Massachusetts Institute of Technology (1986) B.S. Mathematics, Yale University (1983) Submitted to the Department- of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1989 @ Robert Hal Sloan, 1989. All rights reserved The author hereby grants to MIT permission to reproduce and to distribute copies of this thesis document in whole or in part. Signature of Author Department of Electrical Engineering and Computer Science May 23, 1989 Certified by Ronald L. Rivest Professor of Computer Science Thesis Supervisor Accepted by Arthur C. Smith Chairman, Departmental Committee on Graduate Students Abstract In the past several years, there has been a surge of interest in computational learning theory-the formal (as opposed to empirical) study of learning algorithms. One major cause for this interest was the model of probably approximately correct learning, or pac learning, introduced by Valiant in 1984. This thesis begins by presenting a new learning algorithm for a particular problem within that model: learning submodules of the free Z-module Zk. We prove that this algorithm achieves probable approximate correctness, and indeed, that it is within a log log factor of optimal in a related, but more stringent model of learning, on-line mistake bounded learning. We then proceed to examine the influence of noisy data on pac learning algorithms in general. Previously it has been shown that it is possible to tolerate large amounts of random classification noise, but only a very small amount of a very malicious sort of noise. -
Anna Lysyanskaya Curriculum Vitae
Anna Lysyanskaya Curriculum Vitae Computer Science Department, Box 1910 Brown University Providence, RI 02912 (401) 863-7605 email: [email protected] http://www.cs.brown.edu/~anna Research Interests Cryptography, privacy, computer security, theory of computation. Education Massachusetts Institute of Technology Cambridge, MA Ph.D. in Computer Science, September 2002 Advisor: Ronald L. Rivest, Viterbi Professor of EECS Thesis title: \Signature Schemes and Applications to Cryptographic Protocol Design" Massachusetts Institute of Technology Cambridge, MA S.M. in Computer Science, June 1999 Smith College Northampton, MA A.B. magna cum laude, Highest Honors, Phi Beta Kappa, May 1997 Appointments Brown University, Providence, RI Fall 2013 - Present Professor of Computer Science Brown University, Providence, RI Fall 2008 - Spring 2013 Associate Professor of Computer Science Brown University, Providence, RI Fall 2002 - Spring 2008 Assistant Professor of Computer Science UCLA, Los Angeles, CA Fall 2006 Visiting Scientist at the Institute for Pure and Applied Mathematics (IPAM) Weizmann Institute, Rehovot, Israel Spring 2006 Visiting Scientist Massachusetts Institute of Technology, Cambridge, MA 1997 { 2002 Graduate student IBM T. J. Watson Research Laboratory, Hawthorne, NY Summer 2001 Summer Researcher IBM Z¨urich Research Laboratory, R¨uschlikon, Switzerland Summers 1999, 2000 Summer Researcher 1 Teaching Brown University, Providence, RI Spring 2008, 2011, 2015, 2017, 2019; Fall 2012 Instructor for \CS 259: Advanced Topics in Cryptography," a seminar course for graduate students. Brown University, Providence, RI Spring 2012 Instructor for \CS 256: Advanced Complexity Theory," a graduate-level complexity theory course. Brown University, Providence, RI Fall 2003,2004,2005,2010,2011 Spring 2007, 2009,2013,2014,2016,2018 Instructor for \CS151: Introduction to Cryptography and Computer Security." Brown University, Providence, RI Fall 2016, 2018 Instructor for \CS 101: Theory of Computation," a core course for CS concentrators. -
Arxiv:2102.09041V3 [Cs.DC] 4 Jun 2021
Reaching Consensus for Asynchronous Distributed Key Generation ITTAI ABRAHAM, VMware Research, Israel PHILIPP JOVANOVIC, University College London, United Kingdom MARY MALLER, Ethereum Foundation, United Kingdom SARAH MEIKLEJOHN, University College London, United Kingdom and Google, United Kingdom GILAD STERN, The Hebrew University in Jerusalem, Israel ALIN TOMESCU, VMware Research, USA < = We give a protocol for Asynchronous Distributed Key Generation (A-DKG) that is optimally resilient (can withstand 5 3 faulty parties), has a constant expected number of rounds, has $˜ (=3) expected communication complexity, and assumes only the existence of a PKI. Prior to our work, the best A-DKG protocols required Ω(=) expected number of rounds, and Ω(=4) expected communication. Our A-DKG protocol relies on several building blocks that are of independent interest. We define and design a Proposal Election (PE) protocol that allows parties to retrospectively agree on a valid proposal after enough proposals have been sent from different parties. With constant probability the elected proposal was proposed by a nonfaulty party. In building our PE protocol, we design a Verifiable Gather protocol which allows parties to communicate which proposals they have and have not seen in a verifiable manner. The final building block to our A-DKG is a Validated Asynchronous Byzantine Agreement (VABA) protocol. We use our PE protocol to construct a VABA protocol that does not require leaders or an asynchronous DKG setup. Our VABA protocol can be used more generally when it is not possible to use threshold signatures. 1 INTRODUCTION In this work we study Decentralized Key Generation in the Asynchronous setting (A-DKG). -
Four Results of Jon Kleinberg a Talk for St.Petersburg Mathematical Society
Four Results of Jon Kleinberg A Talk for St.Petersburg Mathematical Society Yury Lifshits Steklov Institute of Mathematics at St.Petersburg May 2007 1 / 43 2 Hubs and Authorities 3 Nearest Neighbors: Faster Than Brute Force 4 Navigation in a Small World 5 Bursty Structure in Streams Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 / 43 3 Nearest Neighbors: Faster Than Brute Force 4 Navigation in a Small World 5 Bursty Structure in Streams Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 Hubs and Authorities 2 / 43 4 Navigation in a Small World 5 Bursty Structure in Streams Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 Hubs and Authorities 3 Nearest Neighbors: Faster Than Brute Force 2 / 43 5 Bursty Structure in Streams Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 Hubs and Authorities 3 Nearest Neighbors: Faster Than Brute Force 4 Navigation in a Small World 2 / 43 Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 Hubs and Authorities 3 Nearest Neighbors: Faster Than Brute Force 4 Navigation in a Small World 5 Bursty Structure in Streams 2 / 43 Part I History of Nevanlinna Prize Career of Jon Kleinberg 3 / 43 Nevanlinna Prize The Rolf Nevanlinna Prize is awarded once every 4 years at the International Congress of Mathematicians, for outstanding contributions in Mathematical Aspects of Information Sciences including: 1 All mathematical aspects of computer science, including complexity theory, logic of programming languages, analysis of algorithms, cryptography, computer vision, pattern recognition, information processing and modelling of intelligence. -
Navigability of Small World Networks
Navigability of Small World Networks Pierre Fraigniaud CNRS and University Paris Sud http://www.lri.fr/~pierre Introduction Interaction Networks • Communication networks – Internet – Ad hoc and sensor networks • Societal networks – The Web – P2P networks (the unstructured ones) • Social network – Acquaintance – Mail exchanges • Biology (Interactome network), linguistics, etc. Dec. 19, 2006 HiPC'06 3 Common statistical properties • Low density • “Small world” properties: – Average distance between two nodes is small, typically O(log n) – The probability p that two distinct neighbors u1 and u2 of a same node v are neighbors is large. p = clustering coefficient • “Scale free” properties: – Heavy tailed probability distributions (e.g., of the degrees) Dec. 19, 2006 HiPC'06 4 Gaussian vs. Heavy tail Example : human sizes Example : salaries µ Dec. 19, 2006 HiPC'06 5 Power law loglog ppk prob{prob{ X=kX=k }} ≈≈ kk-α loglog kk Dec. 19, 2006 HiPC'06 6 Random graphs vs. Interaction networks • Random graphs: prob{e exists} ≈ log(n)/n – low clustering coefficient – Gaussian distribution of the degrees • Interaction networks – High clustering coefficient – Heavy tailed distribution of the degrees Dec. 19, 2006 HiPC'06 7 New problematic • Why these networks share these properties? • What model for – Performance analysis of these networks – Algorithm design for these networks • Impact of the measures? • This lecture addresses navigability Dec. 19, 2006 HiPC'06 8 Navigability Milgram Experiment • Source person s (e.g., in Wichita) • Target person t (e.g., in Cambridge) – Name, professional occupation, city of living, etc. • Letter transmitted via a chain of individuals related on a personal basis • Result: “six degrees of separation” Dec. -
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. -
Cryptography Abstracts
Cryptography Abstracts Saturday 10:15 – 12:15 Shafi Goldwasser, MIT Anna Lysyanskaya, Brown University Alice Silverberg, University of California, Irvine Nadia Heninger, UCSD Sunday 8:30 – 10:30 Tal Rabin, IBM Research Tal Malkin, Columbia University Allison Bishop Lewko, University of Texas, Austin Yael Tauman-Kalai, Microsoft Research – New England Saturday 10:15 – 12:15 On Probabilistic Proofs Shafi Goldwasser, MIT ABSTRACT Flavors and applications of verifiable random functions Anna Lysyanskaya, Brown University A random Boolean function is a function where for every input x, the value f(x) is truly random. A pseudorandom function is one where, even though f(x) can be deterministically computed from a small random "seed" s, no efficient algorithm can distinguish f from a random function upon querying it on inputs x1,...,xn of its choice. A verifiable random function (VRF) is a pseudorandom function that can be verified. That is to say, a VRF consists of four algorithms: Generate, Evaluate, Prove, Verify. Alice chooses uses Generate to pick her function f, Evaluate to evaluate it and compute y=f(x), Prove in order to compute a proof p(x) that y is indeed f(x). Bob can then use Verify in order to ascertain that it is indeed the case that y=f(x). At the same time, whenever Bob is not given a proof p(x) for a particular x, no efficient algorithm allows him to determine whether y=f(x) or is random. In this talk I will give a survey of verifiable random functions and their constructions and applications. Elliptic Curve Primality Tests for Numbers in Special Forms Alice Silverberg, University of California, Irvine In joint work with Alex Abatzoglou and Angela Wong, we use elliptic curves with complex multiplication to give primality proofs for integers of certain forms, generalizing earlier work of B. -
Speeding-Up Verification of Digital Signatures Abdul Rahman Taleb, Damien Vergnaud
Speeding-Up Verification of Digital Signatures Abdul Rahman Taleb, Damien Vergnaud To cite this version: Abdul Rahman Taleb, Damien Vergnaud. Speeding-Up Verification of Digital Signatures. Journal of Computer and System Sciences, Elsevier, 2021, 116, pp.22-39. 10.1016/j.jcss.2020.08.005. hal- 02934136 HAL Id: hal-02934136 https://hal.archives-ouvertes.fr/hal-02934136 Submitted on 27 Sep 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Speeding-Up Verification of Digital Signatures Abdul Rahman Taleb1, Damien Vergnaud2, Abstract In 2003, Fischlin introduced the concept of progressive verification in cryptog- raphy to relate the error probability of a cryptographic verification procedure to its running time. It ensures that the verifier confidence in the validity of a verification procedure grows with the work it invests in the computation. Le, Kelkar and Kate recently revisited this approach for digital signatures and pro- posed a similar framework under the name of flexible signatures. We propose efficient probabilistic verification procedures for popular signature schemes in which the error probability of a verifier decreases exponentially with the ver- ifier running time. We propose theoretical schemes for the RSA and ECDSA signatures based on some elegant idea proposed by Bernstein in 2000 and some additional tricks. -
Communication Complexity (For Algorithm Designers)
Full text available at: http://dx.doi.org/10.1561/0400000076 Communication Complexity (for Algorithm Designers) Tim Roughgarden Stanford University, USA [email protected] Boston — Delft Full text available at: http://dx.doi.org/10.1561/0400000076 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 T. Roughgarden. Communication Complexity (for Algorithm Designers). Foundations and Trends R in Theoretical Computer Science, vol. 11, nos. 3-4, pp. 217–404, 2015. R This Foundations and Trends issue was typeset in LATEX using a class file designed by Neal Parikh. Printed on acid-free paper. ISBN: 978-1-68083-115-3 c 2016 T. Roughgarden 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 Cen- ter, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for internal 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.