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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 -
Tarjan Transcript Final with Timestamps
A.M. Turing Award Oral History Interview with Robert (Bob) Endre Tarjan by Roy Levin San Mateo, California July 12, 2017 Levin: My name is Roy Levin. Today is July 12th, 2017, and I’m in San Mateo, California at the home of Robert Tarjan, where I’ll be interviewing him for the ACM Turing Award Winners project. Good afternoon, Bob, and thanks for spending the time to talk to me today. Tarjan: You’re welcome. Levin: I’d like to start by talking about your early technical interests and where they came from. When do you first recall being interested in what we might call technical things? Tarjan: Well, the first thing I would say in that direction is my mom took me to the public library in Pomona, where I grew up, which opened up a huge world to me. I started reading science fiction books and stories. Originally, I wanted to be the first person on Mars, that was what I was thinking, and I got interested in astronomy, started reading a lot of science stuff. I got to junior high school and I had an amazing math teacher. His name was Mr. Wall. I had him two years, in the eighth and ninth grade. He was teaching the New Math to us before there was such a thing as “New Math.” He taught us Peano’s axioms and things like that. It was a wonderful thing for a kid like me who was really excited about science and mathematics and so on. The other thing that happened was I discovered Scientific American in the public library and started reading Martin Gardner’s columns on mathematical games and was completely fascinated. -
Butler Lampson, Martin Abadi, Michael Burrows, Edward Wobber
Outline • Chapter 19: Security (cont) • A Method for Obtaining Digital Signatures and Public-Key Cryptosystems Ronald L. Rivest, Adi Shamir, and Leonard M. Adleman. Communications of the ACM 21,2 (Feb. 1978) – RSA Algorithm – First practical public key crypto system • Authentication in Distributed Systems: Theory and Practice, Butler Lampson, Martin Abadi, Michael Burrows, Edward Wobber – Butler Lampson (MSR) - He was one of the designers of the SDS 940 time-sharing system, the Alto personal distributed computing system, the Xerox 9700 laser printer, two-phase commit protocols, the Autonet LAN, and several programming languages – Martin Abadi (Bell Labs) – Michael Burrows, Edward Wobber (DEC/Compaq/HP SRC) Oct-21-03 CSE 542: Operating Systems 1 Encryption • Properties of good encryption technique: – Relatively simple for authorized users to encrypt and decrypt data. – Encryption scheme depends not on the secrecy of the algorithm but on a parameter of the algorithm called the encryption key. – Extremely difficult for an intruder to determine the encryption key. Oct-21-03 CSE 542: Operating Systems 2 Strength • Strength of crypto system depends on the strengths of the keys • Computers get faster – keys have to become harder to keep up • If it takes more effort to break a code than is worth, it is okay – Transferring money from my bank to my credit card and Citibank transferring billions of dollars with another bank should not have the same key strength Oct-21-03 CSE 542: Operating Systems 3 Encryption methods • Symmetric cryptography – Sender and receiver know the secret key (apriori ) • Fast encryption, but key exchange should happen outside the system • Asymmetric cryptography – Each person maintains two keys, public and private • M ≡ PrivateKey(PublicKey(M)) • M ≡ PublicKey (PrivateKey(M)) – Public part is available to anyone, private part is only known to the sender – E.g. -
Rivest, Shamir, and Adleman Receive 2002 Turing Award, Volume 50
Rivest, Shamir, and Adleman Receive 2002 Turing Award Cryptography and Information Se- curity Group. He received a B.A. in mathematics from Yale University and a Ph.D. in computer science from Stanford University. Shamir is the Borman Profes- sor in the Applied Mathematics Department of the Weizmann In- stitute of Science in Israel. He re- Ronald L. Rivest Adi Shamir Leonard M. Adleman ceived a B.S. in mathematics from Tel Aviv University and a Ph.D. in The Association for Computing Machinery (ACM) has computer science from the Weizmann Institute. named RONALD L. RIVEST, ADI SHAMIR, and LEONARD M. Adleman is the Distinguished Henry Salvatori ADLEMAN as winners of the 2002 A. M. Turing Award, Professor of Computer Science and Professor of considered the “Nobel Prize of Computing”, for Molecular Biology at the University of Southern their contributions to public key cryptography. California. He earned a B.S. in mathematics at the The Turing Award carries a $100,000 prize, with University of California, Berkeley, and a Ph.D. in funding provided by Intel Corporation. computer science, also at Berkeley. As researchers at the Massachusetts Institute of The ACM presented the Turing Award on June 7, Technology in 1977, the team developed the RSA 2003, in conjunction with the Federated Computing code, which has become the foundation for an en- Research Conference in San Diego, California. The tire generation of technology security products. It award was named for Alan M. Turing, the British mathematician who articulated the mathematical has also inspired important work in both theoret- foundation and limits of computing and who was a ical computer science and mathematics. -
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. -
Single-To-Multi-Theorem Transformations for Non-Interactive Statistical Zero-Knowledge
Single-to-Multi-Theorem Transformations for Non-Interactive Statistical Zero-Knowledge Marc Fischlin Felix Rohrbach Cryptoplexity, Technische Universität Darmstadt, Germany www.cryptoplexity.de [email protected] [email protected] Abstract. Non-interactive zero-knowledge proofs or arguments allow a prover to show validity of a statement without further interaction. For non-trivial statements such protocols require a setup assumption in form of a common random or reference string (CRS). Generally, the CRS can only be used for one statement (single-theorem zero-knowledge) such that a fresh CRS would need to be generated for each proof. Fortunately, Feige, Lapidot and Shamir (FOCS 1990) presented a transformation for any non-interactive zero-knowledge proof system that allows the CRS to be reused any polynomial number of times (multi-theorem zero-knowledge). This FLS transformation, however, is only known to work for either computational zero-knowledge or requires a structured, non-uniform common reference string. In this paper we present FLS-like transformations that work for non-interactive statistical zero-knowledge arguments in the common random string model. They allow to go from single-theorem to multi-theorem zero-knowledge and also preserve soundness, for both properties in the adaptive and non-adaptive case. Our first transformation is based on the general assumption that one-way permutations exist, while our second transformation uses lattice-based assumptions. Additionally, we define different possible soundness notions for non-interactive arguments and discuss their relationships. Keywords. Non-interactive arguments, statistical zero-knowledge, soundness, transformation, one-way permutation, lattices, dual-mode commitments 1 Introduction In a non-interactive proof for a language L the prover P shows validity of some theorem x ∈ L via a proof π based on a common string crs chosen by some external setup procedure. -
1 Introduction
Logic Activities in Europ e y Yuri Gurevich Intro duction During Fall thanks to ONR I had an opp ortunity to visit a fair numb er of West Eu rop ean centers of logic research I tried to learn more ab out logic investigations and appli cations in Europ e with the hop e that my exp erience may b e useful to American researchers This rep ort is concerned only with logic activities related to computer science and Europ e here means usually Western Europ e one can learn only so much in one semester The idea of such a visit may seem ridiculous to some The mo dern world is quickly growing into a global village There is plenty of communication b etween Europ e and the US Many Europ ean researchers visit the US and many American researchers visit Europ e Neither Americans nor Europ eans make secret of their logic research Quite the opp osite is true They advertise their research From ESPRIT rep orts the Bulletin of Europ ean Asso ciation for Theoretical Computer Science the Newsletter of Europ ean Asso ciation for Computer Science Logics publications of Europ ean Foundation for Logic Language and Information publications of particular Europ ean universities etc one can get a go o d idea of what is going on in Europ e and who is doing what Some Europ ean colleagues asked me jokingly if I was on a reconnaissance mission Well sometimes a cow wants to suckle more than the calf wants to suck a Hebrew proverb It is amazing however how dierent computer science is esp ecially theoretical com puter science in Europ e and the US American theoretical -
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. -
Cryptography: DH And
1 ì Key Exchange Secure Software Systems Fall 2018 2 Challenge – Exchanging Keys & & − 1 6(6 − 1) !"#ℎ%&'() = = = 15 & 2 2 The more parties in communication, ! $ the more keys that need to be securely exchanged Do we have to use out-of-band " # methods? (e.g., phone?) % Secure Software Systems Fall 2018 3 Key Exchange ì Insecure communica-ons ì Alice and Bob agree on a channel shared secret (“key”) that ì Eve can see everything! Eve doesn’t know ì Despite Eve seeing everything! ! " (alice) (bob) # (eve) Secure Software Systems Fall 2018 Whitfield Diffie and Martin Hellman, 4 “New directions in cryptography,” in IEEE Transactions on Information Theory, vol. 22, no. 6, Nov 1976. Proposed public key cryptography. Diffie-Hellman key exchange. Secure Software Systems Fall 2018 5 Diffie-Hellman Color Analogy (1) It’s easy to mix two colors: + = (2) Mixing two or more colors in a different order results in + + = the same color: + + = (3) Mixing colors is one-way (Impossible to determine which colors went in to produce final result) https://www.crypto101.io/ Secure Software Systems Fall 2018 6 Diffie-Hellman Color Analogy ! # " (alice) (eve) (bob) + + $ $ = = Mix Mix (1) Start with public color ▇ – share across network (2) Alice picks secret color ▇ and mixes it to get ▇ (3) Bob picks secret color ▇ and mixes it to get ▇ Secure Software Systems Fall 2018 7 Diffie-Hellman Color Analogy ! # " (alice) (eve) (bob) $ $ Mix Mix = = Eve can’t calculate ▇ !! (secret keys were never shared) (4) Alice and Bob exchange their mixed colors (▇,▇) (5) Eve will -
Magnetic RSA
Magnetic RSA Rémi Géraud-Stewart1;2 and David Naccache2 1 QPSI, Qualcomm Technologies Incorporated, USA [email protected] 2 ÉNS (DI), Information Security Group CNRS, PSL Research University, 75005, Paris, France [email protected] Abstract. In a recent paper Géraud-Stewart and Naccache [GSN21] (GSN) described an non-interactive process allowing a prover P to con- vince a verifier V that a modulus n is the product of two randomly generated primes (p; q) of about the same size. A heuristic argument conjectures that P cannot control p; q to make n easy to factor. GSN’s protocol relies upon elementary number-theoretic properties and can be implemented efficiently using very few operations. This contrasts with state-of-the-art zero-knowledge protocols for RSA modulus proper generation assessment. This paper proposes an alternative process applicable in settings where P co-generates a modulus n “ p1q1p2q2 with a certification authority V. If P honestly cooperates with V, then V will only learn the sub-products n1 “ p1q1 and n2 “ p2q2. A heuristic argument conjectures that at least two of the factors of n are beyond P’s control. This makes n appropriate for cryptographic use provided that at least one party (of P and V) is honest. This heuristic argument calls for further cryptanalysis. 1 Introduction Several cryptographic protocols rely on the assumption that an integer n “ pq is hard to factor. This includes for instance RSA [RSA78], Rabin [Rab79], Paillier [Pai99] or Fiat–Shamir [FS86]. One way to ascertain that n is such a product is to generate it oneself; however, this becomes a concern when n is provided by a third-party. -
Are All Distributions Easy?
Are all distributions easy? Emanuele Viola∗ November 5, 2009 Abstract Complexity theory typically studies the complexity of computing a function h(x): f0; 1gn ! f0; 1gm of a given input x. We advocate the study of the complexity of generating the distribution h(x) for uniform x, given random bits. Our main results are: • There are explicit AC0 circuits of size poly(n) and depth O(1) whose output n P distribution has statistical distance 1=2 from the distribution (X; i Xi) 2 f0; 1gn × f0; 1; : : : ; ng for uniform X 2 f0; 1gn, despite the inability of these P circuits to compute i xi given x. Previous examples of this phenomenon apply to different distributions such as P n+1 (X; i Xi mod 2) 2 f0; 1g . We also prove a lower bound independent from n on the statistical distance be- tween the output distribution of NC0 circuits and the distribution (X; majority(X)). We show that 1 − o(1) lower bounds for related distributions yield lower bounds for succinct data structures. • Uniform randomized AC0 circuits of poly(n) size and depth d = O(1) with error can be simulated by uniform randomized circuits of poly(n) size and depth d + 1 with error + o(1) using ≤ (log n)O(log log n) random bits. Previous derandomizations [Ajtai and Wigderson '85; Nisan '91] increase the depth by a constant factor, or else have poor seed length. Given the right tools, the above results have technically simple proofs. ∗Supported by NSF grant CCF-0845003. Email: [email protected] 1 Introduction Complexity theory, with some notable exceptions, typically studies the complexity of com- puting a function h(x): f0; 1gn ! f0; 1gm of a given input x. -
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.