Shannon, Beethoven, and the Compact Disc
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The Mathemathics of Secrets.Pdf
THE MATHEMATICS OF SECRETS THE MATHEMATICS OF SECRETS CRYPTOGRAPHY FROM CAESAR CIPHERS TO DIGITAL ENCRYPTION JOSHUA HOLDEN PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c 2017 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR press.princeton.edu Jacket image courtesy of Shutterstock; design by Lorraine Betz Doneker All Rights Reserved Library of Congress Cataloging-in-Publication Data Names: Holden, Joshua, 1970– author. Title: The mathematics of secrets : cryptography from Caesar ciphers to digital encryption / Joshua Holden. Description: Princeton : Princeton University Press, [2017] | Includes bibliographical references and index. Identifiers: LCCN 2016014840 | ISBN 9780691141756 (hardcover : alk. paper) Subjects: LCSH: Cryptography—Mathematics. | Ciphers. | Computer security. Classification: LCC Z103 .H664 2017 | DDC 005.8/2—dc23 LC record available at https://lccn.loc.gov/2016014840 British Library Cataloging-in-Publication Data is available This book has been composed in Linux Libertine Printed on acid-free paper. ∞ Printed in the United States of America 13579108642 To Lana and Richard for their love and support CONTENTS Preface xi Acknowledgments xiii Introduction to Ciphers and Substitution 1 1.1 Alice and Bob and Carl and Julius: Terminology and Caesar Cipher 1 1.2 The Key to the Matter: Generalizing the Caesar Cipher 4 1.3 Multiplicative Ciphers 6 -
CECS 228 Lectures
CECS 228 Lectures Darin Goldstein 1 Modular Arithmetic Introduction The modulus relation is special and is used in computer science all the time. You can think of all numbers in the world of (mod n) as being represented by what is left over when they are divided by n; therefore, all numbers are related to some number between 0 and n-1 in world of (mod n). You are allowed to add, subtract, and multiply in the world of (mod n), but not divide! Why not? What is 4 divided by 2 in the word of (mod 4)? Is it 0 or 2? Calculate the following expressions: • 7 + 9(mod 11) • 4 · 6(mod 11) • 43 · 172(mod 5) • 10017(mod 6) • 97(1023)52(mod 3) 1.1 Application Consider the following network: 1 Imagine that there is a source that is sending data through the network. (Netflix is streaming a movie, for example, to two customers.) For the sake of clarity, assume that the source can send only a single bit through each line segment per time unit. If there is only one customer (either side), then it is clear that the source can simultaneously send two bits of information through the network, both aimed at the same destination. However, if both of the destination nodes are considered customers, then there is contention for the middle link. If we treat the data as if it were water flowing through a pipe, it is clear that the source can only send 1 bit to each destination. In other words, Netflix would have to send the same bit to both customers, one to the left and one to the right, cutting down the throughput from 2 bits with one customer to 1 bit for 2 customers. -
Social Movements and Electromagnetic Cyberspace
rssN 2305-3224 |ililil]ruilffi[ililil] tnlfir i0) 06pa:onaHue u coBpeMeHHocrb. 2012, Ns 6(10) -43- rE OIO-]tr{TI{KA I{ IE O3I{OHOMIIITA Vl[t 81.2 (anr:r.) f79 SOCIAL MOVEMENTS AND ELECTROMAGNETIC CYBERSPACE Gleason G. Revolutions are always unexpected. Many ofthe great revolutions ofthe modem world - the Ameri- can Revolution of 1776, the French Revolution of 1789, the Russian Revolution of 1917. the Chinese Revo- political llH lution of 1949, the Iranian Revolution of 1978 as well as many others - are examples of sweeping change that toppled old regimes and replaced them with a new political order. These revolutions shared many features, but they were also different in many important respects. The revolutions differed in motiva- tion, in the values they championed, and the effects they brought about. All these revolutions prevailed be- cause in each case new political leaders and new social movements combined in ways which exceeded the HH lbl anticipations and capacities of the status-quo regimes which resisted them and which they replaced. It is quite possible that factors auguring for change in mary societies and in many circumstances were anticipated l..a and countered or deterred. Arguably, these were places ripe for revolution in which revolutions did not take place. The balance between the factors of change and the factors of stability shifted toward stability. What is so often unanticipated and unexpected is how the factors shift away from stability toward change [1]. As we survey the "Arab Spring" transformation that swept across the African Maghreb and the Middle East and compare these events with past revolutions, one particular feature stands out - the great speed at which these events took place. -
One-Time Pad History
One-Time Pad A one-time pad is a form of encryption that is difficult to decipher or crack if one is not the intended recipient. If done correctly, the strength of encryption of plaintext can almost be impossible to break in a useful timeframe. The system takes each character from plaintext and uses modular addition with a character from a pad or secret key of the same length of the plaintext to create ciphertext. If the key used to create the ciphertext is really random, as large or larger than the plaintext, never reused in any form, and kept truly secret, the ciphertext is unable to be decrypted in a usable timeframe. Although one-time pads are theoretically sound, there have been a number of practical implementation issues keeping the pads from seeing widespread use. When was the One-Time Pad Discovered? The one-time pad has been invented, an re-invented several times over the years. The technique was first described in 1882 by Frank Miller, and later “re-discovered in 1917” with a successful patent claim made a few years later. The current one-time pad concept is based on the Vernam cipher created by Gilbert Vernam and other co-workers. His cipher combined a message with a key that was read from a punch tape. In the original form of the cipher, the encoded messages could eventually be cracked since the key tape was setup on a loop that resulted in the key being reused making the cipher open to cryptanalysis. The “one-time” aspect of the cipher came into play a bit later when Joseph Mauborgne discovered the fact that if they key tape was fully random, cryptanalysis would be difficult if not impossible. -
Creating a Rocket Industry Rockets and People Volume II: Creating a Rocket Industry
Rockets and People Volume II: Creating a Rocket Industry Rockets and People Volume II: Creating a Rocket Industry Boris Chertok Asif Siddiqi, Series Editor For sale by the Superintendent of Documents, U.S. Government Printing Office Internet: bookstore.gpo.gov Phone: toll free (866) 512-1800; DC area (202) 512-1800 Fax: (202) 512-2250 Mail: Stop SSOP, Washington, DC 20402-0001 The NASA History Series National Aeronautics and Space Administration NASA History Division Office of External Relations Washington, DC June 2006 NASA SP-2006-4110 I dedicate this book to the cherished memory of my wife and friend, Yekaterina Semyonova Golubkina. Library of Congress Cataloging-in-Publication Data Chertok, B. E. (Boris Evseevich), 1912– [Rakety i lyudi. English] Rockets and People: Creating a Rocket Industry (Volume II) / by Boris E. Chertok ; [edited by] Asif A. Siddiqi. p. cm. — (NASA History Series) (NASA SP-2006-4110) Includes bibliographical references and index. 1. Chertok, B. E. (Boris Evseevich), 1912– 2. Astronautics— Soviet Union—Biography. 3. Aerospace engineers—Soviet union— Biography. 4. Astronautics—Soviet Union—History. I. Siddiqi, Asif A., 1966- II. Title. III. Series. IV. SP-2006-4110. TL789.85.C48C4813 2006 629.1’092—dc22 2006020825 Contents Series Introduction by Asif A. Siddiqi ix Introduction to Volume II xxi A Few Notes about Transliteration and Translation xxiii List of Abbreviations xxv 1 Three New Technologies, Three State Committees 1 2 The Return 25 3 From Usedom Island to Gorodomlya Island 43 4 Institute No. 88 and Director -
ELEC 3004 Quiz 1 Review
ELEC 3004 Quiz 1 Review PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Fri, 30 Mar 2012 09:52:21 UTC Contents Articles Signals 1 Signal (electronics) 1 Even and odd functions 3 Linear system 6 Time-invariant system 8 Causal system 10 Sampling 12 Sampling (signal processing) 12 Nyquist–Shannon sampling theorem 16 Aliasing 29 Quantization (signal processing) 34 Convolution 42 Convolution 42 Appendix: Systems & Laplace 53 Ordinary differential equation 53 Laplace transform applied to differential equations 62 Fourier transform 63 Harmonic oscillator 83 References Article Sources and Contributors 94 Image Sources, Licenses and Contributors 96 Article Licenses License 97 1 Signals Signal (electronics) A signal is any stream of quantities in time or spatial sequence. Signals categorizes to the fields of communications, signal processing, and to electrical engineering more generally. Signals may contain and transport information in coded form like modulation. In that case the actual quantities are finally not used, but are decoded in a detector or demodulator. In the physical world, any quantity measurable through time or over space can be taken as a signal. Within a complex society, any set of human information or machine data can also be taken as a signal. Such information or machine data (for example, the dots on a screen, the ink making up text on a paper page, or the words now flowing into the reader's mind) must all be part of systems existing in the physical world – either living or non-living. Despite the complexity of such systems, their outputs and inputs can often be represented as simple quantities measurable through time or across space. -
Pestel Analysis of Russia
A Global Country Study Report On Russia Submitted to Institute Code: 769 Institute Name: GIDC Rajju Shroff ROFEL Institute of Management Studies Vapi In partial Fulfilment of the Requirement of the award for the degree of Master of Business Administration (MBA) By Gujarat Technological University Ahmedabad Prepared by: Students of MBA (Semester - III and IV) PART – I OVERVIEW OF BUSINESS & TRADE IN RUSSIA DEMOGRAPHIC PROFILE OF RUSSIA Population – 138,739,892 (July 2011 est.) Age structure – 0-14 years: 15.2% (male 10,818,203/female 10,256,611) 15-64 years: 71.8% (male 47,480,851/female 52,113,279) 65 years and over: 13% (male 5,456,639/female 12,614,309) (2011 est.) Median age – Total: 38.7 years Male: 35.5 years Female: 41.9 years (2011 est.) Population growth rate – 0.47% (2011 est.) Birth rate – 11.05 births/1,000 population (2011 est.) Death rate – 16.04 deaths/1,000 population (July 2011 est.) Urbanization – Urban population: 73% of total population (2010) Rate of urbanization: -0.2% annual rate of change (2010-15 est.) Sex ratio – At birth: 1.06 male(s)/female Under 15 years: 1.06 male(s)/female 15-64 years: 0.92 male(s)/female 65 years and over: 0.44 male(s)/female Total population ratio: 0.85 male(s)/female (2011 est.) Infant mortality rate – Total: 10.08 deaths/1,000 live births Male: 11.58 deaths/1,000 live births Female: 8.49 deaths/1,000 live births (2011 est.) Life expectancy at birth – Total population: 66.29 years Male: 59.8 years Female: 73.17 years (2011 est.) Ethnic groups – Russian 79.8%, Tatar 3.8%, Ukrainian 2%, -
Vladimir Aleksandrovich Kotelnikov: Pioneer of the Sampling Theorem, Cryptography, Optimal Detection, Planetary Mapping
Open Research Online The Open University’s repository of research publications and other research outputs Vladimir Aleksandrovich Kotelnikov: Pioneer of the sampling theorem, cryptography, optimal detection, planetary mapping Journal Item How to cite: Bissell, Christopher (2009). Vladimir Aleksandrovich Kotelnikov: Pioneer of the sampling theorem, cryptography, optimal detection, planetary mapping. IEEE Communications Magazine, 47(10) pp. 24–32. For guidance on citations see FAQs. c 2009 IEEE Version: Version of Record Link(s) to article on publisher’s website: http://dx.doi.org/doi:10.1109/MCOM.2009.5273804 Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online’s data policy on reuse of materials please consult the policies page. oro.open.ac.uk LYT-HISTORY-October 9/22/09 5:04 PM Page 24 HISTORY OF COMMUNICATIONS EDITED BY MISCHA SCHWARTZ INTRODUCTION BY EDITOR Kotelnikov has been well known for many years as the author Kotelnikov both as a human being and as an outstanding engi- of the monograph Theory of Optimum Noise Immunity. Those neer/scientist portrayed so effectively in Prof. Bissell’s article that of us teaching communication theory many years ago savored follows. It is especially interesting to learn that Dr. Kotelnikov our copies of the book, and often used it to augment textbook was probably the first person to demonstrate the by now well- material covering the subject. What was less known was who this known sampling theorem in the time domain. I commend the man was, and with what other activities he was involved. -
Computer-History2
1948: Information Theory first use of the "bit" term Claude Shannon (1916-2001) Source: Shannon C., "A Mathematical Theory of Communication", C.Shannon, Bell System Technical Journal, 1948 1 / 30 Shannon Entropy (bits) Shannon Entropy = Expected Value (average) of the Information Contained in Each Message b=2, P(x ) = 2-n, =2n i m m m m H(X) = - ∑ P(x ) log P(x ) = - ∑ (2-n) log (2-n) = - log (2-n) ∑ (2-n) i 2 i 2 2 i=1 i=1 n i=1 m 2 -n ∑ P(x ) = ∑ (2 ) = 1 i i=1 i=1 -n H(X) = - log (2 ) (1) = - (-n) log (2) (1) = - (-n) (1) (1) = n (bits) 2 2 log ( ) bits needed to represent a variable that can take one of values 2 m m if m is a power of 2, m=2n, if these values are equally probable, the Entropy equal to the number of bits n 2 / 30 1949: Teorema di Nyquist-Shannon S(t) fM Harry Nyquist ΔT t Claude Shannon (1889-1976) (1916-2001) Dato un segnale analogico S(t) la cui banda di frequenze sia limitata dalla frequenza , fM il segnale S(t) puo© essere univocamente ricostruito a partire dai suoi campioni presi a frequenza = 1 / se > 2 fS ΔT fS fM (es. = 20 KHz, > 40 KHz, ΔT < 1/40.000 = 2.5 10-5 sec. = 25 μsec) fM fS See also 1933: Vladimir Kotelnikov (1908-2005) Information Theory and Radar Astronomy Pioneer Soviet Union, Russian Academy of Science Shannon, Claude E. (January 1949). "Communication in the presence of noise". -
Rockets and People
Rockets and People Volume III:Hot Days of the Cold War For sale by the Superintendent of Documents, U.S. Government Printing Office ISBN 978-0-16-081733-5 Internet: bookstore.gpo.gov Phone: toll free (866) 512-1800; DC area (202) 512-1800 9 0 0 0 0 Fax: (202) 512-2104 Mail: Stop IDCC, Washington, DC 20402-0001 ISBN 978-0-16-081733-5 9 780160 817335 For sale by the Superintendent of Documents, U.S. Government Printing Office ISBN 978-0-16-081733-5 Internet: bookstore.gpo.gov Phone: toll free (866) 512-1800; DC area (202) 512-1800 9 0 0 0 0 Fax: (202) 512-2104 Mail: Stop IDCC, Washington, DC 20402-0001 ISBN 978-0-16-081733-5 9 780160 817335 Rockets and People Volume III:Hot Days of the Cold War Boris Chertok Asif Siddiqi, Series Editor The NASA History Series National Aeronautics and Space Administration NASA History Division Office of External Relations Washington, DC May 2009 NASA SP-2009-4110 Library of Congress Cataloging-in-Publication Data Chertok, B. E. (Boris Evseevich), 1912– [Rakety i lyudi. English] Rockets and People: Hot Days of the Cold War (Volume III) / by Boris E. Chertok ; [edited by] Asif A. Siddiqi. p. cm. — (NASA History Series) (NASA SP-2009-4110) Includes bibliographical references and index. 1. Chertok, B. E. (Boris Evseevich), 1912– 2. Astronautics— Soviet Union—Biography. 3. Aerospace engineers—Soviet Union— Biography. 4. Astronautics—Soviet Union—History. I. Siddiqi, Asif A., 1966– II. Title. III. Series. IV. SP-2009-4110. TL789.85.C48C4813 2009 629.1’092—dc22 2009020825 I dedicate this book to the cherished memory of my wife and friend, Yekaterina Semyonova Golubkina.