Cryptography
This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication. Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie
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Simon Rubinstein-Salzedo
Cryptography
Springer Undergraduate Mathematics Series Advisory Board M.A.J. Chaplain, University of St. Andrews A. MacIntyre, Queen Mary University of London S. Scott, King’s College London N. Snashall, University of Leicester E. Süli, University of Oxford M.R. Tehranchi, University of Cambridge J.F. Toland, University of Bath
More information about this series at http://www.springer.com/series/3423
Simon Rubinstein-Salzedo
Cryptography
123
Simon Rubinstein-Salzedo Palo Alto, CA, USA
ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISBN 978-3-319-94817-1 ISBN 978-3-319-94818-8 (eBook) https://doi.org/10.1007/978-3-319-94818-8 Library of Congress Control Number: 2018946572 Mathematics Subject Classification (2010): 11T71 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents
1
A Quick Overview . . . . . . . . . . . . 1.1 The Setup of Cryptography . 1.2 A Note on Sage . . . . . . . . . 1.3 Problems . . . . . . . . . . . . . .
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1 1 2 3
2
Cæsar 2.1 2.2 2.3 2.4
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5 5 5 6 7
3
Substitution Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 What is a Subs
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