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CHAPMAN & HALL/CRC CRYPTOGRAPHY AND NETWORK SECURITY lnt:roduct:ion t:o Modern Cryptography

CHAP N & HALL/CRC CRYPTOGRAPHY AND NETWORK SECURITY Series Editor Douglas R. Stinson Published Titles Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography Forthcoming Titles Burton Rosenberg, Handbook of Financial Cryptography Maria Isabel Vasco, Spyros Magliveras, Group Theoretic Cryptography and Rainer Steinwandt, Shiu-Kai Chin and Susan Beth Older, A Mathematical Introduction Access Control to

CHAPMAN & HALL/CRC CRYPTOGRAPHY AND NETWORK SECURITY Introduction to Modern Cryptography _jtJna1:han Ka1:z Yehuda Lindell Boca Raton London New York Chapman & Haii/CRC is an imprint of the Taylor & Francis Group, an informa business

Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2008 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business No claim to original Printed in the United States of America on acid-free 109 87 6 5 4 U.S. Government works paper . International Standard Book Number-13: 978-1-58488-551-1 (Hardcover) This book contains information obtained material is quoted with permission, listed. and the publisher cannot assume responsibility quences of their use. Reasonable efforts have been made to publish reliable and sources are indicated. for the validity A wide variety of references are but the author data and information, of all materials or for the conse from authentic and highly regarded sources. Reprinted No part of this book may be reprinted, reproduced, electronic, microfilming, permission from the publishers. or other means, now known or hereafter and recording, mechanical, or in any information storage or retrieyal transmitted, or utilized in any form by any invented, including photocopying, system, without written (http://www.copy For permission to photocopy or use material electronically copyright.com 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. · provides licenses and registration photocopy license by the CCC, a separate right.com/) or contact the Copyright Clearance CCC is a not-for-profit for a variety of users. For organizations system of payment has been arranged. Center, Inc. (CCC) organization that that have been granted a from this work, please access www. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, are used only for and explanation without intent to infringe. identification and Library of Congress Cataloging-in- Publication Data Katz, Jonathan. Introduction to modern cryptography : principles and protocols I Jonathan Katz and Yehuda Lindell. p.cm. Includes bibliographical references ISBN 978-1-58488-551-1 (alk. paper) 1. Computer security. and index. 2. Cryptography. I. Lindell, Yehuda. II. Title. QA76.9.A25K36 005.8--dc22 2007 2007017861 Visit the Taylor & Francis Web site at http:/ /www.taylorandfrancis.com and the CRC Press Web site at http:/ /www.crcpress.com

Preface the basic paradigms to serve as a textbook This book presents phy. It is designed courses as a general uate students), and as a reference (in computer suitable in cryptography introduction and principles for undergraduate- or mathematics (especially for self-study for students, researchers, for beginning grad and practitioners of modern cryptogra departments), or graduate-level science . There are numerous other cryptography text another books available book on the subject ask whether reader may rightly would not have written other than opinion, provides appropriate an unequivocal distinguishes a rigorous treatment for an introduction to the topic. this book if the answer to that question yes. The novelty it from all other books currently of modern cryptography in an accessible manner of this book - and what, in our - is that it available today, and the is needed. were anything We As mentioned, is distinguished precise of these assumptions, in turn (these our focus is on modem (post-1980s) from classical by its emphasis and rigorous cryptography principles proofs of security. in greater We briefly discuss each in Chapter are explored detail 1): cryptography , which on definitions, • The central role of definitions: A key intellectual contribution of first step ·'in the design of any cryptographic has been the recognition that formal definitions The reason, modern cryptQgraphy of security are an essential primitive or-protocol. know what it is you are trying to achieve, when you have definitions appear impossible tography constructions satisfying of security are quite strong achieved such strong definipons to achieve. One of the most amazing is that {under mild and widely-believed and - at first glance - may of cryp assumptions) efficient· aspects can be proven to exist. in retrospect, is simple; ifyop don't how can you hope to know it? As we will see in this book, cryptographic • The importance of formal and precise assumptions: As will be can often 2 and 3, many cryptographic in an unconditional sense. be proven secure in Chapters Security constructions on some widely-believed (albeit unproven) assumption. explained not currently relies, instead, The modern cryptographic must be clearly lows for objective enables evaluation rigorous proofs of security approach stated and unambiguously dictates that any such assumption defined. This not only al of the assumption but, more importantly, next. as described • The possibility of rigorous proofs of security: The previous two ideas lead naturally to the current one, which is the realization that cryp- v

Vl of security and relative to a well-defined from an art to a science. of modern cryptograp schemes were designed . This is the essence cryptography to a clearlY tographic constructions can be proven secure with respect hic stated definition cryptograp hy, and what lJ.aS assumption transformed The importance cryptographic were deemed to be secure if the designers any attacks. In contrast, of schemes with formal, models. Such ing assumption model the real-world assumptions possible to obtain schemes allY, of this idea cannot be over-emphasized . Historic a:o.d could not fi:o.d the desig:Il :o.ed mathematical are guaranteed to be secure unless the underlY definition . By relying that "factoring is false (or the security concerns) atelY did not appropri dillg (e.g., the assumption that are extremely proofs of security ad-hoc fashion, in a largely themselves on long-st_an in well-defi is hard"), security unli�ely it is thllS schemes to be broken. modern cryptography promotes of modern cryptography definitions of cryptography" not only to the "theory is, by now, widely understood A unified approach. The above contributions relevant tance of precise those in the security systems, and rigorous for cryptographic "applied and widely-used constructions time, a proof) of what definition ents have become one of the requirem to be standardized. As such, we do not separate practical (and, most of the security" along with precise is achieved. community proofs of security ; rather, statements are The impor d bY cryptography" from "provable community. of security we present schemes to build secure who use cryptographic tools and appreciate Guide to Using this Book_ · This section is intended primarily for instructors picking to adopt this book up this book on his or her own seeking for their course, may also find it a useful overview of the topics though the student that will be covered. proofs, some mathematical requires and mathemat In par and therefore say in an upper-level algorithms, or computabi the reader is assumed to have· had some exposure level, Required background. This book uses definitions, ical concepts, ticular, college mathematics, made a significant accessible. textbooks example) to understand iity theory. Having s · the presentation that this book is not more difficult , we believe maturity. to proofs at the course or a course on discrete aid this, we have and make it generallY than analogous that (to take one asier · It is our belief that are less rigorous once security it often becomes e made in a particular construc the design choices goals are clearly effort to simplify mathematics formulated, . On the contrary tion. We have structured the book so that the only formal prerequisites course in algorithms on very little probability material: and big-0 notation, and a course in discrete are a Even here we relY with basic , we assume some familiarity and the idea of equating mathematics. modular arithmetic, specifically

Vll efficient are reviewed algorithms with those running in polynomial time. These concepts in Appendix A and/ or when first used in the book. Suggestions for course organization. The core material which we strongly on cryptography, what follows; recommend consists (starred starred of the following should be covered in any introductory course are excluded in below): discussion regarding see further of this book, material sections • Chapters 1-4 (through Section 4.6), discussing modern cryptogra private-key phy, and the basics and message encryption of private-key authenticatio n). classical cryptograp cryptography (both hy, • Chapter cluding 5, illustrating material basic design principles block ciphers on the widely-used DES and AES.1 for block ciphers and in • Chapter 7, introducing concrete mathematical the number-theoretic believed to be needed to un background problems "hard", and providing derstand chapter also gives the first tions are used in cryptograp the RSA, Diffie-Hellman, examples hy. and El Gamal cryptosystems. This of how number-theoretic assump • Chapters 9 and 10, motivating the public-key encryption schemes (including RSA-based setting and El Gamal en and discussing public-key cryption) . • Chapter 12, describing digital signature schemes. • Sections 13.1 and 13.3, introducing the random oracle model and the RSA-FDH signature scheme. that this core material - possibly and proofs- dm be covered time available with more of all proofs could proceed at a more leisurely and going more slowly when introducing omitting some in a 30-35-hour of the'more undergraduate in We believe depth discussion course. Instructors pace, e.g.; giving details the underlying additional Those wishing topics could group theory and number-theoretic be incorporated as discussed next. in either material, to cover additional graduate course, incorporation of other topics as time permits interests) (*) . These sections faster-paced allow flexible the instructor's starred do not constitute As made evident starred at any point subsequent material), starred "core material" by the course outline chapters to their appearance and sections . Specifically, some of the chapters a longer course or a to on are (and depending and sections background. Alternatively, will find that the book has been structured are not less important in any way, but arguably for an introductory course in cryptography . just given (which does not include any may be skipped- or covered in the book - without affecting 1 Although we consider this to be core material, 1 and so this chapter can be skipped if desired. it is not used in the remainder of the book

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