[Foundations.of.Cryptography.Volume.1.Basic.Tools](Oded.Goldreich).pdf

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Foundations of Cryptography Cryptography is concerned with the conceptualization, deﬁnition, and construction of computing systems that address security concerns. The design of cryptographic systems must be based on ﬁrm foundations. This book presents a rigorous and systematic treatment of the foundational issues: deﬁning cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difﬁculty (one-way functions), pseudorandomness, and zero-knowledge proofs. The emphasis is on the clariﬁcation of fundamental concepts and on demonstrat- ing the feasibility of solving cryptographic problems rather than on describing ad hoc approaches. The book is suitable for use in a graduate course on cryptography and as a reference book for experts. The author assumes basic familiarity with the design and analysis of algorithms; some knowledge of complexity theory and probability is also useful. Oded Goldreich is Professor of Computer Science at the Weizmann Institute of Science and incumbent of the Meyer W. Weisgal Professorial Chair. An active researcher, he has written numerous papers on cryptography and is widely considered to be one of the world experts in the area. He is an editor of Journal of Cryptology and SIAM Journal on Computing and the author of Modern Cryptography, Probabilistic Proofs and Pseudorandomness, published in 1999 by Springer-Verlag.

Foundations of Cryptography Basic Tools Oded Goldreich Weizmann Institute of Science

          The Pitt Building, Trumpington Street, Cambridge, United Kingdom    The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcón 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Oded Goldreich 2004 First published in printed format 2001 ISBN 978-0-511-54689-1 OCeISBN ISBN 0-521-79172-3 hardback First published 2001 Reprinted with corrections 2003

To Dana

Contents List of Figures Preface 1 Introduction 1.1. Cryptography: Main Topics 1.1.1. Encryption Schemes 1.1.2. Pseudorandom Generators 1.1.3. Digital Signatures 1.1.4. Fault-Tolerant Protocols and Zero-Knowledge Proofs 1.2. Some Background from Probability Theory 1.3. The Computational Model 1.2.1. Notational Conventions 1.2.2. Three Inequalities 1.3.1. P, NP , and NP -Completeness 1.3.2. Probabilistic Polynomial Time 1.3.3. Non-Uniform Polynomial Time 1.3.4. 1.3.5. Oracle Machines Intractability Assumptions 1.4. Motivation to the Rigorous Treatment 1.4.1. The Need for a Rigorous Treatment 1.4.2. Practical Consequences of the Rigorous Treatment 1.4.3. The Tendency to Be Conservative 1.5. Miscellaneous 1.5.1. Historical Notes 1.5.2. Suggestions for Further Reading 1.5.3. Open Problems 1.5.4. Exercises vii page xii xiii 1 1 2 3 4 6 8 8 9 12 12 13 16 19 20 21 21 23 24 25 25 27 27 28

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