| Description |
1 online resource |
| Contents |
COMPUTATIONAL NUMBER THEORY AND MODERN CRYPTOGRAPHY; CONTENTS; ABOUT THE AUTHOR; PREFACE; ACKNOWLEDGMENTS; Part I Preliminaries; 1 Introduction; 1.1 What is Number Theory?; 1.2 What is Computation Theory?; 1.3 What is Computational Number Theory?; 1.4 What is Modern Cryptography?; 1.5 Bibliographic Notes and Further Reading; References; 2 Fundamentals; 2.1 Basic Algebraic Structures; 2.2 Divisibility Theory; 2.3 Arithmetic Functions; 2.4 Congruence Theory; 2.5 Primitive Roots; 2.6 Elliptic Curves; 2.7 Bibliographic Notes and Further Reading; References; Part II Computational Number Theory |
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5.6 Bibliographic Notes and Further ReadingReferences; Part III Modern Cryptography; 6 Secret-Key Cryptography; 6.1 Cryptography and Cryptanalysis; 6.2 Classic Secret-Key Cryptography; 6.3 Modern Secret-Key Cryptography; 6.4 Bibliographic Notes and Further Reading; References; 7 Integer Factorization Based Cryptography; 7.1 RSA Cryptography; 7.2 Cryptanalysis of RSA; 7.3 Rabin Cryptography; 7.4 Residuosity Based Cryptography; 7.5 Zero-Knowledge Proof; 7.6 Bibliographic Notes and Further Reading; References; 8 Discrete Logarithm Based Cryptography |
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8.1 Diffie-Hellman-Merkle Key-Exchange Protocol8.2 ElGamal Cryptography; 8.3 Massey-Omura Cryptography; 8.4 DLP-Based Digital Signatures; 8.5 Bibliographic Notes and Further Reading; References; 9 Elliptic Curve Discrete Logarithm Based Cryptography; 9.1 Basic Ideas; 9.2 Elliptic Curve Diffie-Hellman-Merkle Key Exchange Scheme; 9.3 Elliptic Curve Massey-Omura Cryptography; 9.4 Elliptic Curve ElGamal Cryptography; 9.5 Elliptic Curve RSA Cryptosystem; 9.6 Menezes-Vanstone Elliptic Curve Cryptography; 9.7 Elliptic Curve DSA; 9.8 Bibliographic Notes and Further Reading; References |
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Part IV Quantum Resistant Cryptography10 Quantum Computational Number Theory; 10.1 Quantum Algorithms for Order Finding; 10.2 Quantum Algorithms for Integer Factorization; 10.3 Quantum Algorithms for Discrete Logarithms; 10.4 Quantum Algorithms for Elliptic Curve Discrete Logarithms; 10.5 Bibliographic Notes and Further Reading; References; 11 Quantum Resistant Cryptography; 11.1 Coding-Based Cryptography; 11.2 Lattice-Based Cryptography; 11.3 Quantum Cryptography; 11.4 DNA Biological Cryptography; 11.5 Bibliographic Notes and Further Reading; References; INDEX |
| Summary |
"The only book to provide a unified view of the interplay between computationalnumber theory and cryptographyComputational number theory and modern cryptography are two of the most important and fundamental research fields in information security. There are many textbooks on computational number theory or cryptography. However, textbooks integrating both topics are rare. This book not only introduces the basic concepts and results in the two fields, but also introduces many advanced topics. Mathematical ideas are presented first, thereupon treating cryptography as an immediate application of the mathematical ideas. The author covers topics from number theory which are relevant for applications in public-key cryptography. The most popular public-key cryptosystems are based on difficult computational problems, such as factorization of large positive integers and the discrete logarithm problem in finite fields or on elliptic curves over finite fields. The book also covers modern topics, such as coding and lattice based cryptography, which are relevant for so-called post-quantum cryptography. The author goes over the basics in the first six chapters, followed by application to the most common cryptographic algorithms in the following three chapters. Finally areas of current research are touched in the last three chapters. Serious mathematical problems behind these applications will be explained at the level accessible to computer scientists and engineers. Makes deep mathematical problems accessible to computer scientists and engineers Based on classroom tested materials used in the US, UK and China Exercises included in every chapter Instructor resources available on the book's Companion Website "-- Provided by publisher |
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"This book not only introduces the basic concepts and results in the two fields, but also introduces many advanced topics"-- Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record and CIP data provided by publisher |
| Subject |
Data encryption (Computer science)
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Number theory -- Data processing
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COMPUTERS -- Security -- Cryptography.
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Data encryption (Computer science)
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Number theory -- Data processing
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| Form |
Electronic book
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| LC no. |
2012042256 |
| ISBN |
9781118188613 |
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1118188616 |
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9781118188590 |
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1118188594 |
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9781118188620 |
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1118188624 |
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9781118188606 |
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1118188608 |
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