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E-raamat: Computational Number Theory and Modern Cryptography

(Massachusetts Institute of Technology, USA)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 07-Nov-2012
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118188590
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 07-Nov-2012
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118188590
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The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. 





Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the books Companion Website 

Computational Number Theory and Modern Cryptography is ideal for  graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference. 
About the Author ix
Preface xi
Acknowledgments xiii
Part I Preliminaries
1 Introduction
3(32)
1.1 What is Number Theory?
3(6)
1.2 What is Computation Theory?
9(6)
1.3 What is Computational Number Theory?
15(14)
1.4 What is Modern Cryptography?
29(3)
1.5 Bibliographic Notes and Further Reading
32(3)
References
32(3)
2 Fundamentals
35(124)
2.1 Basic Algebraic Structures
35(11)
2.2 Divisibility Theory
46(29)
2.3 Arithmetic Functions
75(14)
2.4 Congruence Theory
89(42)
2.5 Primitive Roots
131(10)
2.6 Elliptic Curves
141(13)
2.7 Bibliographic Notes and Further Reading
154(5)
References
155(4)
Part II Computational Number Theory
3 Primality Testing
159(32)
3.1 Basic Tests
159(9)
3.2 Miller-Rabin Test
168(5)
3.3 Elliptic Curve Tests
173(5)
3.4 AKS Test
178(9)
3.5 Bibliographic Notes and Further Reading
187(4)
References
188(3)
4 Integer Factorization
191(44)
4.1 Basic Concepts
191(3)
4.2 Trial Divisions Factoring
194(4)
4.3 ρ and p - 1 Methods
198(7)
4.4 Elliptic Curve Method
205(4)
4.5 Continued Fraction Method
209(5)
4.6 Quadratic Sieve
214(5)
4.7 Number Field Sieve
219(12)
4.8 Bibliographic Notes and Further Reading
231(4)
References
232(3)
5 Discrete Logarithms
235(30)
5.1 Basic Concepts
235(2)
5.2 Baby-Step Giant-Step Method
237(3)
5.3 Pohlig-Hellman Method
240(6)
5.4 Index Calculus
246(5)
5.5 Elliptic Curve Discrete Logarithms
251(9)
5.6 Bibliographic Notes and Further Reading
260(5)
References
261(4)
Part III Modern Cryptography
6 Secret-Key Cryptography
265(28)
6.1 Cryptography and Cryptanalysis
265(12)
6.2 Classic Secret-Key Cryptography
277(8)
6.3 Modern Secret-Key Cryptography
285(6)
6.4 Bibliographic Notes and Further Reading
291(2)
References
291(2)
7 Integer Factorization Based Cryptography
293(44)
7.1 RSA Cryptography
293(9)
7.2 Cryptanalysis of RSA
302(17)
7.3 Rabin Cryptography
319(7)
7.4 Residuosity Based Cryptography
326(5)
7.5 Zero-Knowledge Proof
331(4)
7.6 Bibliographic Notes and Further Reading
335(2)
References
335(2)
8 Discrete Logarithm Based Cryptography
337(16)
8.1 Diffie-Hellman-Merkle Key-Exchange Protocol
337(5)
8.2 ElGamal Cryptography
342(2)
8.3 Massey-Omura Cryptography
344(4)
8.4 DLP-Based Digital Signatures
348(3)
8.5 Bibliographic Notes and Further Reading
351(2)
References
351(2)
9 Elliptic Curve Discrete Logarithm Based Cryptography
353(26)
9.1 Basic Ideas
353(3)
9.2 Elliptic Curve Diffie-Hellman-Merkle Key Exchange Scheme
356(4)
9.3 Elliptic Curve Massey-Omura Cryptography
360(5)
9.4 Elliptic Curve ElGamal Cryptography
365(5)
9.5 Elliptic Curve RSA Cryptosystem
370(1)
9.6 Menezes-Vanstone Elliptic Curve Cryptography
371(2)
9.7 Elliptic Curve DSA
373(1)
9.8 Bibliographic Notes and Further Reading
374(5)
References
375(4)
Part IV Quantum Resistant Cryptography
10 Quantum Computational Number Theory
379(22)
10.1 Quantum Algorithms for Order Finding
379(6)
10.2 Quantum Algorithms for Integer Factorization
385(5)
10.3 Quantum Algorithms for Discrete Logarithms
390(3)
10.4 Quantum Algorithms for Elliptic Curve Discrete Logarithms
393(4)
10.5 Bibliographic Notes and Further Reading
397(4)
References
397(4)
11 Quantum Resistant Cryptography
401(12)
11.1 Coding-Based Cryptography
401(2)
11.2 Lattice-Based Cryptography
403(1)
11.3 Quantum Cryptography
404(2)
11.4 DNA Biological Cryptography
406(3)
11.5 Bibliographic Notes and Further Reading
409(4)
References
410(3)
Index 413
Song Y. Yan, North China University of Technology, P.R. China and Harvard University, USA