Computational Number Theory and Modern Cryptography 1st Edition by Song Yan ISBN 1118188586 978-1118188583

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Product details: 

ISBN 10:  1118188586

ISBN 13:  978-1118188583

Author: Song Y. Yan
The only book to provide a unified view of the interplay between computationalnumber 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 book’s 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. 

Table of contents: 

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

3. Primality Testing
3.1 Basic Tests
3.2 Miller–Rabin Test
3.3 Elliptic Curve Tests
3.4 AKS Test
3.5 Bibliographic Notes and Further Reading
References

4. Integer Factorization
4.1 Basic Concepts
4.2 Trial Divisions Factoring
4.3 ρ and p − 1 Methods
4.4 Elliptic Curve Method
4.5 Continued Fraction Method
4.6 Quadratic Sieve
4.7 Number Field Sieve
4.8 Bibliographic Notes and Further Reading
References

5. Discrete Logarithms
5.1 Basic Concepts
5.2 Baby-Step Giant-Step Method
5.3 Pohlig–Hellman Method
5.4 Index Calculus
5.5 Elliptic Curve Discrete Logarithms
5.6 Bibliographic Notes and Further Reading
References

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
8.1 Diffie–Hellman–Merkle Key-Exchange Protocol
8.2 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

Part IV. Quantum Resistant Cryptography

10. 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

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Tags: Song Yan, Computational Number, Theory and Modern