Computational Number Theory and Modern Cryptography by Yan, Song Y. -- Read -- Imperial Library of Trantor

Index

Cover Series Title Page Copyright About the Author Preface Acknowledgments Part 1: Preliminaries

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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