This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields.
· Unique book on interactions of stream ciphers and number theory.
· Research monograph with many results not available elsewhere.
· A revised edition with the most recent advances in this subject.
· Over thirty research problems for stimulating interactions between the two areas.
· Written by leading researchers in stream ciphers and number theory.
1. Chapter 1: Introduction - p. x 2. Chapter 2: Stream Ciphers - p. 10 3. Chapter 3: Primes, Primitive Roots and Sequences - p. 43 4. Chapter 4: Cyclotomy and Cryptographic Functions - p. 81 5. Chapter 5: Special Primes and Sequences - p. 119 6. Chapter 6: Highly Nonlinear Functions - p. 146 7. Chapter 7: Difference Sets and Sequences - p. 183 8. Chapter 8: Binary Cyclotomic Generators - p. 193 9. Chapter 9: Analysis of Cyclotomic Generators of Order 2 - p. 226 10. Chapter 10: Nonbinary Cyclotomic Generators - p. 250 11. Chapter 11: Generators Based on Permutations - p. 258 12. Chapter 12: Quadratic Partitions and Cryptography - p. 294 13. Chapter 13: Group Characters and Cryptography - p. 316 14. Chapter 14: P-Adic Numbers, Class Numbers and Sequences - p. 336 15. Chapter 15: Prime Ciphering Algorithms - p. 378 16. Chapter 16: Cryptographic Problems and Philosophies - p. 390 17. Apendix A: More About Cyclotomic Numbers - p. 406 18. Apendix B: Cyclotomic Formulae of Orders 6, 8 and 10 - p. 413 19. Apendix C: Finding Practical Primes - p. 421 20. Apendix D: List of Research Problems - p. 424 21. Apendix E: Exercises - p. 427 22. Apendix F: List of Mathematical Symbols - p. 433 23. Bibliography - p. 436 24. Index - p. 471
This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields.
· Unique book on interactions of stream ciphers and number theory.
· Research monograph with many results not available elsewhere.
· A revised edition with the most recent advances in this subject.
· Over thirty research problems for stimulating interactions between the two areas.
· Written by leading researchers in stream ciphers and number theory.
1. Chapter 1: Introduction - p. x 2. Chapter 2: Stream Ciphers - p. 10 3. Chapter 3: Primes, Primitive Roots and Sequences - p. 43 4. Chapter 4: Cyclotomy and Cryptographic Functions - p. 81 5. Chapter 5: Special Primes and Sequences - p. 119 6. Chapter 6: Highly Nonlinear Functions - p. 146 7. Chapter 7: Difference Sets and Sequences - p. 183 8. Chapter 8: Binary Cyclotomic Generators - p. 193 9. Chapter 9: Analysis of Cyclotomic Generators of Order 2 - p. 226 10. Chapter 10: Nonbinary Cyclotomic Generators - p. 250 11. Chapter 11: Generators Based on Permutations - p. 258 12. Chapter 12: Quadratic Partitions and Cryptography - p. 294 13. Chapter 13: Group Characters and Cryptography - p. 316 14. Chapter 14: P-Adic Numbers, Class Numbers and Sequences - p. 336 15. Chapter 15: Prime Ciphering Algorithms - p. 378 16. Chapter 16: Cryptographic Problems and Philosophies - p. 390 17. Apendix A: More About Cyclotomic Numbers - p. 406 18. Apendix B: Cyclotomic Formulae of Orders 6, 8 and 10 - p. 413 19. Apendix C: Finding Practical Primes - p. 421 20. Apendix D: List of Research Problems - p. 424 21. Apendix E: Exercises - p. 427 22. Apendix F: List of Mathematical Symbols - p. 433 23. Bibliography - p. 436 24. Index - p. 471
