Stream Ciphers and Number Theory

Thomas Cusick has 25 years of experience in cryptography, 60 published papers in that subject and 8 Ph. D. students whose thesis work was in that area. He is currently located at the State University of New York in Buffalo, New York.

Contents Preface to the Revised EditionPreface to the First Edition.1 Introduction.2 Stream Ciphers.3 Primes, Primitive Roots and Sequences.4 Cyclotomy and Cryptographic Functions.5 Special Primes and Sequences.6 Highly Nonlinear Functions.7 Difference Sets and Sequences.8 Binary Cyclotomic Generators.9 Analysis of Cyclotomic Generators of Order 2.10 Nonbinary Cyclotomic Generators.11 Generators Based on Permutations.12 Quadratic Partitions and Cryptography.13 Group Characters and Cryptography.14 P-Adic Numbers, Class Numbers and Sequences.15 Prime Ciphering Algorithms.16 Cryptographic Problems and Philosophies.Appendix A: More About Cyclotomic Numbers.Appendix B: Cyclotomic Formulae of Orders 6, 8 and 10.Appendix C: Finding Practical Primes.Appendix D: List of Research Problems.Appendix E: Exercises.Appendix F: List of Mathematical Symbols.Bibliography.Index.