Algebraic Shift Register Sequences

Pseudo-random Sequences Are Essential Ingredients Of Every Modern Digital Communication System Including Cellular Telephones, Gps, Secure Internet Transactions And Satellite Imagery. Each Application Requires Pseudo-random Sequences With Specific Statistical Properties. This Book Describes The Design, Mathematical Analysis And Implementation Of Pseudo-random Sequences, Particularly Those Generated By Shift Registers And Related Architectures Such As Feedback-with-carry Shift Registers. The Earlier Chapters May Be Used As A Textbook In An Advanced Undergraduate Mathematics Course Or A Graduate Electrical Engineering Course; The More Advanced Chapters Provide A Reference Work For Researchers In The Field. Background Material From Algebra, Beginning With Elementary Group Theory, Is Provided In An Appendix. 1. Introduction -- 2. Sequences -- 3. Linear Feedback Shift Registers And Linear Recurrences -- 4. Feedback With Carry Shift Registers And Multiply With Carry Sequences -- 5. Algebraic Feedback Shift Registers -- 6. D-fcsrs -- 7. Galois Mode, Linear Registers, And Related Circuits -- 8. Measures Of Pseudo-randomness -- 9. Shift And Add Sequences -- 10. M-sequences -- 11. Related Sequences And Their Correlations -- 12. Maximal Period Function Field Sequences -- 13. Maximal Period Fcsr Sequences -- 14. Maximal Period D-fcsr Sequences -- 15. Register Synthesis And Lfsr Synthesis -- 16. Fcsr Synthesis -- 17. Afsr Synthesis -- 18. Average And Asymptotic Behavior Of Security Measures -- Appendix A. Abstract Algebra -- Appendix B. Fields -- Appendix C. Finite Local Rings And Galois Rings -- Appendix D. Algebraic Realizations Of Sequences. Mark Goresky, Andrew Klapper. Includes Bibliographical References (p. 481-490) And Index. Pseudo-random sequences are essential ingredients of every modern digital communication system, from cellular telephones to satellite imagery. This book describes the design, mathematical analysis and implementation of pseudo-random sequences. Suitable for graduate students of mathematics or electrical engineering, it also serves as a reference book for researchers in the field. Describes the design, mathematical analysis and implementation of pseudo-random sequences for applications in communications, cryptography and simulations