(Ebook) Algebraic shift register sequences by Mark Goresky; Andrew Klapper ISBN 9781107014992, 1107014999

(Ebook) Algebraic shift register sequences by Mark Goresky; Andrew Klapper ISBN 9781107014992, 1107014999

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