Algebraic Shift Register Sequences

ISBN-13: 9781107014992 / Angielski / Twarda / 2012 / 514 str.

Mark Goresky

Opis

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.

Recenzje

"This elegant text casts highly practical mathematics as replete with miraculous theoretical novelties. It thus serves specialists while simultaneously envincing a broad appeal. Recommended."
D.V. Feldman, Choice magazine

Spis treści

1. Introduction; Part I. Algebraically Defined Sequences: 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; Part II. Pseudo-Random and Pseudo-Noise Sequences: 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; Part III. Register Synthesis and Security Measures: 15. Register synthesis and LFSR synthesis; 16. FCSR synthesis; 17. AFSR synthesis; 18. Average and asymptotic behavior of security measures; Part IV. Algebraic Background: A. Abstract algebra; B. Fields; C. Finite local rings and Galois rings; D. Algebraic realizations of sequences; Bibliography; Index.