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.

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.