Algebraic shift register sequences

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.