Randomness and Register Synthesis of Algebraic Feedback Shift Registers Based on Function Fields

Appeared in: SETA '04, Seoul, Korea, 2004.

Andrew Klapper, 307 Marksbury Building, Dept. of Computer Science, University of Kentucky, Lexington, KY, 40506-00633, klapper at cs.uky.edu. www.cs.uky.edu/~klapper/andy.html

Abstract We study algebraic feedback shift registers (AFSRs) based on quotients of polynomial rings in several variables over a finite field. These registers are natural generalizations of linear feedback shift registers. We describe conditions under which such AFSRs produce sequences with various ideal randomness properties. We also show that there is an efficient algorithm which, given a prefix of a sequence, synthesizes a minimal such AFSR that outputs the sequence.