The asymptotic behavior of π-adic complexity with π2= -2

Authors:
Andrew Klapper
Affiliations:
Dept. of Computer Science, University of Kentucky, Lexington, KY
Venue:
SSC'07 Proceedings of the 2007 international conference on Sequences, subsequences, and consequences
Year:
2007

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Abstract

We study the asymptotic behavior of stream cipher security measures associated with algebraic feedback shift registers and feedback based on the ring Z[√-2]. For non-periodic sequences we consider normalized √2-adic complexity and study the set of accumulation points for a fixed sequence. The the set of accumulation points is a closed subinterval of the real closed interval [0, 1]. We see that this interval is of the form [B, 1 - B] "most" of the time, and that all such intervals occur for some sequence.