Abstract
We study the asymptotic behavior of stream cipher security measures associated with algebraic feedback shift registers and feedback based on the ring \(\mathbb Z [\sqrt{-2}]\). For non-periodic sequences we consider normalized \(\sqrt{2}\)-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.
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Klapper, A. (2007). The Asymptotic Behavior of π-Adic Complexity with π2 = − 2. In: Golomb, S.W., Gong, G., Helleseth, T., Song, HY. (eds) Sequences, Subsequences, and Consequences. Lecture Notes in Computer Science, vol 4893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77404-4_13
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DOI: https://doi.org/10.1007/978-3-540-77404-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77403-7
Online ISBN: 978-3-540-77404-4
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