# American Institute of Mathematical Sciences

August  2007, 1(3): 307-319. doi: 10.3934/amc.2007.1.307

## The asymptotic behavior of N-adic complexity

 1 University of Kentucky, 779A F. Paul Anderson Tower, Lexington, KY 40506-0046, United States

Received  December 2006 Revised  July 2007 Published  July 2007

We study the asymptotic behavior of stream cipher security mea- sures associated with classes of sequence generators such as linear feedback shift registers and feedback with carry shift registers. For nonperiodic sequences we consider normalized measures and study the set of accumulation points for a fixed sequence. We see that the set of accumulation points is always a closed subinterval of $[0, 1]$. For binary or ternary FCSRs we see that this interval is of the form $[B, 1-B]$, a result that is an analog of an earlier result by Dai, Jiang, Imamura, and Gong for LFSRs.
Citation: Andrew Klapper. The asymptotic behavior of N-adic complexity. Advances in Mathematics of Communications, 2007, 1 (3) : 307-319. doi: 10.3934/amc.2007.1.307
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