### The Asymptotic Behavior of N-Adic Complexity

Appeared in: Workshop on Codes and Cryptography (WCC), Bergen 2005.
Authors:

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science,
University of Kentucky, Lexington, KY, 40506-0046, klapper at cs.uky.edu.
www.cs.uky.edu/~klapper/andy.html
**Abstract**
We study the asymptotic behavior of stream cipher security measures
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 the set of
accumulation points is always a closed subinterval of [0,1]. For 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. We also
see that all such intervals occur for infinitely many sequences.

**Index Terms --**
Pseudorandom sequence, stream cipher, feedback with carry
shift register, asymptotic behavior.