Expected Π-Adic Security Measures of Sequences

Authors:
Andrew Klapper
Affiliations:
Department of Computer Science, University of Kentucky, Lexington, USA KY 40506-0046
Venue:
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Year:
2008

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Abstract

Associated with a class of AFSRs based on a ring RandΠ¿ R, there is a security measure, theΠ-adic complexity of a sequence. To understand thenormal behavior of Π-adic complexity we can find theaverage Π-adic complexity, averaged over all sequencesof a given period. This has been done previously for linear andp-adic complexity. In this paper we show that whenΠ2= 2, the average Π-adiccomplexity of period nsequences is nΠO(log(n)).