Abstract
Associated with a class of AFSRs based on a ring R and π ∈ R, there is a security measure, the π-adic complexity of a sequence. To understand the normal behavior of π-adic complexity we can find the average π-adic complexity, averaged over all sequences of a given period. This has been done previously for linear and p-adic complexity. In this paper we show that when π 2 = 2, the average π-adic complexity of period n sequences is n − O(log(n)).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Borevich, Z.I., Shafarevich, I.R.: Number Theory. Academic Press, New York (1966)
Goresky, M., Klapper, A.: Feedback registers based on ramified extensions of the 2-adic numbers. In: Advances in Cryptology — Eurocrypt 1994. LNCS, vol. 718, pp. 215–222. Springer, Heidelberg (1995)
Goresky, M., Klapper, A.: Fibonacci and Galois Mode Implementation of Feedback with Carry Shift Registers. IEEE Trans. Info. Thy. 48, 2826–2836 (2002)
Goresky, M., Klapper, A.: Periodicity and Correlations of d-FCSR Sequences. Designs, Codes, and Crypt. 33, 123–148 (2004)
Klapper, A., Goresky, M.: Feedback Shift Registers, Combiners with Memory, and 2-Adic Span. J. Crypt. 10, 111–147 (1997)
Klapper, A., Xu, J.: Algebraic feedback shift registers. Theor. Comp. Sci. 226, 61–93 (1999)
Klapper, A.: Distributional properties of d-FCSR sequences. J. Complexity 20, 305–317 (2004)
Landau, E.: Ueber die zu einem algebraischen Zahlkörper gehörige Zetafunction und die Ausdehnung der Tschebyschefschen Primzahlentheorie auf das Problem der Vertheilung der Primideale. J. für die reine und angewandte Math. 125, 64–188 (1902)
Lidl, R., Niederreiter, H.: Finite Fields, 2nd edn. Cambridge University Press, Cambridge (1997)
Meidl, W., Niederreiter, H.: Counting functions and expected values for the k-error linear complexity. Finite Fields Appl. 8, 142–154 (2002)
Meidl, W., Niederreiter, H.: On the expected value of linear complexity and the k-error linear complexity of periodic sequences. IEEE Trans. Info. Thy. 48, 2817–2825 (2002)
Meidl, W., Niederreiter, H.: The expected value of joint linear complexity of multisequences. J. Complexity 19, 61–72 (2003)
Niederreiter, H.: A combinatorial approach to probabilistic results on the linear complexity profile of random sequences. J. Crypt. 2, 105–112 (1990)
Xu, J., Klapper, A.: Register synthesis for algebraic feedback shift registers based on non-primes. Designs, Codes, and Crypt. 31, 225–227 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Klapper, A. (2008). Expected π-Adic Security Measures of Sequences. In: Golomb, S.W., Parker, M.G., Pott, A., Winterhof, A. (eds) Sequences and Their Applications - SETA 2008. SETA 2008. Lecture Notes in Computer Science, vol 5203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85912-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-85912-3_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85911-6
Online ISBN: 978-3-540-85912-3
eBook Packages: Computer ScienceComputer Science (R0)