Abstract
Recently, a new class of feedback shift registers (FCSRs) was introduced, based on algebra over the 2-adic numbers. The sequences generated by these registers have many algebraic properties similar to those generated by linear feedback shift registers. However, it appears to be significantly more difficult to find maximal period FCSR sequences. In this paper we exhibit a technique for easily finding FCSRs that generate nearly maximal period sequences. We further show that these sequence have excellent distributional properties. They are balanced, and nearly have the deBruijn property for distributions of subsequences.
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References
E. Bombieri, personal communication.
D. Gollman, Pseudo Random Properties of Cascade Connections of Clock Controlled Shift Registers, Advances in Cryptology, Proceedings of Eurocrypt 84, ed. T. Beth, N. Cot, and I. Ingemarsson, Springer-Verlag LNCS vol. 209, 1985, pp. 93–98.
S. Golomb, Shift Register Sequences. Aegean Park Press, Laguna Hills CA, 1982.
G. Hardy and E. Wright, An Introduction to the Theory of Numbers. Oxford University Press, Oxford UK, 1979.
C. Hooley, On Artin’s conjecture. J. Reine Angew. Math. vol. 22, 1967 pp. 209–220.
E. L. Key, “An Analysis of the structure and complexity of nonlinear binary sequence generators,” IEEE Trans. Info. Theory, vol. IT-22 no. 6, pp. 732–736, Nov. 1976.
A. Klapper, Feedback with Carry Shift Registers over Finite Fields, Proceedings of Leuven Algorithms Workshop, Leuven, Belgium, December, 1994.
A. Klapper and M. Goresky, Feedback Shift Registers, Combiners with Memory, and Arithmetic Codes, Univ. of Kentucky, Dept. of Comp. Sci. Tech. Rep. No. 239-93.
A. Klapper and M. Goresky, 2-Adic Shift Registers, Fast Software Encryption: Proceedings of 1993 Cambridge Security Workshop, ed. R. Anderson, Springer-Verlag LNCS, vol. 809, 1994, pp. 174–178.
A. Klapper, and M. Goresky, Feedback Registers Based on Ramified Extensions of the 2-Adic Numbers, to appear, Proceedings, Eurocrypt 1994, Perugia, Italy
N. Koblitz, p-Adic Numbers, p-Adic Analysis, and Zeta Functions. Graduate Texts in Mathematics Vol. 58, Springer Verlag, N.Y. 1984.
D. Mandelbaum, Arithmetic codes with large distance. IEEE Trans. Info. Theory, vol. IT-13, 1967 pp. 237–242.
J. Pollard The Fast Fourier Transform in a Finite Field, Math. Comp., vol. 25, 1971, pp. 365–374.
R. Rueppel, Analysis and Design of Stream Ciphers. Springer Verlag, New York, 1986.
A. Schönhage and V. Strassen, Schnelle Multiplikation Grosser Zahlen, Computing, vol. 7, 1971, pp. 281–292.
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© 1995 Springer-Verlag Berlin Heidelberg
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Klapper, A., Goresky, M. (1995). Large Period Nearly deBruijn FCSR Sequences. In: Guillou, L.C., Quisquater, JJ. (eds) Advances in Cryptology — EUROCRYPT ’95. EUROCRYPT 1995. Lecture Notes in Computer Science, vol 921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49264-X_21
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DOI: https://doi.org/10.1007/3-540-49264-X_21
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