Abstract
Multiplexed and generalized multiplexed sequences for cryptographic and spread spectrum applications are introduced and their periods determined by using a recent result on the period of nonuniformly decimated sequences. Several published results are thus strenghtened and/or generalized. In particular, the period of the well-known multiplexed sequences is derived without the constraints assumed in the literature. The period of the so-called MEM-BSG sequences is also obtained.
Preview
Unable to display preview. Download preview PDF.
References
R. J. Anderson, ”Solving a class of stream ciphers,” Cryptologia, vol. 14(3), pp. 285–288, 1990.
H. Beker and F. Piper, Cipher Systems: The Protection of Communications. London: Northwood Publications, 1982.
G. R. Blakley and G. B. Purdy, ”A necessary and sufficient condition for fundamental periods of cascade machines to be products of the fundamental periods of their constituent finite state machines,” Information Sciences, vol. 24, pp. 71–91, 1981.
W. G. Chambers and S. M. Jennings, ”Linear equivalence of certain BRM shift-register sequences,” Electron. Lett., vol. 20, pp. 1018–1019, Nov. 1984.
W. G. Chambers, ”Clock-controlled shift registers in binary sequence generators,” IEE Proc. E, vol. 135, pp. 17–24, 1988.
J. Daemen, R. Govaerts, and J. Vandewalle, ”Cryptanalysis of MUX-LFSR based scramblers,” Proc. SPRC '93, Rome, Italy, pp. 55–61, 1993.
J. Dj. Golić and M. V. Živković, ”On the linear complexity of nonuniformly decimated PN-sequences,” IEEE Trans. Inform. Theory, vol. IT-34, pp. 1077–1079, Sep. 1988.
J. Dj. Golić and M. J. Mihaljević, ”Minimal linear equivalent analysis of a variable-memory binary sequence generator,” IEEE Trans. Inform. Theory, vol. IT-36, pp. 190–192, Jan. 1990.
J. Dj. Golić, M. Salmasizadeh, and E. Dawson, ”Autocorrelation weakness of multiplexed sequences,” Proceedings of International Symposium on Information Theory and Its Applications ISITA '94, Sydney, Australia, pp. 983–987, 1994.
J. Dj. Golić, ”A note on nonuniform decimation of periodic sequences,” Cryptography: Policy and Algorithms — Brisbane '95, Lecture Notes in Computer Science, vol. 1029, E. Dawson and J. Golić eds., Springer-Verlag, pp. 125–131, 1996.
S. W. Golomb. Shift Register Sequences. San Francisco: Holden-Day, 1967.
S. M. Jennings, ”A special class of binary sequences,” Ph.D. thesis, University of London, 1980.
S. M. Jennings, ”Multiplexed sequences: some properties of the minimum polynomial,” Proc. Workshop on Cryptography, Burg Feuerstein, 1982, Lecture Notes in Computer Science, vol. 149, T. Beth ed., Springer-Verlag, pp. 189–206, 1983.
S. M. Jennings, ”Autocorrelation function of the multiplexed sequences,” IEE Proc. F, vol. 131, pp. 169–172, April 1984.
R. Lidl and H. Niederreiter, Introduction to finite fields and their applications. Cambridge: Cambridge University Press, 1986.
K. C. Zeng, C. H. Yang, and T. R. N. Rao, ”On the linear consistency test (LCT) in cryptanalysis and its applications,” Advances in Cryptology — CRYPTO '89, Lecture Notes in Computer Science, vol. 435, G. Brassard ed., Springer-Verlag, pp. 164–174, 1990.
N. Zierler, ”Linear recurring sequences,” J. Soc. Indust. Appl. Math., vol. 7, pp. 31–48, 1959.
Specification of the systems of the MAC/packet family. EBU Technical Document 3258-E, Oct. 1986.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Golić, J.D. (1996). On period of multiplexed sequences. In: Pieprzyk, J., Seberry, J. (eds) Information Security and Privacy. ACISP 1996. Lecture Notes in Computer Science, vol 1172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023296
Download citation
DOI: https://doi.org/10.1007/BFb0023296
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61991-8
Online ISBN: 978-3-540-49583-3
eBook Packages: Springer Book Archive