Abstract
In this paper, the distribution of the shortest linear recurring sequence over the ring is studied, it is found that the amount of sequences whose length is n can be calculated and the recurring distribution regulation of the shortest linear recurring sequences is proposed. The possibility of finding the non-recurring distribution of the shortest linear recurring length of some special sequences over the ring is also discussed which can be used in the further research work.
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.
Similar content being viewed by others
References
Meidl, W.: On the Stability of 2n-Periodic Binary Sequences. IEEE Trans. Inform. Theory IT-51, 1151–1155 (2005)
Ye, D.F., Dai, Z.D.: Periodic Sequence Linear Order of Complexity Under Two Marks Replacing (in Chinese). In: Fourth Session of Chinese Cryptology Academic Conference Collection (1996)
Feng, G.L., Tzeng, K.A.: Generalization of The Berlekamp-Massey Algorithm for Multi-Sequence Shift-Register Synthesis with Applications to Decoding Cyclic Codes. IEEE Trans Inform Theory 37(5), 1274–1287 (1991)
Feng, G.L., Tzeng, K.A.: Generalized Euclidean Algorithm for Multi-Sequence Shift-Register Synthesis. IEEE Trans Inform Theory 35(3), 584–594 (1989)
Zhou, Y.J., Zhou, J.J.: The Relationship Between Two Kinds of Sequences Syntheses Algorithm Over Ring Z/(m) (in Chinese). In: Fifth Session of Chinese Cryptology Academic Conference Collection (1998)
Zhou, J.J., Qi, W.F., Zhou, Y.J.: Gröbner Base Extension and Multi-SequencesComprehensive Algorithm Over Z/(m) (in Chinese). Science in China (1995)
Yin, Q., Luo, Y.L.: The Distributing Regulation of The Shortest Lineer Recurring Length Over The Finite Field (in Chinese). Chinese Journal of Computers 28, 1939–1942 (2005)
Yin, Q., Luo, Y.L., Guo, P.: Special Distribution of The Shortest Linear Recurring Sequences in Z/(p) Field. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS (LNAI), vol. 3802, pp. 43–48. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yin, Q., Yuan, ZY., Guo, P. (2007). Further Studies on the Distribution of the Shortest Linear Recurring Sequences for the Stream Cipher over the Ring. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2007. Communications in Computer and Information Science, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74282-1_76
Download citation
DOI: https://doi.org/10.1007/978-3-540-74282-1_76
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74281-4
Online ISBN: 978-3-540-74282-1
eBook Packages: Computer ScienceComputer Science (R0)