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Pure Mathematics 2025
Z4上一类四元广义分圆序列的线性复杂度
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Abstract:
序列的线性复杂度与序列的安全性息息相关。本文利用Galois理论，研究了一类在有限域F4上具有较高线性复杂度的四元序列，得到了其在Galois环Z4上的线性复杂度的确切值。结果显示，这类序列在Galois环Z4上也具有较高的线性复杂度，可以较好地抵抗Reeds-Sloane算法的攻击。
The linear complexity of a sequence is closely related to its cryptographic security. In this paper, we employ Galois theory to investigate a class of quaternary sequence over the finite field F4 with high linear complexity, and determine the exact value of its linear complexity over the Galois ring Z4. The results demonstrate that such sequence maintain relatively high linear complexity in the Galois ring Z4, thereby exhibiting strong resistance against attacks by the Reeds-Sloane algorithm.
| [1] | Zhang, J.W., Zhao, C.A. and Ma, X. (2010) On the Linear Complexity of Generalized Cyclotomic Binary Sequences with Length 2p2. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, E93.A, 302-308. https://doi.org/10.1587/transfun.E93.A.302 |
| [2] | Ding, C.S., Helleseth, T. and Martinnsen, H.M. (2001) New Classes of Binary Sequences with Three-Level Autocorrelation. IEEE Transactions on Information Theory, 47, 428-433. https://doi.org/10.1109/18.904555 |
| [3] | Ding, C.S. and Helleseth, T. (1998) New Generalized Cyclotomy and Its Application. Finite Fields and Their Applications, 4, 140-166. https://doi.org/10.1006/ffta.1998.0207 |
| [4] | Kim, Y.J., Hong, Y.P. and Song, H.Y. (2008) Autocorrelation of Some Quaternary Cyclotomic Sequences of Length 2p. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, E91.A, 3679-3684. https://doi.org/10.1093/ietfec/e91-a.12.3679 |
| [5] | Du, X.N. and Chen, Z.X. (2011) Linear Complexity of Quaternary Sequences Generated Using Generalized Classes Modulo 2p. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, E94.A, 1214-1217. https://doi.org/10.1587/transfun.E94.A.1214 |
| [6] | Ding, C.S., Helleseth, T. and Shan, W. (1998) On the Linear Complexity of Legendre Sequence. IEEE Transactions on Information Theory, 44, 1276-1278. https://doi.org/10.1109/18.669398 |
| [7] | 赵璐, 刘春红, 杜蛟, 等. Z4上两类具有最优自相关四元序列的线性复杂度研究[J]. 电子学报, 2021, 49(4): 631-636. |
| [8] | Chen, Z.X., Du, X.N. and Xiao, G. (2007) Sequences Related to Legendre/Jacobi Sequences. Information Sciences, 177, 4820-2831. https://doi.org/10.1016/j.ins.2007.02.012 |
