Based on the theory of generalized cyclotomic, a new class of binaey generalized cyclotomic sequences of order four with period 2p2 is established. Using the theory of polynomial factor over finite field, the linear complexity and minimal polynomial of the new sequences are researched. Results show that the sequences has larger linear complexity and can resist the attack by B-M algorithm. It is a good sequence from the viewpoint of cryptography.
杜小妮,王国辉,魏万银. 周期为2p2 的四阶二元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2015, 37(10): 2490-2494.
Du Xiao-ni, Wang Guo-hui, Wei Wan-yin. Linear Complexity of Binary Generalized Cyclotomic Sequences of Order Four with Period 2p2. JEIT, 2015, 37(10): 2490-2494.
Golomb S W and Gong G. Signal Design for Good Correlation: For Wireless Communication, Cryptography and Radar Applications[M]. Cambridge: UK, Cambridge University Press, 2005: 174-175.
[2]
Massey J L. Shift register synthesis and BCH decoding[J]. IEEE Transactions on Information Theory, 1969, 15(1): 122-127.
Du Xiao-ni, Yan Tong-jiang, and Shi Yong-fang. Linear complexity of generalized cyclotomic sequences with period pm[J]. Journal of Electronics & Information Technology, 2010, 32(4): 821-824.
[4]
Du Xiao-ni and Chen Zhi-xun. Trace representation of binary generalized cyclotomic squences with length pm[J]. IEICE Transactions on Fundamentals of Electronices Communi- cations and Computer Sciences, 2011, E94-A(2): 761-765.
Li Rui-fang and Ke Pin-hui. The linear complexity of a new class of generalized cyclotomic sequences with period 2pq[J]. Journal of Electronics & Information Technology, 2014, 36(3): 650-654.
[6]
Chang Zu-ling and Li Dan-dan. On the linear complexity of the quaternary cyclotomic sequences with the period 2pq[J]. IEICE Transactions on Fundamental of Electronics Communications and Computer Sciences, 2014, E97-A(2): 679-684.
[7]
Li Xiao-ping, Ma Wen-ping, and Yan Tong-jiang. Linear complexity of binary Whiteman generalized cyclotomic sequences of order 4[J]. IEICE Transactions on Fundamentals of Electronices Communications and Computer Sciences, 2013, 96A(1): 363-366.
[8]
Zhao Chun-e and Ma Wen-ping. Autocorrelation values of generalized cyclotomic sequences of order six[J]. IEICE Transactions on Fundamentals of Electronices Communications and Computer Sciences, 2013, E96-A(10): 2045-2048.
[9]
Edemskiy V and Lvanov A. Linear complexity of quaternary sciences of length pq with low autocorrelation[J]. Journal of Computational and Applied Mathematics, 2014, 259B: 555-560.
[10]
Ke Pin-hui, Lin Chang-lu, and Zhang Sheng-yuan. Linear complexity of quaternary sciences with odd period and low autocorrelation[J]. The Journal of China Universities of Posts and Telecommunications, 2014, 21(5): 89-93.
[11]
Li Dan-dan and Wen Qiao-yan. Linear complexity of generalized cyclotomic quaternary sequences with period pq[J]. IEICE Transactions on Fundamentals of Electronices Communications and Computer Sciences, 2014, E97-A(5): 1153-1158.
[12]
Yan Tong-jiang and Li Xiao-ping. Some note on the generalized cyclotomic sequence of length 2pm and pm[J]. IEICE Transactions on Fundamentals of Electronices Communications and Computer Sciences, 2013, E96-A(10): 997-1000.
[13]
Zhang Jing-wei, Zhao Chang-an, and Ma Xiao. Linear complexity of generalized cyclotomic binary sequences with the period 2pm[J]. Applicable Algebra in Engineering, Communication and Computing, 2010, 21(2): 93-108.
[14]
Zhang Jing-wei, Zhao Chang-an, and Ma Xiao. On the linear complexity of generalized cyclotomic binary sequences with length 2p2[J]. IEICE Transactions on Fundamentals of Electronices Communications and Computer Sciences, 2010, E93-A(1): 302-308.
[15]
Ke Pin-hui and Zhang J. On the linear complexity and autocorrelation of generalized cyclotomic binary sequences with length 2pm[J]. Designs, Codes and Cryptograpy, 2013, 67(3): 325-339.
[16]
Cusick T and Ding Cun-sheng. Stream Ciphers and Number Theory[M]. Elsevier Science, 2004: 198-212.
[17]
Yan Tong-jiang, Huang Bing-jia, and Xiao Guo-zhen. Cryptographic properties of some binary generalized cyclotomic sequences with length p2[J]. Information Science, 2008, 178(4): 1078-1086.
[18]
Ding Cun-sheng and Hellseth. T. New generalized cyclotomy and its applications[J]. Finite Field Their Applications, 1998, 4(2): 140-166.
