Abstract
Cryptographically strong sequences should have long periods, large linear complexity, low correlation, and balance properties. In this paper, we determine the autocorrelation of the q-ary prime n-square sequences with length p n, where p is an odd prime, n is a positive integer and q is a divisor of p − 1. When q is a prime, we also determine the linear complexity of the prime n-square sequences over the prime field F q . It is shown that these sequences have good linear complexity and balance properties, but don’t have desirable autocorrelation properties.
This work was supported by the National Science Foundation of China (Grant No. 60872015 and 60772086).
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References
Burton, D.M.: Elementary Number Theory, 4th edn. McGraw-Hill International Editions, New York (1998)
Ding, C.: Linear Complexity of Generalized Cyclotomic Binary Sequences of Order 2. Finite Fields and Their Applications 3, 159–174 (1997)
Ding, C., Helleseth, T., Shan, W.: On the Linear Complexity of Legendre Sequences. IEEE Trans. Inform. Theory 44, 1276–1278 (1998)
Ding, C., Helleseth, T.: New Generalized Cyclotomy and its Applications. Finite Fields and their Applications 4, 140–166 (1998)
Ding, C.: Linear Complexity of Some Generalized Cyclotomic Sequences. International Journal on Algebra and Computation 8, 431–442 (1998)
Bai, E., Liu, X., Xiao, G.: Linear Complexity of New Generalized Cyclotomic Sequences of Order Two of Length pq. IEEE Trans. Inform. Theory 51, 1849–1853 (2005)
Yan, T., Sun, R., Xiao, G.: Autocorrelation and Linear Complexity of the New Generalized Cyclotomic Sequences. IEICE Trans. Fundamentals E90-A, 857–864 (2007)
Yan, T., Hong, L., Xiao, G.: The Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Four. Information Sciences 178, 807–815 (2008)
Kim, Y.J., Jin, S.Y., Song, H.Y.: Linear Complexity and Autocorrelation of Prime Cube Sequences. In: Boztaş, S., Lu, H.-F(F.) (eds.) AAECC 2007. LNCS, vol. 4851, pp. 188–197. Springer, Heidelberg (2007)
Kim, Y.J., Song, H.Y.: Linear Complexity of Prime n-Square Sequences. In: IEEE International Symposium on Information Theory, Toronto, Canada, pp. 2405–2408 (2008)
Meidl, W.: Remarks on a Cyclotomic Sequence. Designs, Codes, and Cryptography 51, 33–43 (2009)
Sidelnikov, V.M.: Some k-Valued Pseudo-random Sequences and Nearly Equidistance Codes. Problems of Information Transmission 5, 12–16 (1969)
Storer, T.: Cyclotomy and Difference Sets. Markham Publishing Co., Chicago (1967)
Whiteman, A.L.: A Family of Difference Sets. Illinois J. Math. 6, 107–121 (1962)
Lidl, R., Niederreiter, H.: Finite Fields. In: Encyclopedia of Mathematics and its Applications. Addison-Wesley, Reading (1983)
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Liu, F., Peng, D., Tang, X., Niu, X. (2010). On the Autocorrelation and the Linear Complexity of q-Ary Prime n-Square Sequences. In: Carlet, C., Pott, A. (eds) Sequences and Their Applications – SETA 2010. SETA 2010. Lecture Notes in Computer Science, vol 6338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15874-2_11
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DOI: https://doi.org/10.1007/978-3-642-15874-2_11
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