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On cyclotomic generator of order \(r\). (English) Zbl 1078.94511

Summary: The cyclotomic generator of order \(r\) is studied in detail. Their linear complexity, minimal polynomial, and autocorrelation function of its output sequences are calculated. The decimation property of those sequences, the implementation and some applications are also considered.

MSC:

94A60 Cryptography
65C10 Random number generation in numerical analysis
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References:

[1] Boehmer, A. M., Binary pulse compression codes, IEEE Trans. Inform. Theory, IT-13, 156-166 (1967) · Zbl 0152.15409
[2] Chakrabarti, N. B.; Tomlinson, M., Design of sequences with specified autocorrelation and cross correlation, (IEEE Trans. Communications (November 1976)), 1246-1252 · Zbl 0344.94005
[3] Cusick, T. W.; Ding, C.; Renvall, A., Stream Ciphers and Number Theory (1998), North-Holland Mathematical Library, Elsevier/North-Holland: North-Holland Mathematical Library, Elsevier/North-Holland Amsterdam · Zbl 0930.11086
[4] Dickson, L. E., Cyclotomy, higher congruences, and Waring’s problem, Amer. J. Math., 57, 463-474 (1939), (Two references in one volume, but two issues.) · Zbl 0012.29004
[5] Ding, C., Binary cyclotomic generators, (Preneel, B., Fast Software Encryption. Fast Software Encryption, Lecture Notes in Comput. Sci., Vol. 1008 (1995), Springer: Springer Berlin), 29-60 · Zbl 0939.94512
[6] C. Ding, T. Helleseth, W. Shan, On the linear complexity of Legendre sequences, IEEE Trans. Inform. Theory, to appear.; C. Ding, T. Helleseth, W. Shan, On the linear complexity of Legendre sequences, IEEE Trans. Inform. Theory, to appear. · Zbl 0912.94014
[7] Ding, C.; Xiao, G.; Shan, W., The Stability Theory of Stream Ciphers, (Lecture Notes in Comput. Sci., Vol. 561 (1991), Springer: Springer Berlin) · Zbl 0762.94008
[8] Hauge, E. R.; Helleseth, T., DeBruijn sequences, irreducible codes and cyclotomy, Discrete Math., 159, 143-154 (1996) · Zbl 0878.94046
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