Abstract
Pseudorandom binary sequences derived from the ML-sequences over the integer residue ring Z/(2e) are proposed and studied in [1-10]. This paper is divided into two parts. The first part is on the nondegenerative ML-sequences. In this part the so-called quasi-period of a ML-sequence is introduced, and it is noted that a ML-sequence may degenerate in the sense that it has the quasi-period shorter than its period, and the problem of constructing the nondegenerative ML-sequences is solved by giving a criterion for nondegenerative primitive polynomials. In the second part, based on the constructions [1, 6, 7] of some classes of injective mappings which compress ML-sequences over rings to binary sequences, some new classes of the injective compression mappings are proposed and proved.
This work was supported by Chinese Natural Science Foundation (69773015 and 19771088).
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M.Q. Huang, Analysis and Cryptologic Evaluation of Primitive Sequences over an Integer Residue Ring, Doctoral Dissertation of Graduate School of USTC, Academia Sinica. 1988.
Z.D. Dai, M.Q. Huang, A Criterion for Primitiveness of Polynomials over Z/(2d), Chinese Science Bulletin, Vol.36,No.11,June 1991.pp.892–895.
Z.D. Dai and M.Q. Huang, Linear Complexity and the Minimal Polynomials of Linear Recurring Sequences Over Z/(m), System Science and Mathematical Science, Vol.4,No.1,Feb.1991. pp.51–54.
Z.D. Dai, Beth T., Gollman D, Lower Bounds for the Linear Complexity of Sequences over Residue Rings, Advances in Cryptology-EUROCRYPT’90, Spring-Verlag LNCS 473 (1991), Ed.: I.B. Damgard. pp.189–195.
Z.D. Dai, Binary Sequences Derived from ML-Sequences over Rings I:Periods and Minimal Polynomials, J. Cryptology, Vol 5, No4, 1992, pp.193–207.
M.Q. Huang, Z.D. Dai, Projective Maps of Linear Recurring Sequences with Maximal p-adic Periods, Fibonacci Quart 30(1992), No.2, pp.139–143.
K.C. Zeng, Z.D. Dai and M.Q. Huang, Injectiveness of Mappings from Ring Sequences to Their Sequences of Significant Bits, Symposium on Problems of Cryptology, State Key Laboratory of Information Security, Beijing, China, 1995,pp.132–141.
W.F. Qi, J.J. Zhou, Distribution of 0 and 1 in Highst Level of Primitive Sequences over Z/(2e), Science in China, Series A, 40(6), 1997, 606–611.
W.F. Qi, J.J. Zhou, Distribution of 0 and 1 in Highst Level of Primitive Sequences over Z/(2e) (II), Chinese Science Bulletin, 43(8), 1998, 633–635.
W.F. Qi, Compressing Maps of Primitive Sequences over Z/(2e) and Analysis of Their Derivative Sequences, Doctoral Dissertation of ZhengZhou Information Engineering Institute, 1997.
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Qi, W., Yang, J., Zhou, J. (1998). ML-Sequences over Rings Z/(2e): I. Constructions of Nondegenerative ML-Sequences II. Injectivness of Compression Mappings of New Classes. In: Ohta, K., Pei, D. (eds) Advances in Cryptology — ASIACRYPT’98. ASIACRYPT 1998. Lecture Notes in Computer Science, vol 1514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49649-1_25
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DOI: https://doi.org/10.1007/3-540-49649-1_25
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