Abstract
In this paper, we study sequences generated by arbitrary feedback registers (not necessarily feedback shift registers) with arbitrary feedforward functions. We generalize the definition of linear complexity of a sequence to the notions of strong and weak linear complexity of feedback registers. A technique for finding upper bounds for the strong linear complexities of such registers is developed. This technique is applied to several classes of registers. We prove that a feedback shift register whose feedback function is of the form x 1 + h(x 2, ..., xn) can generate long periodic sequences with high linear complexites only if its linear and quadratic terms have certain forms.
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© 1990 Springer-Verlag Berlin Heidelberg
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Chan, A.H., Goresky, M., Klapper, A. (1990). On the Linear Complexity of Feedback Registers. In: Quisquater, JJ., Vandewalle, J. (eds) Advances in Cryptology — EUROCRYPT ’89. EUROCRYPT 1989. Lecture Notes in Computer Science, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46885-4_54
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DOI: https://doi.org/10.1007/3-540-46885-4_54
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