Abstract
On the linear complexity Λ(\( \tilde z \)) of a periodically repeated random bit sequence \( \tilde z \), R. Rueppel proved that, for two extreme cases of the period T, the expected linear complexity E[Λ(\( \tilde z \))] is almost equal to T, and suggested that E[Λ(\( \tilde z \))] would be close to T in general [6, pp. 33–52] [7, 8]. In this note we obtain bounds of E[Λ(\( \tilde z \))], as well as bounds of the variance V ar[Λ(\( \tilde z \))], both for the general case of T, and we estimate the probability distribution of Λ(\( \tilde z \)). Our results on E[Λ(\( \tilde z \))] quantify the closeness of E[Λ(\( \tilde z \))] and T, in particular, formally confirm R. Rueppel’s suggestion.
On leave from Graduate School, Academia Sinica, 100039-08, Beijing, China, with this work supported by SERC grant GR/F 72727.
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© 1991 Springer-Verlag Berlin Heidelberg
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Dai, ZD., Yang, JH. (1991). Linear Complexity of Periodically Repeated Random Sequences. In: Davies, D.W. (eds) Advances in Cryptology — EUROCRYPT ’91. EUROCRYPT 1991. Lecture Notes in Computer Science, vol 547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46416-6_15
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DOI: https://doi.org/10.1007/3-540-46416-6_15
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