Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jco.2005.07.001
Title: The expectation and variance of the joint linear complexity of random periodic multisequences
Authors: Fu, F.-W. 
Niederreiter, H. 
Su, M.
Keywords: Expectation
Generalized discrete Fourier transform
Joint linear complexity
Multisequences
Stream ciphers
Variance
Issue Date: Dec-2005
Citation: Fu, F.-W., Niederreiter, H., Su, M. (2005-12). The expectation and variance of the joint linear complexity of random periodic multisequences. Journal of Complexity 21 (6) : 804-822. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jco.2005.07.001
Abstract: The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. By using the generalized discrete Fourier transform for multisequences, Meidl and Niederreiter determined the expectation of the joint linear complexity of random N-periodic multisequences explicitly. In this paper, we study the expectation and variance of the joint linear complexity of random periodic multisequences. Several new lower bounds on the expectation of the joint linear complexity of random periodic multisequences are given. These new lower bounds improve on the previously known lower bounds on the expectation of the joint linear complexity of random periodic multisequences. By further developing the method of Meidl and Niederreiter, we derive a general formula and a general upper bound for the variance of the joint linear complexity of random N-periodic multisequences. These results generalize the formula and upper bound of Dai and Yang for the variance of the linear complexity of random periodic sequences. Moreover, we determine the variance of the joint linear complexity of random periodic multisequences with certain periods. © 2005 Elsevier Inc. All rights reserved.
Source Title: Journal of Complexity
URI: http://scholarbank.nus.edu.sg/handle/10635/111494
ISSN: 0885064X
DOI: 10.1016/j.jco.2005.07.001
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