The expectation and variance of the joint linear complexity of random periodic multisequences

Authors:
Fang-Wei Fu;Harald Niederreiter;Ming Su
Affiliations:
Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore 117508, Republic of Singapore;Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore;Department of Mathematics, Nankai University, Tianjin 300071, PR China
Venue:
Journal of Complexity
Year:
2005

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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.