Analysis and design of stream ciphers
Analysis and design of stream ciphers
Extension of the Berlekamp-Massey algorithm to N dimensions
Information and Computation
Finite fields
Linear complexity, k-error linear complexity, and the discrete Fourier transform
Journal of Complexity
A Fourier Transform Approach to the Linear Complexity of Nonlinearly Filtered Sequences
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
The expected value of the joint linear complexity of periodic multisequences
Journal of Complexity
IEEE Transactions on Information Theory
Enumeration results on the joint linear complexity of multisequences
Finite Fields and Their Applications
Finite Fields and Their Applications
Counting Functions and Expected Values for the k-Error Linear Complexity
Finite Fields and Their Applications
Error linear complexity measures for multisequences
Journal of Complexity
On the counting function of the lattice profile of periodic sequences
Journal of Complexity
Periodic multisequences with large error linear complexity
Designs, Codes and Cryptography
Generalized Joint Linear Complexity of Linear Recurring Multisequences
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Multisequences with large linear and k-error linear complexity from Hermitian function fields
IEEE Transactions on Information Theory
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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.