A unified view on sequence complexity measures as isometries
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Multi-continued fraction algorithm and generalized B-M algorithm over F2
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Enumeration results on the joint linear complexity of multisequences
Finite Fields and Their Applications
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In the theory of stream ciphers, an important complexity measure to assess the (pseudo-)randomness of a stream generator is the linear complexity, essentially the complexity to approximate the sequence (seen as formal power series) by rational functions. For multisequences with several, i.e. M, streams in parallel (e.g. for broadband applications), simultaneous approximation is considered. This paper improves on previous results by Niederreiter and Wang, who have given an algorithm to calculate the distribution of linear complexities for multisequences, obtaining formulae for M=2 and 3. Here, we give a closed formula numerically verified for M up to 8 and for M=16, and conjectured to be valid for all M∈ℕ. We model the development of the linear complexity of multisequences by a stochastic infinite state machine, the Battery---Discharge---Model, and we obtain the asymptotic probability for the linear complexity deviationd(n) :=L(n)−⌈n·M/(M+1)⌉ for M sequences in parallel as $${prob}(d(n)=d)=\Theta\left(q^{-|d|(M+1)}\right),\forall M\in \mathbb N, \forall d\in\mathbb Z, \forall q=p^k.$$ The precise formula is given in the text.