Abstract
In this paper we show that the output sequences of the generalized self-shrinking generator are particular solutions of a binary homogeneous linear difference equation. In fact, all these sequences are just linear combinations of primary sequences weighted by binary coefficients. We show that in addition to the output sequences of the generalized self-shrinking generator, the complete class of solutions of the corresponding binary homogeneous linear difference equation also includes other balanced sequences that are very suitable for cryptographic applications, as they have the same period and even greater linear complexity than the generalized self-shrinking sequences. Cryptographic parameters of all the above mentioned sequences can be analyzed in terms of linear equation solutions.
This work was supported in part by CDTI (Spain) and the companies INDRA, Unión Fenosa, Tecnobit, Visual Tool, Brainstorm, SAC and Technosafe under Project Cenit-HESPERIA; by Ministry of Science and Innovation and European FEDER Fund under Project TIN2008-02236/TSI; by The University of Newcastle, CEF G0189479.
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Fuster-Sabater, A., Delgado-Mohatar, O., Brankovic, L. (2010). On the Linearity of Cryptographic Sequence Generators. In: Taniar, D., Gervasi, O., Murgante, B., Pardede, E., Apduhan, B.O. (eds) Computational Science and Its Applications – ICCSA 2010. ICCSA 2010. Lecture Notes in Computer Science, vol 6017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12165-4_46
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DOI: https://doi.org/10.1007/978-3-642-12165-4_46
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