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Computing the linear complexity for sequences with characteristic polynomial f^v

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journal contribution
posted on 06.06.2013, 10:08 by Ana SalageanAna Salagean, Alex J. Burrage, Raphael C.-W. Phan
We present several generalisations of the Games–Chan algorithm. For a fixed monic irreducible polynomial f we consider the sequences s that have as a characteristic polynomial a power of f. We propose an algorithm for computing the linear complexity of s given a full (not necessarily minimal) period of s. We give versions of the algorithm for fields of characteristic 2 and for arbitrary finite characteristic p, the latter generalising an algorithm of Ding et al. We also propose an algorithm which computes the linear complexity given only a finite portion of s (of length greater than or equal to the linear complexity), generalising an algorithm of Meidl. All our algorithms have linear computational complexity. The proposed algorithms can be further generalised to sequences for which it is known a priori that the irreducible factors of the minimal polynomial belong to a given small set of polynomials.

History

School

  • Science

Department

  • Computer Science

Citation

SALAGEAN, A.M., BURRAGE, A.J. and PHAN, R.C.-W., 2013. Computing the linear complexity for sequences with characteristic polynomial f^v. Cryptography and Communications, 5 (2), pp. 163 - 177.

Publisher

© Springer

Version

AM (Accepted Manuscript)

Publication date

2013

Notes

This article was published in the journal, Cryptography and Communications [© Springer] and the definitive version is available at: http://dx.doi.org/10.1007/s12095-013-0080-3

ISSN

1936-2447

eISSN

1936-2455

Language

en