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# Modified Berlekamp-Massey algorithm for approximating the k-error linear complexity of binary sequences

Some cryptographical applications use pseudorandom sequences
and require that the sequences are secure in the sense that they cannot be recovered by only knowing a small amount of consecutive terms. Such sequences should therefore have a large linear complexity and also a large k-error linear
complexity. Efficient algorithms for computing the k-error linear complexity of a sequence only exist for sequences of period equal to a power of the characteristic of the field. It is therefore useful to find a general and efficient algorithm to compute a good approximation of the k-error linear complexity. We show that the Berlekamp-Massey Algorithm, which computes the linear complexity of a sequence, can be adapted to approximate the k-error linear complexity profile
for a general sequence over a finite field. While the complexity of this algorithm is still exponential, it is considerably more efficient than the exhaustive search.

## History

## School

- Science

## Department

- Computer Science

## Citation

ALECU, A. and SALAGEAN, A.M., 2007. Modified Berlekamp-Massey algorithm for approximating the k-error linear complexity of binary sequences. IN: S. Galbraith (ed.). Proceedings of the 11-th IMA International conference on Cryptography and coding, Cirencester, UK, December. LNCS 4887. Heidelberg : Springer Verlag, pp. 220-232## Publisher

© Springer Verlag## Publication date

2007## Notes

This conference paper is also available from: http://www.springerlink.com/content/105633/## ISBN

9783540772712## ISSN

0302-9743;1611-3349## Book series

Lecture notes in computer science## Language

- en