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

Authors:
Alexandra Alecu;Ana Sǎlǎgean
Affiliations:
Department of Computer Science, Loughborough University, Loughborough, UK;Department of Computer Science, Loughborough University, Loughborough, UK
Venue:
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Year:
2007

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Abstract

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.