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.
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© 2007 Springer-Verlag Berlin Heidelberg
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Alecu, A., Sălăgean, A. (2007). Modified Berlekamp-Massey Algorithm for Approximating the k-Error Linear Complexity of Binary Sequences. In: Galbraith, S.D. (eds) Cryptography and Coding. Cryptography and Coding 2007. Lecture Notes in Computer Science, vol 4887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77272-9_14
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DOI: https://doi.org/10.1007/978-3-540-77272-9_14
Publisher Name: Springer, Berlin, Heidelberg
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