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On the stability of m-sequences

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conference contribution
posted on 16.03.2012 by Ana Salagean, Alex J. Burrage, Raphael C.-W. Phan
We study the stability of m-sequences in the sense of determining the number of errors needed for decreasing the period of the sequences, as well as giving lower bounds on the k-error linear complexity of the sequences. For prime periods the results are straightforward so we concentrate on composite periods. We give exact results for the case when the period is reduced by a factor which is a Mersenne number and for the case when it is reduced by a prime p such that the order of 2 modulo p equals p 􀀀 1. The general case is believed to be di cult due to its similarity to a well studied problem in coding theory. We also provide results about the relative frequencies of the di erent cases. We formulate a conjecture regarding the minimum number of errors needed for reducing the period at all. Finally we apply our results to the LFSR components of several well known stream ciphers.

History

School

  • Science

Department

  • Computer Science

Citation

SALAGEAN, A.M., BURRAGE, A.J. and PHAN, R.C.-W., 2011. On the stability of m-sequences. IN: 13th International IMA conference on Cryptography and Coding, Oxford, 12-15th Dec., 7089 pp. 259 - 274

Publisher

Springer

Version

AM (Accepted Manuscript)

Publication date

2011

Notes

The original publication is available at www.springerlink.com

Book series

Lecture Notes in Computer Science;7089

Language

en

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