Abstract
Spectra attacks proposed recently are more data efficient than algebraic attacks against stream cipher. They are also time-and-space efficient. A measurement of the security of a stream cipher against spectra attacks is the spectral immunity, the lowest linear complexity of annihilators of the key stream. Under the restriction to binary annihilators, this paper first studies the tight upper bound on spectral immunities of periodic sequences, and sequences whose spectral immunities achieve this upper bound are corresponding to Boolean functions achieving optimal algebraic immunities. Secondly, the asymptotic behavior on spectral immunities of sequences corresponding to \(n\)-variable balanced Boolean functions is discussed, which shows that almost all such sequences have high spectral immunities.
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Acknowledgments
This paper was supported by NSF of China under Grant Nos. 61272042 and 61309017. The authors are grateful to the reviewers for their helpful comments and suggestions.
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Communicated by T. Helleseth.
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Wu, D., Qi, W. & Chen, H. On the spectral immunity of periodic sequences restricted to binary annihilators. Des. Codes Cryptogr. 78, 533–545 (2016). https://doi.org/10.1007/s10623-014-0019-5
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DOI: https://doi.org/10.1007/s10623-014-0019-5