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In this paper, the authors present some new results on the selective discrete Fourier spectra attack, introduced first as the recent Ronjom-Helleseth attack and the modifications due to Gong et al. The focal point of this paper is to fill some gaps in the theory of analysis in terms of Discrete Fourier Transform (DFT). They first analyze a special case of the selective DFT method which the previously introduced algorithm does not account for. They then proceed by introducing fast selective DFT attacks, which are closely related to the fast algebraic attacks in the literature.
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