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Algorithms for Base Point Generation on an Edwards Curve with the Use of Point Divisibility Criteria

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Abstract

New criteria for Edwards curve point divisibility by 2, 4, and other natural numbers are obtained and proved. Using these results, new algorithms are constructed for extracting the root of arbitrary degree in the Edwards curve group and also new algorithms are obtained for generating the base point of such a curve that are proven to have some advantages.

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Correspondence to L. V. Kovalchuk.

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2016, pp. 14–24.

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Kovalchuk, L.V., Bessalov, A.V. & Bespalov, O.Y. Algorithms for Base Point Generation on an Edwards Curve with the Use of Point Divisibility Criteria. Cybern Syst Anal 52, 674–683 (2016). https://doi.org/10.1007/s10559-016-9870-x

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  • DOI: https://doi.org/10.1007/s10559-016-9870-x

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