Comparative analysis of cryptoprimitives on canonical elliptic curves and Edwards curves

Authors

  • В.А. Кулібаба

DOI:

https://doi.org/10.30837/rt.2019.3.198.15

Keywords:

elliptic curves, Edwards curves, cryptanalysis, digital signature

Abstract

The article provides a comparative analysis of the basic transformations on canonical elliptic curves and Edwards curves. Comparisons of the performance of group operations in groups of points of elliptic curves and Edwards curves are given. The possibility of using the Pollard algorithm for cryptanalysis of Edwards curves, as well as the acceleration of the sequence generation for the ro-Polard algorithm for Edwards curves is shown, which allows to accelerate the execution of cryptanalysis. The paper proposes an assessment of the resistance of Edwards curves against attacks of the type “full disclosure” using the discrete logarithm in the Edwards curve point group.

References

Bernstein D.J., Lange T. Faster Addition and Doubling on Elliptic Curves // Advancesin Cryptology—ASIACRYPT’2007 (Proc. 13th Int. Conf. On the Theory and Applicationof Cryptology and Information Security. Kuching, Malaysia. December 2–6, 2007). Lect. Notes Comp. Sci. V. 4833. Berlin : Springer, 2007. PP. 29–50.

Edwards H.M. A normal form for elliptic curves // Bulletin of the American Mathematical Society, Volume 44, Number 3, July 2007, PP. 393-422

Hisil Huseyin, Koon-Ho Wong Kenneth, Carter Gary, Dawson Ed. Twisted Edwards Curves Revisited // ASIACRYPT. 5350. New York: Springer, 2008. PP. 326-343

Балагура Д.С. Методы оценки сложности криптоанализа для криптографических приложений в группе точек эллиптической кривой, учитывающие вероятность коллизий / Д.С. Балагура, Ю.И. Горбенко // Радиотехника. 2005. Вып. 142. С. 205 – 214.

Бессалов А.В. Эллиптические кривые в форме Эдвардса и криптография: монография. Киев : ІВЦ «Видавництво «Політехника»», 2017. 272с.

Горбенко І. Д. Прикладна криптологія : підручник / І. Д. Горбенко, Ю. І. Горбенко ; вид. 2-ге. Харків : Форт, 2013. 878 с.

Горбенко Ю.І., Єсіна М.В., Кулібаба В.А. Сутність та умови здійснення атаки на зв’язаних ключах відносно ектронних підписів IBS-1 та IBS-2 ДСТУ ISO/IEC 14888-3 // Системи обробки інформації. 2016. № 7. С. 113-118. (http://www.hups.mil.gov.ua/periodic-app/article/16934)

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How to Cite

Кулібаба, В. (2019). Comparative analysis of cryptoprimitives on canonical elliptic curves and Edwards curves. Radiotekhnika, 3(198), 203–208. https://doi.org/10.30837/rt.2019.3.198.15

Issue

No. 198 (2019): Radiotekhnika

Section

Articles

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