Randomization of CSIDH algorithm on quadratic and twisted Edwards curves

Бессалов, Анатолій Володимирович and Ковальчук, Людмила Васильївна and Абрамов, Сергій Вадимович (2022) Randomization of CSIDH algorithm on quadratic and twisted Edwards curves Кібербезпека: освіта, наука, техніка, 1 (17). pp. 128-144. ISSN 2663-4023

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Abstract

The properties of quadratic and twisted supersingular Edwards curves that form quadratic twist pairs with order over a prime field are considered. A modification of the CSIDH algorithm based on the isogenies of these curves is presented. The parameters of these two classes of supersingu-lar Edwards curves for are calculated and tabulated. An example of the implementation of the CSIDH algorithm as a non-interactive secret sharing scheme based on the secret and public keys of Alice and Bob is given. A new randomized CSIDH algorithm with random equiprobable selection of a curve from two classes at each step of the isogeny chain is proposed. This algorithm is proposed as an alternative to "constant time CSIDH". An estimate of the probability of a successful side channel at-tack in a randomized algorithm is given. It is noted that all calculations in the CSIDH algorithm neces-sary to calculate the common secret are reduced only to the calculation of the isogenic curve parameter and are performed by field operations, scalar multiplication and doubling the points of the isogeny kernel. In the new algorithm, it is proposed to abandon the calculation of the isogenic function of a random point , which significantly speeds up the algorithm.

Item Type: Article
Additional Information: https://doi.org/10.28925/2663-4023.2022.17.128144
Uncontrolled Keywords: Keywords: curve in generalized Edwards form, complete Edwards curve, twisted Edwards curve, quadratic Edwards curve, curve order, point order, isomorphism, isogeny, randomization, w-coordinates, square, non-square
Subjects: Статті у журналах > Фахові (входять до переліку фахових, затверджений МОН)
Divisions: Факультет інформаційних технологій та математики > Кафедра інформаційної та кібернетичної безпеки імені професора Володимира Бурячка
Depositing User: професор Анатолій Володимирович Бессалов
Date Deposited: 07 Nov 2022 13:16
Last Modified: 07 Nov 2022 13:16
URI: https://elibrary.kubg.edu.ua/id/eprint/42376

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