On oriented supersingular elliptic curves

被引：18

作者：

Onuki, Hiroshi ^{[1
]}

机构：

[1] Univ Tokyo, Dept Math Informat, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1138656, Japan

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2021年 / 69卷

关键词：

Supersingular elliptic curves; Isogeny graphs;

D O I：

10.1016/j.ffa.2020.101777

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We revisit theoretical background on OSIDH (Oriented Supersingular Isogeny Diffie-Hellman protocol), which is an isogeny-based key-exchange protocol proposed by Col and Kohel at NutMiC 2019. We give a proof of a fundamental theorem for OSIDH. The theorem was stated by Col and Kohel without proof. Furthermore, we consider parameters of OSIDH, give a sufficient condition on the parameters for the protocol to work, and estimate the size of the parameters for a certain security level. (c) 2020 Elsevier Inc. All rights reserved.

引用

页数：18

共 50 条

[31] Constructing supersingular elliptic curves with a given endomorphism ring
Chevyrev, Ilya
Galbraith, Steven D.
LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2014, 17 : 71 - 91
[32] An Effective Lower Bound on the Number of Orientable Supersingular Elliptic Curves
Leroux, Antonin
SELECTED AREAS IN CRYPTOGRAPHY, SAC 2022, 2024, 13742 : 263 - 281
[33] Ramification in the division fields of elliptic curves with potential supersingular reduction
Lozano-Robledo Á.
Research in Number Theory, 2 (1)
[34] Supersingular zeros of divisor polynomials of elliptic curves of prime conductor
Kazalicki, Matija
Kohen, Daniel
RESEARCH IN THE MATHEMATICAL SCIENCES, 2017, 4
[35] Computing a Sequence of 2-Isogenies on Supersingular Elliptic Curves
Yoshida, Reo
Takashima, Katsuyuki
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2013, E96A (01) : 158 - 165
[36] On the Plus and the Minus Selmer Groups for Elliptic Curves at Supersingular Primes
Kitajima, Takahiro
Otsuki, Rei
TOKYO JOURNAL OF MATHEMATICS, 2018, 41 (01) : 273 - 303
[37] Loops of isogeny graphs of supersingular elliptic curves at j=0
Ouyang, Yi
Xu, Zheng
FINITE FIELDS AND THEIR APPLICATIONS, 2019, 58 : 174 - 176
[38] A Quantum Algorithm for Computing Isogenies between Supersingular Elliptic Curves
Biasse, Jean-Francois
Jao, David
Sankar, Anirudh
PROGRESS IN CRYPTOLOGY - INDOCRYPT 2014, 2014, 8885 : 428 - 442
[39] Higher codimension Iwasawa theory for elliptic curves with supersingular reduction
Kataoka, Takenori
ANNALES MATHEMATIQUES DU QUEBEC, 2024, 48 (02): : 379 - 406
[40] On isogeny graphs of supersingular elliptic curves over finite fields
Adj, Gora
Ahmadi, Omran
Menezes, Alfred
FINITE FIELDS AND THEIR APPLICATIONS, 2019, 55 : 268 - 283

← 1 2 3 4 5 →