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
收藏
页数：18
相关论文
共 50 条
  • [21] Finding orientations of supersingular elliptic curves and quaternion orders
    Arpin, Sarah
    Clements, James
    Dartois, Pierrick
    Eriksen, Jonathan Komada
    Kutas, Peter
    Wesolowski, Benjamin
    DESIGNS CODES AND CRYPTOGRAPHY, 2024, 92 (11) : 3447 - 3493
  • [22] Normalizers of split Cartan subgroups and supersingular elliptic curves
    Merel, Loic
    DIOPHANTINE GEOMETRY, PROCEEDINGS, 2007, 4 : 237 - 255
  • [23] SUPERSINGULAR ELLIPTIC-CURVES AND CONGRUENCES FOR LEGENDRE POLYNOMIALS
    LANDWEBER, PS
    LECTURE NOTES IN MATHEMATICS, 1988, 1326 : 69 - 93
  • [24] The main conjecture for CM elliptic curves at supersingular primes
    Pollack, R
    Rubin, K
    ANNALS OF MATHEMATICS, 2004, 159 (01) : 447 - 464
  • [25] The parity conjecture for elliptic curves at supersingular reduction primes
    Kim, Byoung Du B. D.
    COMPOSITIO MATHEMATICA, 2007, 143 (01) : 47 - 72
  • [26] Classes of isomorphism for supersingular elliptic curves of characteristic ≥3
    Morain, F
    UTILITAS MATHEMATICA, 1997, 52 : 241 - 253
  • [27] Endomorphism rings of supersingular elliptic curves over Fp
    Li, Songsong
    Ouyang, Yi
    Xu, Zheng
    FINITE FIELDS AND THEIR APPLICATIONS, 2020, 62
  • [28] Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves
    Xiao, Guanju
    Luo, Lixia
    Deng, Yingpu
    JOURNAL OF MATHEMATICAL CRYPTOLOGY, 2021, 15 (01) : 454 - 464
  • [29] On the Iwasawa theory of CM elliptic curves at supersingular primes
    McConnell, G
    COMPOSITIO MATHEMATICA, 1996, 101 (01) : 1 - 19
  • [30] On the growth of μ-invariant in Iwasawa theory of supersingular elliptic curves
    Ray, Jishnu
    ACTA ARITHMETICA, 2022, 202 (03) : 241 - 252
12345