Supersingular Twisted Edwards Curves Over Prime Fields. I. Supersingular Twisted Edwards Curves with j-Invariants Equal to Zero and 123

被引：3
|
作者：
Bessalov, A. V. [1 ]
Kovalchuk, L. V. [1 ]
机构：
[1] NTUU Igor Sikorsky KPI, Inst Phys & Technol, Kiev, Ukraine
来源：
CYBERNETICS AND SYSTEMS ANALYSIS | 2019年 / 55卷 / 03期
关键词：
supersingular curve; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; twisted pair; order of point; Legendre's symbol; quadratic residue; quadratic nonresidue;
D O I：
10.1007/s10559-019-00140-9
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
An analysis of existence conditions of supersingular twisted Edwards curves over a prime field is given. Theorems on the conditions of existence of supersingular curves with j-invariants equal to zero and 12(3) in different classes of curves are formulated and proved. Based on these results, concrete parameters for some supersingular curves are obtained. A generalization of the results obtained earlier using an isomorphism of curves in Weierstrass and Edwards forms is given.
引用
收藏
页码：347 / 353
页数：7
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