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

被引：0
|
作者：
A. V. Bessalov
L. V. Kovalchuk
机构：
[1] Institute of Physics and Technology of the NTUU “Igor Sikorsky KPI,
[2] ”,undefined
来源：
Cybernetics and Systems Analysis | 2019年 / 55卷
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：
暂无
中图分类号：
学科分类号：
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 123 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.
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页码：347 / 353
页数：6
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