Explicit construction of the square-root Velu's formula on Edwards curves

被引：0

作者：

Takahashi, Shu ^{[1
]}

Onuki, Hiroshi ^{[1
]}

Takagi, Tsuyoshi ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1138656, Japan

来源：

JSIAM LETTERS | 2022年 / 14卷

关键词：

isogenies; Edwards curve; Velu's formula; resultants;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The square-root Velu's formula (Velu's formula) is known to be effective way to speed up the computations of higher-degree isogeny used for isogeny-based cryptosystems such as CSIDH and B-SIDH. The original formula was proposed using Montgomery curves, and Moriya et al. then extended it to Edwards curves without specific construction method. In this study, we explicitly show how to construct Velu's formula on Edwards curves. In particular, we provide a method for adjusting for the differences between two resultants. We also compare the computational complexity with the original Velu's formula and find that it is up to 8% faster.

引用

页码：108 / 111

页数：4

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