Analysis of 2-Isogeny Properties of Generalized Form Edwards Curves

被引：0

作者：

Bessalov, Anatoly ^{[1
]}

Kovalchuk, Lyudmila ^{[2
]}

Sokolov, Volodymyr ^{[1
]}

Skladannyi, Pavlo ^{[1
]}

Radivilova, Tamara ^{[3
]}

机构：

[1] Borys Grinchenko Kyiv Univ, Kiev, Ukraine

[2] Natl Tech Univ Ukraine, Igor Sikorsky Kyiv Polytech Inst, Kiev, Ukraine

[3] Kharkiv Natl Univ Radio Elect, Kharkiv, Ukraine

来源：

CYBERSECURITY PROVIDING IN INFORMATION AND TELECOMMUNICATION SYSTEMS (CPITS 2020) | 2020年 / 2746卷

关键词：

Generalized Edwards Form Curve; Complete Edwards Curve; Twisted Edwards Curve; Quadratic Edwards Curve; Curve Order; Points Order; Addition of Points; Isomorphism; Isogeny;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The analysis of the 2-isogeny existence conditions of generalized Edwards form curves over a prime field, including complete, quadratic, and twisted Edwards curves, is presented. An overview of the properties of these three classes of curves is given. Generalization of the results known for the classes of complete and quadratic curves to the class of twisted Edwards curves is obtained. A modified law of point's addition is used to correctly determine the isogeny degree.

引用

页码：1 / 13

页数：13

共 50 条

[31] EMBEDDING AND FACTORIZATION PROPERTIES OF THE PRODUCT OF GENERALIZED SIERPINSKI CURVES
Michalik, Daria
HOUSTON JOURNAL OF MATHEMATICS, 2013, 39 (02): : 717 - 732
[32] Hypergeometric properties of genus 3 generalized Legendre curves
Goodson, Heidi
JOURNAL OF NUMBER THEORY, 2018, 186 : 121 - 136
[33] The 3-Isogeny Selmer Groups of the Elliptic Curves y2=x3+n2
Chan, Stephanie
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2024, 2024 (09) : 7571 - 7593
[34] The generalized Verschiebung map for curves of genus 2
Brian Osserman
Mathematische Annalen, 2006, 336 : 963 - 986
[35] Genus 2 curves and generalized theta divisors
Brivio, Sonia
Favale, Filippo F.
BULLETIN DES SCIENCES MATHEMATIQUES, 2019, 155 : 112 - 140
[36] FORM ANALYSIS OF CENTRAL VEIN PRESSURE CURVES .1. NORMAL CURVES
HEINZ, N
LUCKMANN, E
SAEGLER, J
ZEITSCHRIFT FUR KREISLAUFFORSCHUNG, 1971, 60 (05): : 433 - &
[37] The generalized Verschiebung map for curves of genus 2
Osserman, Brian
MATHEMATISCHE ANNALEN, 2006, 336 (04) : 963 - 986
[38] Efficient FPGA Implementations of Point Multiplication on Binary Edwards and Generalized Hessian Curves Using Gaussian Normal Basis
Azarderakhsh, Reza
Reyhani-Masoleh, Arash
IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, 2012, 20 (08) : 1453 - 1466
[39] FORM ANALYSIS OF CENTRAL VENOUS PRESSURE CURVES .2. TRICUSPID VALVE INSUFFICIENCY
HEINZ, N
LUCKMANN, E
ZEITSCHRIFT FUR KREISLAUFFORSCHUNG, 1971, 60 (10): : 910 - &
[40] ANALYSIS OF ASTEROID LIGHTCURVES .2. PHASE CURVES IN A GENERALIZED HG-SYSTEM
LAGERKVIST, CI
MAGNUSSON, P
ASTRONOMY & ASTROPHYSICS SUPPLEMENT SERIES, 1990, 86 (02): : 119 - 165

← 1 2 3 4 5 →