Coordinate system for elliptic curve cryptosystem on twisted Edwards curve

机译：椭圆形爱德华兹曲线上的椭圆曲线密码系统的坐标系

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This paper proposes a coordinate system in which a point (x, y) is represented as (X, Y, Z, W), where x = X/Z and y = Y/W are satisfied. In the proposed coordinate system, the cost of scalar multiplication, which is the dominant operation of elliptic curve cryptosystems, on the twisted Edwards curve ±x2 + y2 = 1 + dx2y2 is the same as the existing lowest cost in a mixed coordinate system, and implementation of scalar multiplication becomes easier.

机译：本文提出了一个坐标系统，其中点（x，y）表示为（X，Y，Z，W），其中x = X / Z并且y = Y / W。在所提出的坐标系中，椭圆曲线密码系统在扭曲的爱德华兹曲线±x2 + y2 = 1 + dx2y2上的标量乘法运算的成本与现有最低成本相同，并且标量乘法的实现变得更加容易。

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《IEEE International Conference on Consumer Electronics-Taiwan》|2016年|1-2|共2页
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Masaaki Shirase;
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关键词
Elliptic curves; Elliptic curve cryptography; Integrated circuits; Online banking; Galois fields; Jacobian matrices;

机译：椭圆曲线;椭圆曲线密码学;集成电路;在线银行; Galois域; Jacobian矩阵;

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专利

1. Efficient Lightweight Hardware Structures of Point Multiplication on Binary Edwards Curves for Elliptic Curve Cryptosystems [J] . Rashidi Bahram, Abedini Mohammad Journal of circuits, systems and computers . 2019,第9期

机译：椭圆曲线密码系统在二进制Edwards曲线上的点乘法的高效轻量级硬件结构
2. Full-custom hardware implementation of point multiplication on binary Edwards curves for application-specific integrated circuit elliptic curve cryptosystem applications [J] . Bahram Rashidi, Sayed Masoud Sayedi, Reza Rezaeian Farashahi Circuits, Devices & Systems, IET . 2017,第6期

机译：针对专用集成电路椭圆曲线密码系统应用的二进制Edwards曲线上点乘法的全定制硬件实现
3. SUPERSINGULAR TWISTED EDWARDS CURVES OVER PRIME FIELDS. Ⅱ. SUPERSINGULAR TWISTED EDWARDS CURVES WITH THE j-INVARIANT EQUAL TO 66~3 [J] . Bessalov A. V, Kovalchuk L. V Cybernetics and Systems Analysis . 2019,第5期

机译：超奇异的扭曲爱德华兹曲线遍及主要领域。 Ⅱ。 j不等式等于66〜3的超奇异扭曲爱德华曲线
4. Coordinate system for elliptic curve cryptosystem on twisted Edwards curve [C] . Masaaki Shirase IEEE International Conference on Consumer Electronics-Taiwan . 2016

机译：扭曲Edwards曲线椭圆曲线密码系统的坐标系
5. Low-Resource and Fast Elliptic Curve Implementations over Binary Edwards Curves [D] . Koziel, Brian 2016

机译：二进制Edwards曲线的低资源和快速椭圆曲线实现
6. An Enhanced Biometric-Based Authentication Scheme for Telecare Medicine Information Systems Using Elliptic Curve Cryptosystem [O] . Yanrong Lu, Lixiang Li, Haipeng Peng, -1

机译：基于椭圆曲线密码系统的远程医疗医学信息系统的基于生物特征的增强认证方案
7. A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem [O] . Brian Baldwin, Richard Moloney, Andrew Byrne, 2012

机译：椭圆曲线密码系统的扭曲爱德华兹曲线的硬件分析
8. Some Improvements on Signed Window Algorithms for Scalar Multiplications in Elliptic Curve Cryptosystems [R] . Vo, San C. 2001

机译：椭圆曲线密码体制中标量乘法的符号窗口算法的一些改进

Coordinate system for elliptic curve cryptosystem on twisted Edwards curve

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