A High Speed Coprocessor for Elliptic Curve Scalar Multiplications over F_p

机译：F_P的椭圆曲线标量乘法的高速协处理器

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We present a new hardware architecture to compute scalar multiplications in the group of rational points of elliptic curves defined over a prime field. We have made an implementation on Altera FPGA family for some elliptic curves defined over randomly chosen ground fields offering classic cryptographic security level. Our implementations show that our architecture is the fastest among the public designs to compute scalar multiplication for elliptic curves defined over a general prime ground field. Our design is based upon the Residue Number System, guaranteeing carry-free arithmetic and easy parallelism. It is SPA resistant and DPA capable.

机译：我们提出了一种新的硬件架构，用于计算在椭圆场定义的椭圆曲线的Rational曲线组中的标量乘法。我们已经在Altera FPGA系列上实现了一些在随机所选择的地面字段上定义的一些椭圆曲线，提供经典密码安全级别。我们的实现表明，我们的架构是公共设计中最快的，以计算在一般原子地面上定义的椭圆曲线的标量乘法。我们的设计基于残留号系统，保证无携带算术和容易的平行度。它是水疗和DPA的能力。

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《International Workshop on Cryptographic Hardware and Embedded Systems》|2010年||共17页
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作者
Nicolas Guillermin;
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中图分类 TP3-53;
关键词
Elliptic curve; High speed; RNS; Prime field; FPGA;

机译：椭圆曲线;高速;RN;PRIME字段;FPGA;

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专利

1. Faster Point Scalar Multiplication on Short Weierstrass Elliptic Curves over F_p using Twisted Hessian Curves over F_(p~2) [J] . Michal Wronski Journal of Telecommunications and Information Technology . 2016,第3期

机译：使用F_（p〜2）上的扭曲Hessian曲线在F_p上的短Weierstrass椭圆曲线上进行快速点标量乘法
2. Microblaze-based parallel implementations of elliptic curve scalar multiplication over F_p on FPGA [J] . Ahmed Mohamed Bellemou, Nadjia Benblidia, Mohamed Anane, International Journal of Internet Technology and Secured Transactions . 2020,第1a2期

机译：基于MicroBlaze的椭圆曲线标量在FPGA上的F_P乘法乘法
3. MicroBlaze-Based Multiprocessor Embedded Cryptosystem on FPGA for Elliptic Curve Scalar Multiplication Over F_p [J] . Bellemou A., Benblidia N., Anane M., Journal of circuits, systems and computers . 2019,第3期

机译：FPGA上基于MicroBlaze的多处理器嵌入式加密系统，用于F_p上的椭圆曲线标量乘法
4. A High Speed Coprocessor for Elliptic Curve Scalar Multiplications over F_p [C] . Nicolas Guillermin International Workshop on Cryptographic Hardware and Embedded Systems . 2010

机译：F_P的椭圆曲线标量乘法的高速协处理器
5. GPU and ASIC Acceleration of Elliptic Curve Scalar Point Multiplication. [D] . Leboeuf, Karl. 2012

机译：椭圆曲线标量点乘法的GPU和ASIC加速。
6. Symmetric digit sets for elliptic curve scalar multiplication without precomputation [O] . Clemens Heuberger, Michela Mazzoli -1

机译：椭圆形标量乘法的无对称数字集
7. Efficient Elliptic Curve Cryptosystems from a Scalar Multiplication Algorithm with Recovery of the y-Coordinate on a Montgomery-Form Elliptic Curve [O] . Katsuyuki Okeya, Kouichi Sakurai 2001

机译：高效椭圆曲线密码系统从标量乘法算法恢复蒙哥马利形式椭圆曲线上的y坐标
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

A High Speed Coprocessor for Elliptic Curve Scalar Multiplications over F_p

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