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FPGA Implementation of Elliptic-Curve Diffie Hellman Protocol

Computers, Materials & Continua 2022年第10期73卷 1879-1894页

作者： Sikandar Zulqarnain Khan Sajjad Shaukat Jamal Asher Sajid Muhammad Rashid Department of Aeronautical Engineering Estonian Aviation AcademyTartu61707Estonia Department of Mathematics College of ScienceKing Khalid UniversityAbha61413Saudi Arabia Department of Electrical Engineering Bahria UniversityIslamabad44000Pakistan Department of Computer Engineering Umm Al-Qura UniversityMakkah21955Saudi Arabia

This paper presents an efficient crypto processor architecture for key agreement using ECDH(Elliptic-curve Diffie Hellman)protocol over GF2163.The composition of our key-agreement architecture is expressed in consisting of the following:(i)Elliptic-curve point multiplication architecture for public key generation(DESIGN-I)and(ii)integration of DESIGN-I with two additional routing multiplexers and a controller for shared key generation(DESIGN-II).The arithmetic operators used in DESIGN-I and DESIGNII contain an adder,squarer,a multiplier and inversion.A simple shift and add multiplication method is employed to retain lower hardware ***,an essential inversion operation is operated using the Itoh-Tsujii algorithm with similar hardware resources of used squarer and multiplier *** proposed architecture is implemented in a Verilog *** implementation results are given on a Xilinx Virtex-7 FPGA(field-programmable gate array)*** DESIGN-I and DESIGN-II over GF2163,(i)the utilized Slices are 3983 and 4037,(ii)the time to compute one public key and a shared secret is 553.7μs and 1170.7μs and(iii)the consumed power is 29μW and 57μ***,the achieved area optimized and power reduced results show that the proposed ECDH architecture is a suitable alternative(to generate a shared secret)for the applications that require low hardware resources and power consumption.

关键词： Elliptic curve cryptography point multiplication key-agreement diffie hellman area optimized architecture FPGA

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A Complete Set of Addition Laws for Twisted Jacobi Intersection Curves

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Wuhan University Journal of Natural Sciences 2011年第5期16卷 435-438页

作者： WU Hongfeng FENG Rongquan College of Sciences North China University of TechnologyBeijing 100144 China School of Mathematical Sciences and Laboratory ofMathematics and Applied Mathematics (LMAM) Peking UniversityBeijing 100871 China

A complete system of addition laws on an elliptic curve E is a collection of addition laws with the property that for any pair of points P1, P2 on E at least one of the addition laws in the collection can be used to compute P1＋P2. This paper proposes a complete set of the addition laws for arbitrary twisted Jacobi intersection curve.

关键词： elliptic curve twisted Jacobi intersection curve complete addition law point multiplication cryptography

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