Embedded implementation of Edwards curve- and extended Jacobi quartic curve-based cryptosystems

C. Peretti, P. Gastaldo, M. Stramezzi, R. Zunino
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引用次数: 1

Abstract

This research addresses the computationally-effective implementation of cryptographic protocols based on elliptic curves, and targets in particular cryptosystems that should be hosted on embedded programmable processors. In principle, the implementation of Elliptic Curve Cryptography (ECC) requires one to deal with different design options, which stem from the available degrees of freedom: elliptic curve family, coordinate system, and point multiplication procedure. On the other hand, theoretical studies already proved that exist only a few setups leading to computational efficient implementations. The goal of present paper is to analyze from an applicative point of view such setups, which mainly involve two specific families of elliptic curves: Edwards curves and extend Jacobi quartic curves. The presented experimental session shows a few interesting outcomes; first, ECC schemes implemented by using either Edwards curves or extended Jacobi quartic curves can obtain remarkable performances in terms of computational efficiency also on low-cost, low-resources processors. Second, the experiments showed that in some cases the number of Fp operations is not enough to accurately estimate the overall performance of an ECC-based cryptosystem.
基于Edwards曲线和扩展Jacobi四次曲线的密码系统的嵌入式实现
本研究解决了基于椭圆曲线的密码协议的计算有效实现,并针对应该托管在嵌入式可编程处理器上的特定密码系统。原则上,实现椭圆曲线加密(ECC)需要处理不同的设计选项,这些选项源于可用的自由度:椭圆曲线族、坐标系统和点乘法过程。另一方面,理论研究已经证明,只有少数设置导致计算效率的实现。本文的目的是从应用的角度分析这类设置,主要涉及两类特殊的椭圆曲线:Edwards曲线和扩展Jacobi四次曲线。提出的实验阶段显示了一些有趣的结果;首先,采用Edwards曲线或扩展Jacobi四次曲线实现的ECC方案在低成本、低资源处理器上也能获得显著的计算效率。其次,实验表明,在某些情况下,Fp操作的数量不足以准确估计基于ecc的密码系统的整体性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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