一种基于多基表示的标量乘扩展算法

发布时间：2018-06-05 20:48

本文选题：椭圆曲线密码体制 + 标量乘　；参考：《小型微型计算机系统》2017年12期

【摘要】：标量乘是椭圆曲线密码体制操作中最耗时、最主要的工作,所以椭圆曲线密码体制的快速实现问题的关键归结为椭圆曲线标量乘法的计算.为了提高椭圆曲线密码的效率,在已有的二进制域椭圆曲线标量乘算法的基础上,结合扩展系数集和半点运算方法,提出一种新的形如d(1/2)a3b5c7z的标量k的多基表示算法和相应的多基标量乘算法.在美国国家标准技术研究所推荐的椭圆曲线NIST B-163、NIST B-233和NIST B-283上进行实验,结果表明,新算法以增加少量预计算存储为代价,有效降低了算法复杂度,提高了标量乘算法的效率,使标量乘法的运算更高效.相比于相关工作,提高了约14.4%~41.4%.因此,新算法可以较好地应用到智能卡等计算资源、存储资源受限的领域中.
[Abstract]:Scalar multiplication is the most time-consuming and important work in the operation of elliptic curve cryptosystem, so the key to the fast realization of elliptic curve cryptosystem is the calculation of elliptic curve scalar multiplication. In order to improve the efficiency of elliptic curve cryptography, based on the existing scalar multiplication algorithm of elliptic curve in binary domain, the extended coefficient set and the half-point operation method are combined. A new multi-basis representation algorithm for scalar k like d(1/2)a3b5c7z and a corresponding multi-scalar multiplication algorithm are proposed. Experiments are carried out on the elliptic curve NIST B-163 NIST B-233 and NIST B-283 recommended by the National Institute of National Standards and Technology. The results show that the new algorithm reduces the complexity of the algorithm and improves the efficiency of the scalar multiplication algorithm at the cost of increasing a small amount of predictive storage. Make scalar multiplication more efficient. Compared with the related work, the increase of about 14. 4% 41.4. Therefore, the new algorithm can be well applied to smart card and other computing resources, storage resources are limited in the field.
【作者单位】：扬州大学信息工程学院;
【基金】：国家自然科学基金项目(61472343)资助江苏省普通高校研究生科研创新计划项目(KYLX15_1362)资助
【分类号】：TN918.1

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