基于Pell预计算和混合坐标系的增强型wNAF算法  

AN IMPROVED WNAF ALGORITHM BASED ONPELL PRECOMPUTATION AND MIXED COORDINATE SYSTEM

作　　者：安永丽 伍莉 An Yongli;Wu Li(School of Artificial Intelligence,North China University of Science and Technology,Tangshan 063000,Hebei,China;Key Laboratory of Industrial Intelligent Perception of Hebei Province,Tangshan 063000,Hebei,China)

机构地区：[1]华北理工大学人工智能学院,河北唐山063000 [2]河北省工业智能感知重点实验室,河北唐山063000

出　　处：《计算机应用与软件》2025年第3期253-259,318,共8页Computer Applications and Software

基　　金：国家科技部重点研发专项(2017YFE0135700);河北省高层次人才工程项目(A201903011);河北省自然科学基金项目(F2018209358)。

摘　　要：为了提升标量乘运算的效率,提出一种基于Pell预计算(Pell Precomputation,PP)和混合坐标系(Mixed Coordinates,MC)的增强型wNAF算法。在预计算阶段用Pell数代替奇数和素数,减少点加和倍点运算次数;在评估阶段引入新型混合坐标系策略,将仿射坐标系、雅可比坐标系和修正的雅可比坐标系相结合,减少标量乘算法中求逆运算次数。经过实验分析,PPMC方案下增强型wNAF算法的平均计算复杂度降低50%。与现有算法相比,提出的增强型算法拥有更低的计算复杂度和更高的标量乘算法效率。To improve the efficiency of scalar multiplication,an improved wNAF algorithm is proposed by using Pell precomputation and mixed coordinates.The algorithm replaced odd number and prime number with Pell number in the precomputation stage,which reduced the number of point addition and double point operations.In the evaluation stage,a new mixed coordinate system strategy was introduced,which combined Affine Coordinate,Jacobian Coordinate and Modified Jacobian Coordinate,effectively reducing the number of modular inversion operations in the scalar multiplication algorithm.After experimental analysis,the average computational complexity of the enhanced wNAF algorithm under the PPMC scheme is reduced by 50%.Compared with existing algorithms,the enhanced algorithm proposed in this paper has lower computational complexity and higher scalar multiplication algorithm efficiency.

关 键 词：椭圆曲线加密 标量乘 Pell预计算 混合坐标系 wNAF算法 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]