CAJ | 학술논문

基于求逆转换为乘法的思想，利用仿射坐标提出了直接计算椭圆曲线上7P的算法，该算法运算量为I+23M+10S，比现有的算法节省了一次求逆运算，同时也给出了直接计算7k P的快速算法，该算法比重复计算k次7P更有效。结合多基数系统将这些新算法应用到标量乘法中，实验结果表明，在NIST推荐的椭圆曲线上，新算法的效率优于徐凯平等人所提的算法及传统的ternary-binary、3-NAF、Dimitro算法，相交处I/M可降至2.4。
기우구역전환위승법적사상，이용방사좌표제출료직접계산타원곡선상7P적산법，해산법운산량위I+23M+10S，비현유적산법절성료일차구역운산，동시야급출료직접계산7k P적쾌속산법，해산법비중복계산k차7P경유효。결합다기수계통장저사신산법응용도표량승법중，실험결과표명，재NIST추천적타원곡선상，신산법적효솔우우서개평등인소제적산법급전통적ternary-binary、3-NAF、Dimitro산법，상교처I/M가강지2.4。
Based on the idea of trading inversions for multiplications, an efficient algorithm is proposed to compute 7P directly over prime field FP in terms of affine coordinates, its computational complexity is I+23M+10S, saving one inver-sion compared with traditional method. Moreover, a new method is given to compute 7k P directly, which is more efficient than k repeated 7P . Finally, apply these new algorithms to scalar multiplication combined with MBNS. The experimental results show that on the elliptic curves recommended by NIST, the efficiency of new algorithm is superior to algorithm given by Xu kai-ping and other traditional algorithms, such as ternary-binary, 3-NAF, Dimitro algorithms, and the ration I/M of break-even point can be reduced to 2.4.