CAJ | 학술논문

为了提高椭圆曲线中最基本、最耗时的标量乘法的效率,基于Extended DBNS以及半点运算的理论,提出了一种新的二进制域上椭圆曲线GF(2m)标量k的多基表示方法,并在此基础上给出了改进后的多基链标量乘法。在美国国家标准技术研究所(NIST)推荐的椭圆曲线上,实验结果表明,当预计算点的存储个数N =2,N =5时,新算法比Purohit等提出的算法效率分别至少提高了29.1%、35.0%,比洪银芳等提出的算法效率分别至少提高了7.8%、6.4%。新算法通过增加少量的预计算存储空间,有效降低了标量乘法的运算量,使标量乘法的运算更高效。因此,该算法可以较好地应用到无线传感器网络等计算资源受限的领域中。
위료제고타원곡선중최기본、최모시적표량승법적효솔,기우Extended DBNS이급반점운산적이론,제출료일충신적이진제역상타원곡선GF(2m)표량k적다기표시방법,병재차기출상급출료개진후적다기련표량승법。재미국국가표준기술연구소(NIST)추천적타원곡선상,실험결과표명,당예계산점적존저개수N =2,N =5시,신산법비Purohit등제출적산법효솔분별지소제고료29.1%、35.0%,비홍은방등제출적산법효솔분별지소제고료7.8%、6.4%。신산법통과증가소량적예계산존저공간,유효강저료표량승법적운산량,사표량승법적운산경고효。인차,해산법가이교호지응용도무선전감기망락등계산자원수한적영역중。
In order to improve the efficiency of the most basic and time-consuming scalar multiplication on elliptic curve,based on the theory of extended DBNS and point halving,not only propose a new method of MBNS of the scalar k on binary domain elliptic curve GF (2m),but also show the improved scalar multiplication algorithm using multi-base chain. In the United States National Institute of Stand-ards and Technology (NIST) recommended elliptic curve,the experimental results show that when the stored number of precalculated point N=2,N=5,efficiency of the new algorithm is increased by 29. 1%,35. 0% at least than that proposed by Purohit,increased by 7. 8% and 6. 4% at least than that proposed by Hong Yinfang. By adding a small amount of calculation storage space,the new algorithm can effectively reduce the computational complexity of scalar multiplication,which leads the scalar multiplication operation more effi-cient. Therefore,the algorithm can be applied to the domain of wireless sensor network and other limited computing resources.