通信学报
通信學報
통신학보
JOURNAL OF CHINA INSTITUTE OF COMMUNICATIONS
2009年
12期
113-118
,共6页
公钥密码%椭圆曲线密码体制%多点乘%联合稀疏型%联合Hamming密度
公鑰密碼%橢圓麯線密碼體製%多點乘%聯閤稀疏型%聯閤Hamming密度
공약밀마%타원곡선밀마체제%다점승%연합희소형%연합Hamming밀도
public key cryptography%elliptic curve cryptosystem%multiple point multiplication%joint sparse form%joint Hamming density
许多椭圆曲线密码体制需要计算多点乘aP+bQ.Solinas、李学俊和张亚娟分别给出了整数对的三元和五元联合稀疏型,将计算多点乘所需的点加运算次数由0.751分别降低为0.51、0.3871和0.365 41.给出了整数对的七元联合稀疏型的定义和算法,并证明其联合Hamming密度仅为0.341 5.将七元联合稀疏型用于多点乘计算,使所需的点加次数降低至0.341 51次,进一步提高了aP+bQ的计算效率.
許多橢圓麯線密碼體製需要計算多點乘aP+bQ.Solinas、李學俊和張亞娟分彆給齣瞭整數對的三元和五元聯閤稀疏型,將計算多點乘所需的點加運算次數由0.751分彆降低為0.51、0.3871和0.365 41.給齣瞭整數對的七元聯閤稀疏型的定義和算法,併證明其聯閤Hamming密度僅為0.341 5.將七元聯閤稀疏型用于多點乘計算,使所需的點加次數降低至0.341 51次,進一步提高瞭aP+bQ的計算效率.
허다타원곡선밀마체제수요계산다점승aP+bQ.Solinas、리학준화장아연분별급출료정수대적삼원화오원연합희소형,장계산다점승소수적점가운산차수유0.751분별강저위0.51、0.3871화0.365 41.급출료정수대적칠원연합희소형적정의화산법,병증명기연합Hamming밀도부위0.341 5.장칠원연합희소형용우다점승계산,사소수적점가차수강저지0.341 51차,진일보제고료aP+bQ적계산효솔.
Many elliptic cuive clyptosystems require the computation of the multiple point multiplication aP+bQ.Softnab,Li X J and Zhang Y J suggested respectively three and five element joint sparse form(JSF),and the number of point addition of the multiple point multiplication was decreased from 0.751 to 0.51,0.3871 and 0.365 41 respectively.The definition and algorithm of seven element JSF was presented,and then it's showed that the average joint Hamming density is only 0.341 5.The number of point addition of the multiple point multiplication is further decreased to 0.341 51.So,computing aP+bQ by using seven element JSF is faster than by previous JSF representations.
