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| 基于多基数系统的有效标量乘算法 |
| Fast Scalar Multiplication Based on MBNS |
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| DOI：10.3969/j.issn.1671-5322.2013.02.006 |
| 中文关键词: 椭圆曲线密码体制 标量乘法 双基数系统(DBNS) 多基数系统(MBNS) |
| 英文关键词: Elliptic Curve Cryptosystems Scalar Multipication Double-base number system Muti-base number system |
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| 中文摘要: |
| 首先给出了椭圆曲线上点P的7倍点公式7P,当[i]/[m]=6时,它比直接计算节省运算量7.4％～30.56％.作为双基数系统的一个推广,多基数系统具有标量表示长度更短、汉明重量更小的特点,较适用于椭圆曲线标量乘的快速计算.结合以上给出的公式,提出了一个以2,3和7作为基底的多基数系统计算椭圆曲线标量乘的有效算法,所提方法计算量更少. |
| 英文摘要: |
| Firstly,this paper gives the 7P formula of point P which is on the elliptic curve,and it saves 7.4%～30.56% than directly computation.Then as a generalization of double base chains,multibase number system is very suitable for efficient computation of scalar multiplication of a point of elliptic curve because of shorter representation length and hamming weight.Combined with the given formulas for computing the 7-fold of an elliptic curve point P,an efficient scalar multiplication algorithm of elliptic curve is proposed using 2,3 and 7 as basis of the multi based number system and the proposed algorithms cost less. |
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