基于双基表示的并列点乘算法

A New Simultaneous Scalar Multiplication Based on Dobule-Base Number System

双基表示是一种整数表示法,它将任意整数表示成2和3的混合幂次的和或差的形式,并列点乘是一种快速的点乘算法,应用于一些椭圆曲线密码体制中.本文在现有的双基表示算法以及并列点乘算法的基础上,提出了新的双基表示算法以及基于该双基表示算法的并列点乘算法,该算法利用了一些特殊点的快速计算公式,从而有效地提高了并列点乘算法的执行效率.实验表明,在密钥长度为160比特,[S]/[I]=0.8时,当[I]/[M]=30,新算法的效率比基于JSF表示的并列点乘算法提高了22%;当[I]/[M]=10,新算法比JSF表示提高了6%;当[I]/[M]=8,新算法比JSF表示提高了3%.

Dobule-base number system is a representation of the intergers as the sum of mixed powers of two and three. Simultaneous scalar multiplication is a fast point multiplication algorithm, and applied to some elliptic curve cryptography systems. Based on the original dobule-base system and simultaneous scalar multiplication, a new dobule-base system algorithm and simultaneous scalar multiplication algorithm based on this dobule-base system algorithm is presented in this paper.Due to the fast underlying fields arithmetic, the new simultaneous scalar multiplication algorithm enhances simultaneous scalar multiplication efficiently. Experiments prove that,with the 160 bits secret key and [ S]/[ I] = 0.8,our method performed 22% improvement better than JSF when [I]/[g] = 30,6% when [I]/[M] = 10,3% when [I]/[M] = 8.