基于半点和多基表示的标量乘法扩展算法

摘要

在半点运算和多基表示思想的基础上,结合Extended DBNS方法,提出一种形如d(1/2)a3b5c的新标量k的多基表示,其中,d属于一个给定的整数集,并给出相应的多基链的标量乘法.数值实验结果表明,该算法以增加少量的预计算存储为代价,能有效降低标量乘法的计算复杂度和多基链的链长.%This paper proposes a representation ora scalar k in the form of d(1/2)a3b5c , where d belongs to a given digit set.This representation is a combination of the point halving and MBNS representation using the method of Extended DBNS.A scalar multiplication relying on the representation is given.Experimental results show that the approach leads to a shorter MBNS expansion and a lower complexity in elliptic curve scalar multiplication at the cost of a few pre-computations and storages.