Abstract: In accordance with the problem that the fast implementation of elliptic curve cryptosystems relies on the efficient computation of scalar multiplication, this paper improves the mixed binary and ternary method to express n, generalizes the mixed binary, ternary and quinary method to express . Based on the computation of double point, triple point, and quintuple point, it computes scalar multiplication nP by using proper operations. Results show that the approaches lead to lower complexity which contributes to the efficient implementation of elliptic curve scalar multiplication.

Key words: elliptic curve cryptosystem, scalar multiplication, Non-Adjacent Form(NAF)

摘要： 椭圆曲线密码体制的快速实现依赖于标量乘(nP)的有效计算，该文改进 的二进制和三进制的混合表示方法，并且将其推广到 的二进制、三进制和五进制的混合表示。该算法在已知二倍点、三倍点和五倍点运算量的基础上，经过恰当的运算计算标量乘。试验结果表明，该算法减少计算标量乘的运算量，能有效地计算标量乘。

关键词: 椭圆曲线密码体制, 标量乘, 非相邻形式

CLC Number: 

• TP309