Abstract: Recoding k and direct computing kp by introducing the balanced ternary to scalar multiplication can improve its efficiency. This paper gives an algorithm which recodes k as balanced ternary string, and proposes a balanced ternary algorithm to scalar multiplication. In this case, the average efficiency is improved 5.4% relative to the binary algorithm. When precomputation is used, the average efficiency is improved 73.18% and 15.58% relative to the algorithm which uses binary and binary precomputation, and the accounts which need to store is declined observably.

Key words: Elliptic Curve Cryptography(ECC), scalar multiplication, balanced ternary algorithm, binary algorithm, precomputation

摘要： 把对称三进制引入到椭圆曲线密码体制标量乘法中，对k进行重新编码，直接计算kP，以改进标量乘法的运算效率。给出将k重新编码为对称三进制串的算法，提出对称三进制标量乘法算法。相对于二进制标量乘法算法，平均效率提升5.4%。当进行预计算时，相对于二进制算法和二进制预计算算法，平均效率分别提升73.18%、15.58%，并且能减少需要存储的点数。

关键词: 椭圆曲线密码体制, 标量乘法, 对称三进制算法, 二进制算法, 预计算

CLC Number: 

• TP311