Abstract: This paper researches the arithmetic in GF(3m), the arithmetic on elliptic curve over GF(3m) and Elliptic Curve Cryptography(ECC) protocol. It designs and implements an EC cryptographic algorithm library, tests and analyzes GF(3m)-ECC algorithms. Results show that GF(3m)-ECC algorithms can provide the same performance as ECC algorithms on GF(2m) and GF(p), and can be applied into ECC security protocols design.

Key words: Elliptic Curve Cryptography(ECC), scalar multiplication, finite field of characteristic three

摘要： 研究GF(3m)有限域算术、GF(3m)上的椭圆曲线群算术和椭圆曲线密码协议。设计并实现椭圆曲线密码算法库，对各种GF(3m)-ECC密码算法进行仿真和性能分析，结果表明GF(3m)-ECC算法与GF(2m)和GF(p)上的ECC算法效率相当，可以应用到基于ECC的各种安全协议设计中。

关键词: 椭圆曲线密码体制, 标量乘法, 三元域

CLC Number: 

• TP309