基于椭圆曲线的数字签名和加密算法.pdf

第 37 卷第 4 期计算机工程 2011 年 2 月

Computer Engineering February 2011


·安全技术· 文章编号:1000—3428(2011)04—0168—02 文献标识码:A 中图分类号:

基于椭圆曲线的数字签名和加密算法
许德武,陈伟
(浙江师范大学数理与信息工程学院,浙江金华 321004)
摘要:直接将 ElGamal 签名方案移植到椭圆曲线密码系统上会出现未定义的两点相乘运算。为解决上述问题,改进签名生成及验证过程,
使用代数运算代替椭圆曲线上的数乘运算,给出改进算法的可行性证明及安全性分析。对 MV 加密算法进行改进,降低其膨胀率,通过实
验证明其执行速度快于 RSA 和 ECC-E 算法。执行效率及密钥长度方面的优势使 2 种改进算法能更有效地应用于智能卡计算中。
关键词:椭圆曲线;数字签名;加密;ElGamal 算法;MV 算法
Digital Signature and Encrypt Algorithm Based on Elliptic Curve
XU De-wu, CHEN Wei
(College of Mathematics Physics & Information Engineering, Zhejiang Normal University, Jinhua 321004, China)
【Abstract】Applying ElGamal signature scheme to the elliptic curve cryptosystem may introduce an undefined operation of point multiplex in
elliptic curve. In order to solve the problem, this paper improves processes of signature generation and validation, using a simple algebra operation
instead of multiplication operation, and presents feasibility and security analysis. Menezes Vanstone(MV) algorithm is improved to reduce its data
expand rate. Experimental results show that its operation speed is faster than RSA or ECC-E. Execution efficiency and key length of the improved
algorithms make them more efficient in the application of smart putation.
【Key words】elliptic curve; digital signature; encrypt; ElGamal algorithm; Meneze