F_2~m上基于ONB的椭圆曲线加密软件的设计与实现

Design and Implementation of Elliptic Curve Encryption Based on ONB over F^m_2

1 引言目前,椭圆曲线密码体制(Elliptic Curve Cryptography,ECC)被认为能比其他公钥体制提供更好的加密强度、更快的执行速度和更小的密钥长度。ECC的安全性基于椭圆曲线离散对数问题的难解性。在实际应用的ECC中,椭圆曲线采用的是基于有限域F_p或F_2~m的椭圆曲线群。F_p中的域元素为整数集合{0,1,2,…,p-1},其中p为素数。

This paper comprehensively introduces the mathematics theory for elliptic curve encryption based on ONB over Fm2. like the ONB denotation of element over Fm2 the elliptic curve over Fm2 and some computing rules. Based on the theoretical introduction, an ECC-based encryption scheme is designed. The mechanism for key exchange is described in details for further applications. Underlying the given theoretical analysis and protocol description, an ECC software is implemented. The software is characterized by excellent security as well as high efficiency.