基于环Z_n上圆锥曲线上的A-EKE协议及其应用  

Applications of A-EKE Protocol with ElGamal Signature Scheme Based on the Conic Curve over Z_n

作　　者：郝思佳[1] 方颖珏[2] 王标[1] 邬静阳 

机构地区：[1]国际关系学院信息科技系 [2]深圳大学数学与计算科学学院 [3]总装备部63956部队

出　　处：《计算机科学》2011年第B10期119-123,共5页Computer Science

摘　　要：提出了一个基于环Zn上圆锥曲线用ElGamal签名算法实现的A-EKE协议并给出了方案的数值模拟。方案具备A-EKE协议、ElGamal签名算法和环Zn上圆锥曲线的组合优势,A-EKE协议同时使用对称和公钥密码算法为计算机网络基于口令的身份认证系统提供了安全性和鉴别性,在通信主机上存储口令的单向哈希值而非口令明文,并在扩充部分要求用户发送一条含有口令明文的加密消息来验证身份,使得攻击者即使获得了口令哈希值也无法向主机冒充用户;用ElGamal签名算法实现A-EKE,协议加强了方案的健壮性;方案能够能够抵抗主动攻击,重放攻击,中间人攻击,保护口令不受离线字典攻击和破坏口令文件的攻击。方案运算在环Zn上的圆锥曲线上,综合利用了大数分解的困难性和环上圆锥曲线群上离散对数问题的困难性,从而增强了该方案的安全性,且具有明文嵌入方便、运算速度快、更易于实现等优点,尤其是标准二进制的引入能够节约1/4计算量,对于工程实现具有现实意义。This paper proposed a scheme in which A-EKE is formed on the basis of conic curve over residue class ring Zn using ElGamal signature algorithm,and presented the numerical simulation of the scheme.This scheme has combining advantages：A-EKE Protocol using a combination of asymmetric（public-key） and symmetric（secret-key） cryptography provides security and identification for communication on computer network.A-EKE allows hosts not to store cleartext passwords,and thus can prevent the attacker from mimicking the user to the host.Implementing the scheme using ElGamal signature algorithm also strengthens the scheme.The scheme can secure against active attack,overlay attack,man-in-the-middle attack,off-line dictionary attack and password profile compromise.Comprehensively using the difficulties in factorizing large integer and computing discrete logarithm with Conic Curve over Zn,the security of this scheme is increased.For the facility of plaintext embedding and the computing of rank and point on conic Cn（a,b）,the scheme has the advantages of speedy operation and easy realization,especially by using the NAF.These advantageous properties of the schemes have pragmatic significance for the design and realization of secure and efficient identity authentication and key negotiation system.

关 键 词：剩余类环Zn 圆锥曲线 EKE A-EKE 标准二进制 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]