北京航空航天大学学报 ›› 2009, Vol. 35 ›› Issue (9): 1067-1071.

• 论文 • 上一篇    下一篇

基于双难题的环 Zn 上圆锥曲线的数字签名

林 松1, 李舟军1, 王 标2   

  1. 1. 北京航空航天大学 计算机学院, 北京 100191;
    2. 国际关系学院 信息科技系, 北京 100091
  • 收稿日期:2008-08-04 出版日期:2009-09-30 发布日期:2010-09-14
  • 作者简介:林 松(1970-),男,福建莆田人,博士后,linsong@buaa.edu.cn.
  • 基金资助:

    国家自然科学基金资助项目(60473057,90604007,90718017)

Signature on conic curve over Zn based on two hard problems

Lin Song1, Li Zhoujun1, Wang Biao2   

  1. 1. School of Computer Science and Technology, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. Information Science and Technology Department, University of International Relations, Beijing 100091, China
  • Received:2008-08-04 Online:2009-09-30 Published:2010-09-14

摘要: 通过对一个剩余类环 Zn上圆锥曲线Cn(a,b) 数字签名方案(Xiao06方案)的安全性分析,发现该方案的公开参数选取和算法设计存在问题,导致利用韦达定理可以分解模数 n ,说明Xiao06方案的安全性不是基于整数分解难题的.针对此缺陷,采取保密部分参数和修改验证算法的方法,提出了一个改进的环 Zn 上圆锥曲线的数字签名方案,并且给出了改进方案的数值模拟.分析表明,改进的方案是一个同时基于离散对数和整数分解双难题的环 Zn 上圆锥曲线的数字签名方案,不仅保留了原Xiao06方案的优点(明文嵌入方便,求逆元速度快,元素阶的计算及曲线上点的运算容易),还具有很强的抗破解能力.

Abstract: The security of the digital signature scheme (Xiao06 scheme) on conic curve Cn(a,b) over the residue class ring Zn was analyzed. The analysis result indicates that the published parameters can make the modulus n be factorized using the Weda-s theorem, and shows that the Xiao06 scheme is not a scheme whose security based on the integer factorization problem. To address this issue, an improved digital signature scheme on conic curve over Zn was proposed. Some parameters were kept secretly, and the verification algorithm was modified in the improved scheme. Furthermore, the numerical simulation of the improved scheme was given. The analysis shows that the improved scheme is a digital signature scheme based on two hard problems in computing discrete logarithm and factorizing integer simultaneously, and that the improved scheme has not only the merits (convenience for plaintext embedding, quickness for the inverse operation, and easiness for element order and points computing in curve) of the Xiao06 scheme, but also the advantage of strong anti-cracking ability.

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