Volume 35 Issue 9
Sep.  2009
Turn off MathJax
Article Contents
Lin Song, Li Zhoujun, Wang Biaoet al. Signature on conic curve over Zn based on two hard problems[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(9): 1067-1071. (in Chinese)
Citation: Lin Song, Li Zhoujun, Wang Biaoet al. Signature on conic curve over Zn based on two hard problems[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(9): 1067-1071. (in Chinese)

Signature on conic curve over Zn based on two hard problems

  • Received Date: 04 Aug 2008
  • Publish Date: 30 Sep 2009
  • 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.

     

  • loading
  • [1] Diffie W, Hellman M E. New direction in cryptography[J]. IEEE Transactions on Information Theory, 1976, 22(6):644-654 [2] McCurley K C.A key distribution system equivalent to factoring[J]. Cryptology, 1988, 1(2):95-106 [3] 吴秋新,杨义先,胡正名.同时基于离散对数和素因子分解的新的数字签名方案[J].北京邮电大学学报, 2001, 24(1): 61-65 Wu Qiuxin, Yang Yixian, Hu Zhengming. New signature schemes based on discrete logarithms and factoring[J]. Journal of Beijing University of Posts and Telecommunications,2001,24(1):61-65(in Chinese) [4] 董晓蕾,曹珍富,李晓红.基于双难题的两个数字签名方案的密码分析[J].上海交通大学学报, 2006, 40(7):1174-1177 Dong Xiaolei, Cao Zhenfu, Li Xiaohong. Cryptanalysis of two signature schemes based on two hard problems[J]. Journal of Shanghai Jiaotong University, 2006, 40(7):1174-1177(in Chinese) [5] 李子臣,徐国爱,杨义先.He-Wu数字签名方案的攻击方法[J].北京邮电大学学报, 1999, 22(4):6-8 Li Zichen, Xu Guoai, Yang Yixian. Cryptanalysis of improved Rabin-s crypto-system[J]. Journal of Beijing University of Posts and Telecommunications, 1999, 22(4): 6-8(in Chinese) [6] 张明志.用圆锥曲线分解整数[J].四川大学学报:自然科学版,1996,33(4):356-359 Zhang Mingzhi. Factoring integer with conics[J]. Journal of Sichuan University:Natural Science Edition,1996,33(4):356-359(in Chinese) [7] 曹珍富.基于有限域 FP 上圆锥曲线的公钥密码系统 刘木兰,龚奇敏.密码学进展—ChinaCrypt’98.北京:科学出版社,1998:45-49 Cao Zhenfu. A public key cryptosystem based on the conic curve over finite fields FP //Liu Mulan, Gong Qimin. Advances in Cryptology-ChinaCrypt’98. Beijing: Science Press, 1998:45-49 (in Chinese) [8] 孙琦,朱文余,王标.环 Zn 上圆锥曲线和公钥密码协议[J].四川大学学报:自然科学版,2005,42(3):471-478 Sun Qi, Zhu Wenyu, Wang Biao. The conic curves over Zn and public-key cryptosystem protocol[J]. Journal of Sichuan University:Natural Science Edition,2005,42(3):471-478(in Chinese) [9] 王标,朱文余,孙琦.基于剩余类环 Zn 圆锥曲线的公钥密码体制[J].四川大学学报:工程科学版, 2005,37(5):112-117 Wang Biao, Zhu Wenyu, Sun Qi. Public-key cryptosystem based on the conic curves over Zn [J]. Journal of Sichuan University:Engineering Science Edition,2005,37(5):112-117(in Chinese) [10] 肖龙,王标,孙琦.基于环 Zn 上的圆锥曲线数字签名和多重数字签名[J].西安交通大学学报,2006,40(6):648-651 Xiao Long, Wang Biao, Sun Qi. Digital signature and multiple digital signatures based on the conic curve over Zn [J]. Journal of Xi-an Jiaotong University, 2006, 40(6):648-651(in Chinese)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views(3280) PDF downloads(1031) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return