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�������պ����ѧѧ�� 2009, Vol. 35 Issue (9) :1067-1071    DOI:
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����˫����Ļ� Zn ��Բ׶���ߵ�����ǩ��
�� ��1, ���۾�1, �� ��2*
1. �������պ����ѧ �����ѧԺ, ���� 100191;
2. ���ʹ�ϵѧԺ ��Ϣ�Ƽ�ϵ, ���� 100091
Signature on conic curve over Zn based on two hard problems
Lin Song1, Li Zhoujun1, Wang Biao2*
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

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ժҪ ͨ����һ��ʣ���໷ Zn��Բ׶����Cn(a,b) ����ǩ������(Xiao��06����)�İ�ȫ�Է���,���ָ÷����Ĺ�������ѡȡ���㷨��ƴ�������,��������Τ�ﶨ����Էֽ�ģ�� n ,˵��Xiao��06�����İ�ȫ�Բ��ǻ��������ֽ������.��Դ�ȱ��,��ȡ���ܲ��ֲ������޸���֤�㷨�ķ���,�����һ���Ľ��Ļ� Zn ��Բ׶���ߵ�����ǩ������,���Ҹ����˸Ľ���������ֵģ��.��������,�Ľ��ķ�����һ��ͬʱ������ɢ�����������ֽ�˫����Ļ� Zn ��Բ׶���ߵ�����ǩ������,����������ԭXiao��06�������ŵ�(����Ƕ�뷽��,����Ԫ�ٶȿ�,Ԫ�ؽ׵ļ��㼰�����ϵ����������),�����к�ǿ�Ŀ��ƽ�����.
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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.
Keywords�� digital signature   integer factorization   discrete logarithm   conic curve     
Received 2008-08-04;


About author: �� ��(1970-),��,����������,��ʿ��,linsong@buaa.edu.cn.
�� ��, ���۾�, �� ��.����˫����Ļ� Zn ��Բ׶���ߵ�����ǩ��[J]  �������պ����ѧѧ��, 2009,V35(9): 1067-1071
Lin Song, Li Zhoujun, Wang Biao.Signature on conic curve over Zn based on two hard problems[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2009,V35(9): 1067-1071
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