辛几何上的Cartesian认证码的构造

Construction of Cartesian authentication codes from symplectic geometry

利用有限域上的辛几何构造一个Cartesian认证码 .计算了认证码的参数 ,并在假定按照等概率分布来选择编码规则下 ,计算了成功模仿攻击概率PI 和成功替换攻击概率PS,它们都达到了最优或接近最优 ,为实现一些好的实用认证技术在理论上提供了可靠的基础 ,也给出了构造Cartesian认证码的技巧 .推广了万哲先先生得到的结果 ,使他的结果成为在一种特殊情况下的结论 .

One new construction of so called Cartesian authentication code from symplectic geometry is presented. The size parameters of the authentication codes are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities P I and P S of a successful impersonation attack and a successful substitution attack, respectively, of this code are also computed.Moreover, this code so constructed, for which P I and P S is nearly optimal, is also determined. This paper develops Wan Zhe xian′s construction, and Wan′s result become a special condition for this research.