笛卡尔积与认证码

该文研究了笛卡尔积与认证码的关系,根据笛卡儿积的结构特点,提出了一种将认证符信息嵌入到编码规则的思想,从工程应用的角度实现了基于笛卡尔积的各阶欺骗概率相等的最优Cartesian认证码的构造,并给出了基于笛卡尔积和拉丁方的各阶欺骗概率相等的安全认证码的构造方案。以上两种构造方案均无需预先存储编码矩阵,既节约了大量的存储空间,又可以获得所需要的安全性。

Cartesian Product and Authentication Codes

The relation between the Cartesian product and authentication codes is studied in this paper. A new idea to use the private keys to carry the information of the authentication symbols is presented, which is based on the character of Cartesian product’ structure. And the Cartesian product–based optimal authentication codes with equal cheating probabilities of all orders are constructed, which can be easily designed and can be applied well to engineering. In this paper, the secret authentication codes with equal cheating probabilities of all orders are also constructed which are founded on Cartesian product and Latin square. The two construction methods mentioned above need no pre-storing encoder matrix, so that a mass of storage is saved. At the same time, the two schemes can offer an enough security level expected.