Abstract: To design a simple and practical authentication scheme is one of the important issues in the authentication codes research. Applying partition of positive integers and Anzahl theorem of subgroups of classical groups, a class of authentication codes was obtained and all parameters of this scheme were computed. Simultaneously, supposing that the secret key was chosen according to the uniform probability distribution, security analysis of the scheme was given. The construction increased the number of the source state dramatically, which indicates that this code has better traits than some other codes obtained by matrices method before.

Key words: authentication codes, classical group, finite field, partition, secret key

摘要： 设计简单而实用的认证方案是认证码研究中的重要问题。利用正整数的无序分拆及典型群子群的计数定理得到了一类认证码，计算出了全部参数，并给出了密钥等概率选取时的安全性分析。该构造大幅增加了源状态数，这表明该认证码比以前采用矩阵法获得的一些认证码具有更好的特征。

关键词: 认证码, 典型群, 有限域, 无序分拆, 密钥