Abstract: Although classical cipher is simple and efficient, but it has a serious defect of being cracked easily under the current social computing power. A new classical cipher model based on rough sets was developed to solve this problem. Firstly, two features of rough sets were integrated into the model to weaken the statistical law of the model. One feature is that certainty contains uncertainty in rough sets, another is that the approximate space scale tends to increase sharply with the slight increase of the domain size. Secondly, the ability of producing random sequences of the model was improved by using mixed congruence method. Finally, part of plaintext information was involved in the encryption process by using self-defined arithmetic and congruence method to enhance the anti-attack ability of the model. The analysis shows that the model not only has the same level of time and space complexity as traditional classical cipher, but also has nearly ideal performance of diffusion and confusion, which completely overcomes the defects that classical cipher can be easily cracked, and can effectively resist the attacks such as exhaustive method and statistical analysis method.

Key words: rough set, classical cipher, approximation space, uncertainty, symmetric cipher

摘要： 针对传统古典密码虽然具备简洁高效的特性，但其在当前社会计算能力下极易被破解这一问题，提出一种利用粗糙集方法设计古典密码模型的算法。在该模型的构造中，首先充分融入粗糙集的确定性中蕴含着不确定性以及近似空间规模会随论域微增而急剧增大的特点，来弱化模型的统计规律；其次，借助混合同余法来提升模型产生随机序列的能力；最后，结合自定义运算和同余方法特性来让部分明文信息参与到加密过程中，进一步增强模型抗攻击的能力。研究分析表明，该模型不仅在时间和空间复杂度上与传统古典密码处于同一级别，而且具备了近乎理想的扩散与混淆性能，完全弥补了古典密码容易被破解的缺陷，能有效抵御穷举法和统计分析法的攻击。

关键词: 粗糙集, 古典密码, 近似空间, 不确定性, 对称密码