Abstract: Tent mapping is widely used in the field of cryptography because of its uniform distribution characteristics. One-dimensional integer dynamic tents mapping model has some limitations because of its low dimensionality, low complexity, poor cryptographic characteristics and safety performance. In order to solve this problem, the one-dimensional integer dynamic tent map model is extended to a two-dimensional integer dynamic tent model. There is a perturbation mechanism between the sequences generated by the two-dimensional integer dynamic tents mapping model, which increases the complexity of the sequence, but the extreme value of this disturbance is not complicated and the computation is low. The model is compared with the one-dimensional integer dynamic tent map, and the self-information, mutual information, uniformity, phase space and chaos of the model are analyzed. The simulation results show that the two-dimensional integer dynamic tents mapping model overcomes the defects of one-dimensional model with poor homogeneity, and its iterative generation sequence has good uniform distribution characteristics and mutual independence, and its cryptographic characteristics are more perfect.

Key words: two-dimensional tent map, integer, dynamic tent map, complexity

摘要： 帐篷映射由于具有均匀分布特性，被广泛应用到密码学研究领域。一维整数动态帐篷映射模型由于其维数低，复杂度较低，密码学特性和安全性能较差，在密码学领域的应用有着一定的局限性。为了解决这一问题，将一维整数动态帐篷映射模型拓展为二维整数动态帐篷映射模型。二维整数动态帐篷映射模型产生的序列之间存在着扰动机制，进而增加了序列的复杂度，但这种扰动极值并不复杂，计算量较低。将该模型与一维整数动态帐篷映射进行了比较，并分析了该模型的自信息、互信息、均匀性、相空间、混沌性等特性。仿真结果表明，二维整数动态帐篷映射模型克服了一维模型均匀性较差的缺陷，其迭代生成序列具有良好的均匀分布特性及相互独立性，其密码学特性更加完善。

关键词: 二维帐篷映射, 整数, 动态帐篷映射, 复杂度