Abstract:

The one-dimensional and two-dimensional integer tent maps are analyzed, and a three-dimensional dynamic integer tent map is proposed. Based on the extended dimension perturbations are applied to further extend the model accuracy. The dynamic behaviors of the integer tent map system under the disturbance mechanism, computational precision and spatial dimension are studied. The information entropy, mutual information, difference characteristic, Lyapunov exponent and randomness of the three-dimensional are simulated and analyzed. The results indicate that disturbance mechanism, computational precision and spatial dimension have a profound impact on the dynamic behaviors of the integer tent map. The three-dimensional integer tent map realized with high perturbation and high precision have excellent cryptographic performance.

Key words: dynamic integer tent map, disturbance, precision, dimension

摘要：

对一维和二维整数帐篷映射进行分析，提出三维动态整数帐篷映射。在扩展维数的基础上施加扰动，进一步扩展模型的精度，研究了扰动机制、计算精度及空间维度作用下整数帐篷映射系统动力学行为产生的变化。对三维模型的信息熵、互信息、差值特性、分布特性、最大Lyapunov指数及随机性进行仿真分析。结果表明，扰动机制、计算精度及空间维数均对动态整数帐篷映射的混沌动力学行为有深刻的影响，在高扰动、高精度情况下实现的三维动态整数帐篷映射具有优越的密码学性能。

关键词: 动态整数帐篷映射, 扰动, 精度, 维度