n -Dimensional Discrete Cat Map Generation Using Laplace Expansions

Different from existing methods that use matrix multiplications and have high computation complexity, this paper proposes an efficient generation method ofn-dimensional (nD) Cat maps using Laplace expansions. New parameters are also introduced to control the spatial configurations of thenDCat matrix. Thus, the proposed method provides an efficient way to mix dynamics of all dimensions at one time. To investigate its implementations and applications, we further introduce a fast implementation algorithm of the proposed method with time complexityO(n⁴)and a pseudorandom number generator using the Cat map generated by the proposed method. The experimental results show that, compared with existing generation methods, the proposed method has a larger parameter space and simpler algorithm complexity, generatesnDCat matrices with a lower inner correlation, and thus yields more random and unpredictable outputs ofnDCat maps.