$n$ -Dimensional Discrete Cat Map Generation Using Laplace Expansions.

Area of Science:

• Mathematics
• Computational Science
• Chaos Theory

Background:

• Existing n-dimensional Cat map generation methods rely on matrix multiplications, leading to high computational complexity.
• There is a need for more efficient and controllable methods for generating high-dimensional Cat maps.

Purpose of the Study:

• To propose an efficient generation method for n-dimensional Cat maps using Laplace expansions.
• To introduce new parameters for controlling spatial configurations of the Cat matrix.
• To develop a fast implementation algorithm and a pseudorandom number generator based on the proposed method.

Main Methods:

• Utilized Laplace expansions for efficient generation of n-dimensional Cat maps.
• Introduced novel parameters to control spatial configurations of the Cat matrix.
• Developed a fast implementation algorithm with O(n^4) time complexity.

Main Results:

• The proposed method offers a larger parameter space and simpler algorithm complexity compared to existing methods.
• Generated n-dimensional Cat matrices exhibit lower inner correlation.
• The method yields more random and unpredictable outputs for n-dimensional Cat maps.

Conclusions:

• The proposed Laplace expansion-based method provides an efficient and controllable approach for generating n-dimensional Cat maps.
• The developed algorithm and pseudorandom number generator demonstrate practical applicability.
• This method enhances the randomness and unpredictability of Cat map outputs, beneficial for various applications.