A New Family of Generalized 3D Cat Maps

TL;DR

This paper introduces a new family of 36 3D chaotic cat maps with enhanced parameters and longer periods, improving their cryptographic security and extending applicability to higher dimensions.

Contribution

It proposes a novel family of 3D cat maps with more parameters and longer periods, generalizing existing models and enabling extensions to higher dimensions.

Findings

More independent map parameters than existing 3D cat maps

Longer average period lengths for the new family

Can be extended to higher-dimensional cases

Abstract

Since the 1990s chaotic cat maps are widely used in data encryption, for their very complicated dynamics within a simple model and desired characteristics related to requirements of cryptography. The number of cat map parameters and the map period length after discretization are two major concerns in many applications for security reasons. In this paper, we propose a new family of 36 distinctive 3D cat maps with different spatial configurations taking existing 3D cat maps [1]-[4] as special cases. Our analysis and comparisons show that this new 3D cat maps family has more independent map parameters and much longer averaged period lengths than existing 3D cat maps. The presented cat map family can be extended to higher dimensional cases.