A New Family of Generalized 3D Cat Maps

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.