  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.
