Period distribution analysis of some linear maps

This paper discusses period properties of some linear maps which are employed in various applications such as image encryption, public key cryptography and watermarking. Conditions for the bijectiveness of such maps and the existence of a period are presented. Period structure is also given. Then, the recurrence equation theory is adopted to address the period distribution problem. Finally, a framework to solve the problem is proposed with a demonstration of its effectiveness and efficiency into some applications.

► Period properties of some linear maps, which are often employed in various applications, are analyzed.
► Conditions for bijectiveness and existence of a period of a linear map are given.
► Recurrence equation theory is adopted to model the period distribution problem.
► A framework to solve the period distribution problem is proposed.
► Some applications are also presented to demonstrate the effectiveness and efficiency of the proposed framework.