Annulling Traps & Fixed Traps in Chaos Cryptography

In recent years, the sophistication of attackers in cryptographic algorithms has been alarmingly increased in all media, wireled, optical and wireless. As a result, stronger cryptographic algorithms have been developed to assure data integrity and confidentiality, among them those that are based on chaotic functions. Chaotic functions in cryptography are natural random number generators with non repetitive behavior and yet reproducible if the chaotic function and the initial conditions are known; random number generators are key functions in almost all secure communication systems. However, we have found that under certain circumstances, the chaotic behavior of a function may be obliterated. In this paper we discuss two trap conditions in chaotic functions that are encountered under specific initial conditions; one collapses the chaotic process and we call it chaos annulling trap (CAT), and the other produces the same output and we call it chaos fixed trap (CFT). We also propose two possible methods that may help to identify functions and initial conditions that cause one of these two traps.