Stream cipher systems have a great role in data encryption field. The security of these systems is a direct function of the complexity of the used key sequence generators. Many scientific efforts has been made to develop a complex structure of these generators that ensures the nonlinearity and complexity of the generated pseudorandom sequences. Fuzzy logic is one of the technologies that allow realistic complex models of the real world to be defined with some simple and understandable fuzzy variables and fuzzy rules. The pseudorandom sequences generators (used in stream ciphers) can be described by a fuzzy set and degree of membership to a certain parameters of the key sequence generators. (Muna, 1999), (Elmer, 2012), (Marc & Lars, 2005).
Fuzzy sets are a further development of the mathematical concept of a set. Sets were first studied formally by the German mathematician Geory Cantor (1845-1918). His theory of sets met much resistance during his lifetime, but nowadays most mathematicians believe it is possible to express most, if not all, of the mathematics in the language of set theory. Many researchers are considering the consequences of 'fuzzifying' set theory, and much mathematical literature is the result (Peter, 1995). The notion of fuzzy set was introduced by Lotfi Zadeh in 1965. He developed many of the methods of fuzzy logic based on this single notion. It took a couple of decades for the rationale of fuzzy sets to be understood and applied by other scientists. Fuzzy Logic, as a robust soft computing method has demonstrated its ability in many different applications. Moreover, fuzzy systems have several important features which make them suitable for many requested applications. Various methods have been suggested for automatic generation and adjustment of fuzzy rules without the aid of human experts.