Pseudo Random Number Generators (PRNGs) are widely used in science and technology, it is a critical component in modern cryptographic systems, communication systems, statistical simulation systems and any scientific area incorporating Monte Carlo methods~\cite{Vadim2011692,Marchi20093328,citeulike:867581,thecolourblue:1046} and many others. By the way, the Monte Carlo method appeared on the scientific scene in the late 1940s, for problems involving particle scattering in nuclear physics~\cite{Dyadkin1997258}. In the present era, there are few scientific fields that do not use random number. One of the most important applications of PRNGs is in cryptography to generate cryptographic keys, and to randomly initialize certain variables in cryptographic protocols.
-Moreover, the idea o f applying chaos theory to randomness has produced important works very recently ~\cite{james1995,Gonzalez1999109,Ergun2007235,Zhou20093442,Gonzalez2002259,Behnia20113455}. Chaos theory has been established since 1970s by many different research areas, such as physics, mathematics, engineering, and biology, etc. ~\cite{Hao1993}. Since 1990s, many researchers have noticed that there exists the close relationship between chaos and cryptography ~\cite{Brown1996,Fridrich98symmetricciphers}; many properties of chaotic systems have their corresponding counterparts in traditional cryptosystems. Chaotic systems have several significant features favorable to secure communications, such as ergodicity, sensitivity to initial condition, control parameters and random like behaviour, which can be connected with some
+Moreover, the idea o f applying chaos theory to randomness has produced important works very recently ~\cite{james1995,Gonzalez1999109,Ergun2007235,Zhou20093442,Gonzalez2002259,Behnia20113455}. Chaos theory has been established since 1970s by many different research areas, such as physics, mathematics, engineering, and biology, etc. ~\cite{Hao1993}. Since 1990s, many researchers have noticed that there exists the close relationship between chaos and cryptography ~\cite{Brown1996,Fridrich98symmetricciphers,Zaher20113721,Wong200367,Roland2001429,MS199850}; many properties of chaotic systems have their corresponding counterparts in traditional cryptosystems. Chaotic systems have several significant features favorable to secure communications, such as ergodicity, sensitivity to initial condition, control parameters and random like behaviour, which can be connected with some
conventional cryptographic properties of good ciphers, such as confusion/diffusion. With all these advantages scientists
expected to introduce new and powerful tools of chaotic cryptography. Cryptography is the art of achieving security by
encoding messages to make them non-readable. Nowaday, some efficient techniques for encoding based on discrete time chaotic systems are presented in ~\cite{Djema2009,Belmouhoub2005}. A good random number generation improves the cryptographic security ~\cite{Behnia2008408}.
