+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,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}.
+
+Several test suites are readily available to researchers in academia and industry who wish to analyze their newly developed PRNG. Some general purpose test suites are Diehard by George Marsaglia ~\cite{Marsaglia1996}, the National Institute of Standards and Technology Statistical Test Suite ~\cite{ANDREW2008}, and Comparative test parameters~\cite{Menezes1997}. Systematic tests of pseudorandom number generators have received much attention. Finally, The TestU01 testsuite by L'Ecuyer and Simard ~\cite{Lecuyer2009} appears to define the current state of the art in the field.
