Several Application Methods Based On Chaos

In this paper, we discussed the design of several Pseudo-random Number Generator (PRNG) and True Random Number Generator (TRNG) based on chaos and a new chaos generated by switching fractional system and a novel simple way of anti-control of chaos for continuous-time linear fractional order systems. All these research are through the methods of both theoretically and numerically.We extend a class of one-dimensional smooth map. Make sure that for each desired intervals of the parameter the map’s Lyapunov exponent is positive. And then, we propose a novel parameter perturbation method based on the good property of the extended one-dimensional smooth map. We perturb the parameter r in each iteration by the real number x, generated by the iteration. Auto-correlation function and the NIST statistical test suite have been taken to illustrate the method’s randomness last; we propose the application of this method in image encryption. Experiments show that the Pseudo-random Sequences are suitable to image encryption.We propose a novel True Random Number Generator used mouse movement and a one-dimensional chaotic map. We utilize the x-coordinate of the mouse movement to be the length of an iteration segment of our True Random Numbers (TRNs), and the y-coordinate to be the initial value of this iteration segment. And when it iterates, we perturb the parameter with the real value produced by the TRNG itself. And we find that the TRNG we proposed conquers several flaws of some former mouse based TRNG. At last we take experiments and the NIST statistical test suite to test the randomness of our algorithm, results illustrate that our TRNG is suitable to produce TRNs.We analyze an existed chaos generated by an existed switching fractional system both theoretically and numerically. We try to research the relationship between the parameter of the system and the dynamic behaviors of the chaos in the analytic and the numerical ways. Then we epitomize some simple rules of generating chaos or chaos-like system by switching fractional systems. At last, we proposed a new switching fractional system, which can generate chaos or chaos-like dynamic behaviors.We propose a new algorithm to generate pseudo-random number generator, which we call Couple Map Lattice based on Discrete Chaotic Iteration (CMLDCI) that combine the couple map lattice (CML) and chaotic iteration. And we can proof that this method can be written in a form of chaos map which is under the sense of Devaney chaos. In addition, we test the new algorithm in NIST800-22statistical test suits and we use it in image encryption.We in the first time propose a way of anti-control of chaos for continuous-time linear fractional order systems. We use a simple and traditional way called tracking control, which design a control term to let the continuous-time linear fractional order systems track already chaotic systems. This anti-control of chaos needs not to count Lyapunov exponent and can be easily used in practice.