Pseudo Random Numbers Generator Based On Chaotic Systems

The arrival of big data lead to the rapid expansion of information and there exists lots of potential safety problems in the dissemination of information,then the security of cryptographic algorithm that encrypts and decrypts information received widespread attention.Among them,the generated pseudo-random sequence have been widely used in information encryption,electronic transactions,network transmission and other secure communication fields.Therefore,how to construct a PRNG with high safety and efficiency turn into a current research hotspot.In view of the good randomness,unpredictability and ergodicity of chaos,meanwhile,the low-dimensional chaotic system has the advantages of simple structure and can generate series within very short time while the high-dimensional chaotic system has more complex chaotic characteristics and stronger randomness,we design a chaos-based PRNG by combining the characteristics of two kinds of different chaotic maps.The main work is as follows:Firstly,to overcome the influence of finite precision effect on the degradation characteristics of chaotic system and improve the statistical performance of the generated random sequences,a new method of generating 64 bits pseudo random numbers based on 6th-order CNN is provided.With this method,we reduced the effect of chaotic degradation on the performance of the random numbers by controlling the input and output of 6th-order CNN in each iteration.At the same time,the repetition of the generated sequence was effectively avoided by the XOR of random sequence produced by Logistic map and variable parameters.Meanwhile,the key space and the period of output sequences were enlarged.The PRNG by the new design is easy to implement in software.It can generate 64 bits pseudo random numbers each time and has a high generating rate.The simulation test results show that the generated random numbers can pass the statistical test suite NIST SP800-22 and GM-T0005-2012 completely.It displays good randomness and can be applied in the fields of information security,such as secure communication.Besides,through the key space analysis,key sensitivity analysis,correlation analysis of generated sequences and attack analysis of the method,it is proved that the pseudo-random number generation method designed in this paper has high security.Finally,we applied the generated random sequence to digital images by XOR operation.Comparing the statistics performance(entropy analysis,histogram analysis and correlation analysis)of the images before and after encryption,we find the original information was covered totally.And the encryption method is secure enough to resist entropy attack and statistical attack.Therefore,our designed PRNG has high practicality and can generate pseudo random sequence with good statistical performance.