Entropy Measurement And Security Analysis Of Non-stationary Chaotic Encryption

Chaos is a kind of quasi-randomness motion in the deterministic system.It is widely used in the field of chaotic secure communication because of its excellent properties,such as initial value sensitivity,long-term unpredictability,fast decaying autocorrelation and aperiodicity.In practical application,chaotic source is the core of chaotic secure communication system.However,there are security risks of chaotic system with fixed parameters.The attacker can estimate the parameters effectively only by intercepting the discrete sampled data of the chaotic output sequence.In order to improve the security of secure communication system,it is necessary to construct a more secure chaotic source.Shannon entropy and its extended entropy are often used to measure the security of security systems.However,these entropy formulas are all based on an ideal hypothesis,that is,the probability density function of random variables is known by the guesser.In the practical secure communication system,the attacker often does not know the probability density function of the secure system,which means that there are some limitations in constructing the secure system based on Shannon entropy and its extended entropy.In view of the above problems,the following aspects are studied and analyzed in this paper:Firstly,focusing on the limitation of Shannon entropy,a entropy formula is proposed to measure the uncertainty of the system when its probability density is unknown;To overcome the limitation of non-stationary entropy,entropy formulas are proposed to measure the uncertainty of the system when the probability density is known and unknown respectively.These work will lay a theoretical basis for secure communication.Secondly,concentrating on the security risks of the chaotic system with fixed parameters,a chaotic system with time-variant parameters is proposed.Taking Chua chaotic system as an example,the design of Chua chaotic system with time-variant parameters is introduced in detail.Based on the sampling continuous feedback control parameter estimation method and the non-stationary extended entropy proposed in this paper,the optimal parameter configuration is given.Chua chaotic system with time-variant parameters can resist the parameter estimation method and have high uncertainty.Because the probability density function of the system is unknown,its uncertainty can be even higher than that of the uniform distributionFinally,a local impulsive synchronization scheme is proposed for Chua chaotic system with time-variant parameters.Based on the theory of impulsive differential equations,the relationship between the pulse synchronization interval and the pulse feedback intensity is studied.In addition,the synchronization performance of the system is analyzed when the parameters are mismatched.Finally,the scheme of chaotic masking secure communication is designed,and the effectiveness of the scheme is verified.These work can lay a foundation for the practical application of chaotic secure communication system.