The Research On Heat Flow Cryptosystem Based On The Method Of Reproducting Kernel

Network communication technology has already come into all aspects of social life, information communication has become more and more popular, human society will enter into the digital era. It is a important tool to exchange data information in human society and therefore the requirement of data transmission over network becomes more and more urgent.The heat flow cryptosystem with the classical backward heat flow problems, taking partial differential equation and the inverse problem as a tool could handle discrete information, and continuous information, and be suitable for images and other multi-dimensional information. Because encryption and decryption involved complex and little results of higher-order partial differential equations at present, this system had strong anti-attack ability. The characteristics of the system made it be applied in the code field. This system adopts the pseudo-parabolic partial differential equation for a cipher coder and therefore the method study on Sobolev equation is necessary which has the fast calculation and high precision. However, reasonable precision and reliability numerical solution depends on numerical method to a large extent. So it is especially important to find an algorithm who meets high accuracy, good stability, less computation and good convergence. The equations on the linear and nonlinear model were solved by the reproducing kernel method respectively, this method is based on the theory of the reproducing kernel space. The reproducing kernel spaces are constructed with the initial boundary value problem, we obtain the reproducing kernel function, by which the complete normal orthogonal system is constructed. The exact solution of the system is represented in the form of series. By truncating the series, the approximate solution uniformly converges to the exact solution. Finally, simulation experiments and security analysis are present by the proposed method. Results obtained and theory analysis show that the heat flow cryptosystem is realized by the computer correctly and the proposed method is stable, high calculative efficiency and computational accuracy.