Transport layer security (TLS) protocol is the most widely used security protocol in modern network communications. However, protocol vulnerabilities caused by the design of the network protocol or its implementation by programmers emerge one after another. Meanwhile, various versions of TLS protocol implementations exhibit different behavioral characteristics. Researchers are attempting to find the differences in protocol implementations based on differential testing, which is conducive to discovering the vulnerabilities. This paper provides a solution to find the differences more efficiently by targeting the TLS protocol handshake process. The differences of different implementations during the fuzzing process, such as code coverage and response data, are taken to guide the mutation of test cases, and the seeds are mutated based on the TLS protocol syntax. In addition, the definition of duplicate discrepancies is theoretically explored to investigate the root cause of the discrepancies and to reduce the number of duplicate cases that are caused by the same reason. Besides, the necessary conditions for excluding duplicate cases are further analyzed to develop the deduplication strategy. The proposed method is developed based on open-source tools, i.e., NEZHA and TLS-diff. Three types of widely used TLS protocol implementations, i.e., OpenSSL, BoringSSL, and LibreSSL, are taken for experimental testing. The experimental results show that the proposed method can effectively improve the ability to find differences between different implementations. Under the same test scale or the same time, the amount of discrepancies increases by about 20% compared to TLS-diff, indicating the effectiveness of the deduplication strategy.

For a class of two-dimensional nonlinear partial differential equation with the source term,a simple lattice Boltzmann model with amending function is proposed and studied using the Chapman-Enskog expansion technique and multiple-scale analysis. In this paper, some partial differential equation are simulated, the numerical results and exact solutions are shown to be almost completely fitting with each other. The lattice Boltzmann method is further extended to two-dimensional partial differential equation.

The lattice Boltzmann method (LBM) was proposed as a novel mesoscopic numerical method, and is widely used to simulate complex nonlinear fluid systems. In this paper, we develop a lattice Boltzmann model with amending function and source term to solve a class of initial value problems of the FitzHugh Nagumo systems, which arises in the periodic oscillations of neuronal action potential under constant current stimulation higher than the threshold value. Firstly, we construct a non-standard lattice Boltzmann model with the proper amending function and source term. For different evolution equations, local equilibrium distribution functions and amending function are selected, and the nonlinear FitzHugh Nagumo systems can be recovered correctly by using the Chapman Enskog multi-scale analysis. Secondly, through the integral technique, we obtain a new method on how to construct the amending function. In order to guarantee the stability of the present model, the L stability of the lattice Boltzmann model is analyzed by using the extremum principle, and we get a sufficient condition for the stability that is the initial value u0(x) must satisfy |u0(x)|1 and the parameters must satisfy i-(1+)(t)/(x), (i=1-4). Thirdly, based on the results of the grid independent analysis and numerical simulation, it can be concluded that the present model is convergent with two order space accuracy. Finally, some initial boundary value problems with analytical solutions are simulated to verify the effectiveness of the present model. The results are compared with the analytical solutions and numerical solutions obtained by the modified finite difference method (MFDM). It is shown that the numerical solutions agree well with the analytical solutions and the global relative errors obtained by the present model are smaller than the MFDM. Furthermore, some test problems without analytical solutions are numerically studied by the present model and the MFDM. The results show that the numerical solutions obtained by the present model are in good agreement with those obtained by the MFDM, which can validate the effectiveness and stability of the LBM. In conclusion, our model not only can enrich the applications of the lattice Boltzmann model in simulating nonlinear partial difference equations, but also help to provide valuable references for solving more complicated nonlinear partial difference systems. Therefore, this research has important theoretical significance and application value.