Security Analysis While Transitioning from Monolithic Applications to Microservices

Microservice architectures have evolved as an enticing alternative to more typical monolithic software application approaches. Microservices give various benefits in terms of code base knowledge, deployment, testability, and scalability. As the information technology (IT) industry expands, it makes sense for IT behemoths to adopt the microservice, but new software solutions creates new security vulnerabilities, as the technology is young and the faults have not been adequately mapped out. Authentication and authorization are key components of any software with a significant number of users. However, owing to the lack of microservice research, which derives from their relatively young, there are no specified design standards for how authentication and authorization are best performed in a microservice. This thesis analizes existing microservice in order to safeguard it using a security design pattern for authentication and authorization. Different security patterns were assessed and different degrees of security helped in identifying an acceptable security vs. performance trade-off.The objective was to strengthen the patterns' validity as known security patterns. Another purpose was to establish a security pattern that was suitable for the microservice

A determining form for the damped driven Nonlinear Schr\"odinger Equation- Fourier modes case

In this paper we show that the global attractor of the 1D damped, driven, nonlinear Schr\"odinger equation (NLS) is embedded in the long-time dynamics of a determining form. The determining form is an ordinary differential equation in a space of trajectories $X=C_b^1(\mathbb{R}, P_mH^2)$ where $P_m$ is the $L^2$-projector onto the span of the first $m$ Fourier modes. There is a one-to-one identification with the trajectories in the global attractor of the NLS and the steady states of the determining form. We also give an improved estimate for the number of the determining modes

A determining form for the subcritical surface quasi-geostrophic equation

We construct a determining form for the surface quasi-geostrophic (SQG) equation with subcritical dissipation. In particular, we show that the global attractor for this equation can be embedded in the long-time dynamics of an ordinary differential equation (ODE) called a determining form. Indeed, there is a one-to-one correspondence between the trajectories in the global attractor of the SQG equation and the steady state solutions of the determining form. The determining form is a true ODE in the sense that its vector field is Lipschitz. This is shown by combining De Giorgi techniques and elementary harmonic analysis. Finally, we provide elementary proofs of the existence of time-periodic solutions, steady state solutions, as well as the existence of finitely many determining parameters for the SQG equation

A Determining Form for the Subcritical Surface Quasi-Geostrophic Equation

We construct a determining form for the surface quasi-geostrophic (SQG) equation with subcritical dissipation. In particular, we show that the global attractor for this equation can be embedded in the long-time dynamics of an ordinary differential equation (ODE) called a determining form. Indeed, there is a one-to-one correspondence between the trajectories in the global attractor of the SQG equation and the steady state solutions of the determining form. The determining form is a true ODE in the sense that its vector field is Lipschitz. This is shown by combining De Giorgi techniques and elementary harmonic analysis. Finally, we provide elementary proofs of the existence of time-periodic solutions, steady state solutions, as well as the existence of finitely many determining parameters for the SQG equation