The secret life of software applications

One of the most undervalued problems by smartphone users is the security of data on their mobile devices. Today smartphones and tablets are used to send messages and photos and especially to stay connected with social networks, forums and other platforms. These devices contain a lot of private information like passwords, phone numbers, private photos, emails, etc. and an attacker may choose to steal or destroy this information. The main topic of this thesis is the security of the applications present on the most popular stores (App Store for iOS and Play Store for Android) and of their mechanisms for the management of security. The analysis is focused on how the architecture of the two systems protects users from threats and highlights the real presence of malware and spyware in their respective application stores. The work described in subsequent chapters explains the study of the behavior of 50 Android applications and 50 iOS applications performed using network analysis software. Furthermore, this thesis presents some statistics about malware and spyware present on the respective stores and the permissions they require. At the end the reader will be able to understand how to recognize malicious applications and which of the two systems is more suitable for him. This is how this thesis is structured. The first chapter introduces the security mechanisms of the Android and iOS platform architectures and the security mechanisms of their respective application stores. The Second chapter explains the work done, what, why and how we have chosen the tools needed to complete our analysis. The third chapter discusses about the execution of tests, the protocol followed and the approach to assess the “level of danger” of each application that has been checked. The fourth chapter explains the results of the tests and introduces some statistics on the presence of malicious applications on Play Store and App Store. The fifth chapter is devoted to the study of the users, what they think about and how they might avoid malicious applications. The sixth chapter seeks to establish, following our methodology, what application store is safer. In the end, the seventh chapter concludes the thesis.

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.