State of the art and future perspectives on security metrics and their applications

In modern society, security issues of IT Systems are intertwined with interdisciplinary aspects, from social life to sustainability, and threats endanger many aspects of every- one’s daily life. To address the problem, it’s important that the systems that we use guarantee a certain degree of security, but to achieve this, it is necessary to be able to give a measure to the amount of security. Measuring security is not an easy task, but many initiatives, including European regulations, want to make this possible. One method of measuring security is based on the use of security metrics: those are a way of assessing, from various aspects, vulnera- bilities, methods of defense, risks and impacts of successful attacks then also efficacy of reactions, giving precise results using mathematical and statistical techniques. I have done literature research to provide an overview on the meaning, the effects, the problems, the applications and the overall current situation over security metrics, with particular emphasis in giving practical examples. This thesis starts with a summary of the state of the art in the field of security met- rics and application examples to outline the gaps in current literature, the difficulties found in the change of application context, to then advance research questions aimed at fostering the discussion towards the definition of a more complete and applicable view of the subject. Finally, it stresses the lack of security metrics that consider interdisciplinary aspects, giving some potential starting point to develop security metrics that cover all as- pects involved, taking the field to a new level of formal soundness and practical usability.

Diagnosing criticality in symmetric and chiral clock models

Quantum clock models are statistical mechanical spin models which may be regarded as a sort of bridge between the one-dimensional quantum Ising model and the one-dimensional quantum XY model. This thesis aims to provide an exhaustive review of these models using both analytical and numerical techniques. We present some important duality transformations which allow us to recast clock models into different forms, involving for example parafermions and lattice gauge theories. Thus, the notion of topological order enters into the game opening new scenarios for possible applications, like topological quantum computing. The second part of this thesis is devoted to the numerical analysis of clock models. We explore their phase diagram under different setups, with and without chirality, starting with a transverse field and then adding a longitudinal field as well. The most important observables we take into account for diagnosing criticality are the energy gap, the magnetisation, the entanglement entropy and the correlation functions.