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Voting systems aim to provide trustworthiness in elections; however, they have always been a target of malicious behaviours due to difficulties in designing such complex systems and the enormous value of controlling the election results, causing unfair election outcome, loss of personal privacy and trust in democracy. This thesis aims to shed light on how voting systems, in particular, paper-based ones can be evaluated so as to provide a better level of confidence in their trustworthiness. This thesis advances the evaluation of the paper-based voting systems using formal methods with automated analysis. In analysis of security protocols, the formal definitions of protocol requirements need to be constructed precisely. To this end, a formal framework regarding the anonymity requirement has been given and demonstrated to be appropriate for the analysis of voting systems. Similarly, it has been demonstrated that the assumptions under which voting systems are secure should be well-defined for a rigorous security analysis with the automated analysis of the Three Ballot voting system. Moreover, a novel approach has been proposed to analyse cryptographic voting systems under a passive attacker model using the Pret a Voter voting system as case study. Finally, an active powerful attacker has been adapted into the analysis of voting systems, and an automated formal analysis of vVote voting system has been conducted , which is under development for use in Victorian Electoral Commission (VEC) elections, Australia in 2014. With the analyses of voting systems performed in this thesis, the formal approach developed here has been demonstrated to be successful in the automated analysis of such complex systems using the process; algebra, Communicating Sequential Processes (CSP), and the model checker, Failures-Divergence Refinement (FDR)

With an overall theme of information flow, this thesis has two main strands. In the first part of the thesis, I review existing information flow properties, highlighting a recent definition known as opacity [25]. Intuitively, a predicate cP is opaque if for every run in which cP is true, there exists an indistinguishable run in which it is false, where a run can be regarded as a sequence of events. Hence, the observer is never able to establish the truth of cPo The predicate cP can be defined according to requirements of the system, giving opacity a great deal of flexibility and versatility. Opacity is then studied in relation to several well-known definitions for information flow. As will be shown, several of these properties can be cast as variations of opacity, while others have a relationship by implication with the opacity property [139]. This demonstrates the flexibility of opacity, at the same time establishing its distinct character. In the second part of the thesis, I investigate information flow in voting systems. Pret a Voter [36] is the main exemplar, and is compared to other schemes in the case study. I first analyse information flow in Pret a Voter and the FOO scheme [59], concentrating on the core protocols. The aim is to investigate the security requirements of each scheme, and the extent to which they can be captured using opacity. I then discuss a systems-based analysis of Pret a Voter [163], which adapts and extends an earlier analysis of the Chaum [35] and Neff [131]' [132]' [133] schemes in [92]. Although this analysis has identified several potential vulnerabilities, it cannot be regarded as systematic, and a more rigorous approach may be necessary. It is possible that a combination of the information flow and systems- based analyses might be the answer. The analysis of coercion-resistance, which is performed on Pret a Voter and the FOO scheme, may exemplify this more systematic approach. Receipt-freeness usually means that the voter is unable to construct a proof of her vote. Coercion-resistance is a stronger property in that it accounts for the possibility of interaction between the coercer and the voter during protocol execution. It appears that the opacity property is ideally suited to expressing the requirements for coercion-resistance in each scheme. A formal definition of receipt-freeness cast as a variation of opacity is proposed [138], together with suggestions on how it might be reinforced to capture coercion-resistance. In total, the thesis demonstrates the remarkable flexibility of opacity, both in expressing differing security requirements and as a tool for security analysis. This work lays the groundwork for future enhancement of the opacity framework.

Cette thèse porte sur l'étude de différents aspects de la sécurité des protocoles de vote électronique à distance. Ces protocoles décrivent comment organiser des élections par Internet de manière sécurisée. Ils ont notamment pour but d'apporter des garanties de secret du vote, et de vérifiabilité - ie, il doit être possible de s'assurer que les votes sont correctement comptabilisés. Nos contributions portent sur deux aspects principaux. Premièrement, nous proposons une nouvelle technique d'analyse automatique de propriétés d'équivalence, dans le modèle symbolique. De nombreuses propriétés en lien avec la vie privée s'expriment comme des propriétés d'équivalence, telles que le secret du vote en particulier, mais aussi l'anonymat ou la non-traçabilité. Notre approche repose sur le typage: nous mettons au point un système de typage qui permet d'analyser deux protocoles pour prouver leur équivalence. Nous montrons que notre système de typage est correct, c'est-à-dire qu'il implique effectivement l'équivalence de traces, à la fois pour des nombres bornés et non bornés de sessions. Nous comparons l'implémentation d'un prototype de notre système avec les autres outils existants pour l'équivalence symbolique, sur divers protocoles de la littérature. Cette étude de cas montre que notre procédure est bien plus efficace que la plupart des autres outils - au prix d'une perte de précision (notre outil peut parfois échouer à prouver certaines équivalences). Notre seconde contribution est une étude des définitions du secret du vote et de la vérifiabilité - ou, plus précisément, la vérifiabilité individuelle, une propriété qui requiert que chaque votant soit en mesure de vérifier que son propre vote a bien été pris en compte. Nous prouvons, aussi bien dans les modèles symboliques que calculatoire, que le secret du vote implique la vérifiabilité individuelle, alors même que l'intuition et des résultats voisins déjà établis semblaient indiquer que ces deux propriétés s'opposent. Notre étude met également en évidence une limitation des définitions existantes du secret du vote par jeux cryptographiques : elles supposent une urne honnête, et par conséquent expriment des garanties significativement plus faibles que celles que les protocoles visent à assurer. Nous proposons donc une nouvelle définition (par jeu) du secret du vote, contre une urne malhonnête. Nous relions notre définition à une notion de secret du vote par simulation, pour montrer qu'elle apporte des garanties fortes. Enfin, nous menons une étude de cas sur plusieurs systèmes de vote existants. / In this thesis we study several aspects of the security of remote electronic voting protocols. Such protocols describe how to securely organise elections over the Internet. They notably aim to guarantee vote privacy - ie, votes must remain secret -and verifiability - it must be possible to check that votes are correctly counted. Our contributions are on two aspects. First, we propose a new approach to automatically prove equivalence properties in the symbolic model. Many privacy properties can be expressed as equivalence properties, such as in particular vote privacy, but also anonymity or unlinkability. Our approach relies on typing: we design a type system that can typecheck two protocols to prove their equivalence. We show that our type system %, together with some additional conditions on the messages exchanged by the protocols, soundly implies trace equivalence, both for bounded and unbounded numbers of sessions. We compare a prototype implementation of our typechecker with other existing tools for symbolic equivalence, on a variety of protocols from the literature. This case study shows that our procedure is much more efficient than most other tools - at the price of losing precision (our tool may fail to prove some equivalences). Our second contribution is a study of the definitions of privacy and verifiability - more precisely, individual verifiability, a property that requires each voter to be able to check that their own vote is counted. We prove that, both in symbolic and computational models, privacy implies individual verifiability, contrary to intuition and related previous results that seem to indicate that these two properties are opposed. Our study also highlights a limitation of existing game-based definitions of privacy: they assume the ballot box is trusted, which makes for significantly weaker guarantees than what protocols aim for. Hence we propose a new game-based definition for vote privacy against a dishonest ballot box. We relate our definition to a simulation-based notion of privacy, to show that it provides meaningful guarantees, and conduct a case study on several voting schemes.