Probabilistic Opacity for Markov Decision Processes

Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an external observer, the value of interest for opacity is a measure of the set of runs disclosing the secret. We extend this definition to the richer framework of Markov decision processes, where non deterministic choice is combined with probabilistic transitions, and we study related decidability problems with partial or complete observation hypotheses for the schedulers. We prove that all questions are decidable with complete observation and $\omega$-regular secrets. With partial observation, we prove that all quantitative questions are undecidable but the question whether a system is almost surely non opaque becomes decidable for a restricted class of $\omega$-regular secrets, as well as for all $\omega$-regular secrets under finite-memory schedulers

Probabilistic Disclosure: Maximisation vs. Minimisation

We consider opacity questions where an observation function provides to an external attacker a view of the states along executions and secret executions are those visiting some state from a fixed subset. Disclosure occurs when the observer can deduce from a finite observation that the execution is secret, the epsilon-disclosure variant corresponding to the execution being secret with probability greater than 1 - epsilon. In a probabilistic and non deterministic setting, where an internal agent can choose between actions, there are two points of view, depending on the status of this agent: the successive choices can either help the attacker trying to disclose the secret, if the system has been corrupted, or they can prevent disclosure as much as possible if these choices are part of the system design. In the former situation, corresponding to a worst case, the disclosure value is the supremum over the strategies of the probability to disclose the secret (maximisation), whereas in the latter case, the disclosure is the infimum (minimisation). We address quantitative problems (comparing the optimal value with a threshold) and qualitative ones (when the threshold is zero or one) related to both forms of disclosure for a fixed or finite horizon. For all problems, we characterise their decidability status and their complexity. We discover a surprising asymmetry: on the one hand optimal strategies may be chosen among deterministic ones in maximisation problems, while it is not the case for minimisation. On the other hand, for the questions addressed here, more minimisation problems than maximisation ones are decidable

Probabilistic Opacity in Refinement-Based Modeling

Given a probabilistic transition system (PTS) $\cal A$ partially observed by an attacker, and an $\omega$-regular predicate $\varphi$over the traces of $\cal A$, measuring the disclosure of the secret $\varphi$ in $\cal A$ means computing the probability that an attacker who observes a run of $\cal A$ can ascertain that its trace belongs to $\varphi$. In the context of refinement, we consider specifications given as Interval-valued Discrete Time Markov Chains (IDTMCs), which are underspecified Markov chains where probabilities on edges are only required to belong to intervals. Scheduling an IDTMC $\cal S$ produces a concrete implementation as a PTS and we define the worst case disclosure of secret $\varphi$ in ${\cal S}$ as the maximal disclosure of $\varphi$ over all PTSs thus produced. We compute this value for a subclass of IDTMCs and we prove that refinement can only improve the opacity of implementations

Probabilistic Opacity for a Passive Adversary and its Application to Chaum\u27s Voting Scheme

A predicate is opaque for a given system, if an adversary will never be able to establish truth or falsehood of the predicate for any observed computation. This notion has been essentially introduced and studied in the context of transition systems whether describing the semantics of programs, security protocols or other systems. In this paper, we are interested in studying opacity in the probabilistic computational world. Indeed, in other settings, as in the Dolev-Yao model for instance, even if an adversary is $99\%$ sure of the truth of the predicate, it remains opaque as the adversary cannot conclude for sure. In this paper, we introduce a computational version of opacity in the case of passive adversaries called cryptographic opacity. Our main result is a composition theorem: if a system is secure in an abstract formalism and the cryptographic primitives used to implement it are secure, then this system is secure in a computational formalism. Security of the abstract system is the usual opacity and security of the cryptographic primitives is IND-CPA security. To illustrate our result, we give two applications: a short and elegant proof of the classical Abadi-Rogaway result and the first computational proof of Chaum\u27s visual electronic voting scheme

Quantitative Verification of Opacity Properties in Security Systems

Preprin

Verifying Opacity Properties in Security Systems

We delineate a methodology for the specification and verification of flow security properties expressible in the opacity framework. We propose a logic, opacTL, for straightforwardly expressing such properties in systems that can be modelled as partially observable labelled transition systems. We develop verification techniques for analysing property opacity with respect to observation notions. Adding a probabilistic operator to the specification language enables quantitative analysis and verification. This analysis is implemented as an extension to the PRISM model checker and illustrated via a number of examples. Finally, an alternative approach to quantifying the opacity property based on entropy is sketched

Proceedings of the 3rd International Workshop on Formal Aspects in Security and Trust (FAST2005)

The present report contains the pre-proceedings of the third international Workshop on Formal Aspects in Security and Trust (FAST2005), held in Newcastle upon Tyne, 18-19 July 2005. FAST is an event affliated with the Formal Methods 2005 Congress (FM05). The third international Workshop on Formal Aspects in Security and Trust (FAST2005) aims at continuing the successful effort of the previous two FAST workshop editions for fostering the cooperation among researchers in the areas of security and trust. The new challenges offered by the so-called ambient intelligence space, as a future paradigm in the information society, demand for a coherent and rigorous framework of concepts, tools and methodologies to provide user\u27s trust&confidence on the underlying communication/interaction infrastructure. It is necessary to address issues relating to both guaranteeing security of the infrastructure and the perception of the infrastructure being secure. In addition, user confidence on what is happening must be enhanced by developing trust models effective but also easily comprehensible and manageable by users

Verifying Opacity Properties in Security Systems

We delineate a methodology for the specification and verification of flow security properties expressible in the opacity framework. We propose a logic, opacTL, for straightforwardly expressing such properties in systems that can be modelled as partially observable labelled transition systems. We develop verification techniques for analysing property opacity with respect to observation notions. Adding a probabilistic operator to the specification language enables quantitative analysis and verification. This analysis is implemented as an extension to the PRISM model checker and illustrated via a number of examples. Finally, an alternative approach to quantifying the opacity property based on entropy is sketched