The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given functional and defines a functor on (complete) pseudometric spaces. Other notions of behavioural pseudometrics have also been proposed, one of them ($ε$-distance) based on $ε$-bisimulation. $ε$-Distance has the advantages that it is intuitively easy to understand, it relates systems that are conceptually close (for example, an imperfect implementation is close to its specification), and it comes equipped with a natural notion of $ε$-coupling. Finally, this distance is easy to compute. We show that $ε$-distance is also the greatest fixpoint of a functional and provides a functor. The latter is obtained by replacing the Kantorovich distance in the lifting functor with the Lévy-Prokhorov distance. In addition, we show that $ε$-couplings and $ε$-bisimulations have an appealing coalgebraic characterization.

Cryptographic approaches, such as secure multiparty computation, can be used to securely compute a function of a distributed graph without centralizing the data of each participant. However, the output of the protocol can leak sensitive information about the structure of the original graph. In particular, we propose an approach by which an adversary observing the result of a private protocol for the computation of the number of common neighbors between all pairs of vertices, can reconstruct the adjacency matrix of the graph. In fact, this can only be done up to co-squareness, a notion we introduce, as two different graphs can have the same matrix of common neighbors. To realize this, we consider two adversary models, one who observes the common neighbors matrix only and a more informed one that has partial knowledge of the original graph. Our results demonstrate that, from their common neighbors matrix, graphs can be reconstructed with high accuracy (up to co-squareness). The proposed reconstruction is also interesting in itself from the point of view of graph theory.

Insider threats are a growing concern for organizations due to the amount of damage that their members can inflict by combining their privileged access and domain knowledge. Nonetheless, the detection of such threats is challenging, precisely because of the ability of the authorized personnel to easily conduct malicious actions and because of the immense size and diversity of audit data produced by organizations in which the few malicious footprints are hidden. In this paper, we propose an unsupervised insider threat detection system based on audit data using Bayesian Gaussian Mixture Models. The proposed approach leverages a user-based model to optimize specific behaviors modelization and an automatic feature extraction system based on Word2Vec for ease of use in a real-life scenario. The solution distinguishes itself by not requiring data balancing nor to be trained only on normal instances, and by its little domain knowledge required to implement. Still, results indicate that the proposed method competes with state-of-the-art approaches that use stronger hypotheses, presenting a good recall of 88%, accuracy and true negative rate of 93%, and a false positive rate of 6.9%. For our experiments, we used the benchmark dataset CERT version 4.2.

Flow-sensitive labels used by dynamic enforcement mechanisms might themselves encode sensitive information, which can leak. Metalabels, employed to represent the sensitivity of labels, exhibit the same problem. This paper derives a new family of enforcers-k-Enf, for 2 ≤ k ≤ ∞-that uses label chains, where each label defines the sensitivity of its predecessor. These enforcers satisfy Block-safe Noninterference (BNI), which proscribes leaks from observing variables, label chains, and blocked executions. Theorems in this paper characterize where longer label chains can improve the permissiveness of dynamic enforcement mechanisms that satisfy BNI. These theorems depend on semantic attributes-k-precise, k-varying, and k-dependent-of such mechanisms, as well as on initialization, threat model, and lattice size.

This paper proposes a measure-theoretic reconstruction of the approximation schemes developed for labeled Markov processes: approximants are seen as quotients with respect to sets of temporal properties expressed in a simple logic. This gives the possibility of customizing approximants with respect to properties of interest and is thus an important step towards using automated techniques intended for finite state systems, e.g. model checking, for continuous state systems. The measure-theoretic apparatus meshes well with an enriched logic, extended with a greatest fix-point, and gives means to define approximants which retain cyclic properties of their target.

We observe that equivalence is not a robust concept in the presence of numerical information - such as probabilities-in the model. We develop a metric analogue of weak bisimulation in the spirit of our earlier work on metric analogues for strong bisimulation. We give a fixed point characterization of the metric. This makes available conductive reasoning principles and allows us to prove metric analogues of the usual algebraic laws for process combinators. We also show that quantitative properties of interest are continuous with respect to the metric, which says that if two processes are close in the metric then observable quantitative properties of interest are indeed close. As an important example of this we show that nearby processes have nearby channel capacities - a quantitative measure of their propensity to leak information.

We study approximate reasoning about continuous-state labeled Markov processes. We show how to approximate a labeled Markov process by a family of finite-state labeled Markov chains. We show that the collection of labeled Markov processes carries a Polish space structure with a countable basis given by finite state Markov chains with rational probabilities. The primary technical tools that we develop to reach these results are: a finite-model theorem for the modal logic used to characterize bisimulation; and a categorical equivalence between the category of Markov processes (with simulation morphisms) with the /spl omega/-continuous dcpo Proc, defined as the solution of the recursive domain equation Proc=/spl Pi//sub Labels/ P/sub Prob/(Proc). The correspondence between labeled Markov processes and Proc yields a logic complete for reasoning about simulation for continuous-state processes.

This paper gives a logical characterization of probabilistic bisimulation for Markov processes. Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition. Bisimulation can be characterized by several inequivalent logics; we report five in this paper and there are surely many more. We do not need any finite branching assumption yet there is no need of infinitely conjunction. We give an algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation.

In this paper we introduce a new class of labelled transition systems-Labelled Markov Processes-and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems where the state space is not necessarily discrete, it could be the reals, for example. We assume that it is a Polish space (the underlying topological space for a complete separable metric space). The mathematical theory of such systems is completely new from the point of view of the extant literature on probabilistic process algebra; of course, it uses classical ideas from measure theory and Markov process theory. The notion of bisimulation builds on the ideas of Larsen and Skou and of Joyal, Nielsen and Winskel. The main result that we prove is that a notion of bisimulation for Markov processes on Polish spaces, which extends the Larsen-Skou definition for discrete systems, is indeed an equivalence relation. This turns our to be a rather hard mathematical result which, as far as we know, embodies a new result in pure probability theory. This work heavily uses continuous mathematics which is becoming an important part of work on hybrid systems.