Task-Structured Probabilistic I/O Automata

In the Probabilistic I/O Automata (PIOA) framework, nondeterministicchoices are resolved using perfect-information schedulers,which are similar to history-dependent policies for Markov decision processes(MDPs). These schedulers are too powerful in the setting of securityanalysis, leading to unrealistic adversarial behaviors. Therefore, weintroduce in this paper a novel mechanism of task partitions for PIOAs.This allows us to define partial-information adversaries in a systematicmanner, namely, via sequences of tasks.The resulting task-PIOA framework comes with simple notions of externalbehavior and implementation, and supports simple compositionalityresults. A new type of simulation relation is defined and proven soundwith respect to our notion of implementation. To illustrate the potentialof this framework, we summarize our verification of an ObliviousTransfer protocol, where we combine formal and computational analyses.Finally, we present an extension with extra expressive power, usinglocal schedulers of individual components

Using Probabilistic I/O Automata to Analyze an Oblivious Transfer Protocol

We demonstrate how to carry out cryptographic security analysis ofdistributed protocols within the Probabilistic I/O Automata frameworkof Lynch, Segala, and Vaandrager.This framework provides tools for arguing rigorously about theconcurrency and scheduling aspects of protocols, and about protocolspresented at different levels of abstraction.Consequently, it can help in making cryptographic analysis moreprecise and less susceptible to errors.We concentrate on a relatively simple two-party Oblivious Transferprotocol, in the presence of a semi-honest adversary (essentially, aneavesdropper).For the underlying cryptographic notion of security, we use a versionof Canetti's Universally Composable security.In spite of the relative simplicity of the example, the exercise isquite nontrivial.It requires taking many fundamental issues into account,including nondeterministic behavior, scheduling, resource-boundedcomputation, and computational hardness assumptions for cryptographicprimitives

Task-Structured Probabilistic I/O Automata

"May 28, 2009."Modeling frameworks such as Probabilistic I/O Automata (PIOA) and Markov Decision Processes permit both probabilistic and nondeterministic choices. In order to use these frameworks to express claims about probabilities of events, one needs mechanisms for resolving nondeterministic choices. For PIOAs, nondeterministic choices have traditionally been resolved by schedulers that have perfect information about the past execution. However, these schedulers are too powerful for certain settings, such as cryptographic protocol analysis, where information must sometimes be hidden. Here, we propose a new, less powerful nondeterminism-resolution mechanism for PIOAs, consisting of tasks and local schedulers. Tasks are equivalence classes of system actions that are scheduled by oblivious, global task sequences. Local schedulers resolve nondeterminism within system components, based on local information only. The resulting task-PIOA framework yields simple notions of external behavior and implementation, and supports simple compositionality results. We also define a new kind of simulation relation, and show it to be sound for proving implementation. We illustrate the potential of the task-PIOAframework by outlining its use in verifying an Oblivious Transfer protocol

Complexity Results for Reachability in Cooperating Systems and Approximated Reachability by Abstract Over-Approximations

This work deals with theoretic aspects of cooperating systems, i.e., systems that consists of cooperating subsystems. Our main focus lies on the complexity theoretic classification of deciding the reachability problem and on efficiently establishing deadlock-freedom in models of cooperating systems. The formal verification of system properties is an active field of research, first attempts of which go back to the late 60's. The behavior of cooperating systems suffers from the state space explosion problem and can become very large. This is, techniques that are based on an analysis of the reachable state space have a runtime exponential in the number of subsystems. The consequence is that even modern techniques that decide whether or not a system property holds in a system can become unfeasible. We use interaction systems, introduced by Sifakis et al. in 2003, as a formalism to model cooperating systems. The reachability problem and deciding deadlock-freedom in interaction systems was proved to be PSPACE-complete. An approach to deal with this issue is to investigate subclasses of systems in which these problems can be treated efficiently. We show here that the reachability problem remains PSPACE-complete in subclasses of interaction systems with a restricted communication structure. We consider structures that from trees, stars and linear arrangements of subsystems. Our result motivates the research of techniques that treat the reachability problem in these subclasses based on sufficient conditions which exploit characteristics of the structural restrictions. In a second part of this work we investigate an approach to efficiently establish the reachability of states and deadlock-freedom in general interaction systems. We introduce abstract over-approximations -- a concept of compact representations of over-approximations of the reachable behavior of interaction systems. Families of abstract over-approximations are the basis for our approach to establish deadlock-freedom in interaction systems in polynomial time in the size of the underlying interaction system. We introduce an operator called Edge-Match for refining abstract over-approximations. The strength of our approach is illustrated on various parametrized instances of interaction systems. Furthermore, we establish a link between our refinement approach and the field of relational database theory and use this link in order to make a preciseness statement about our refinement approach

Hierarchical and compositional verification of cryptographic protocols

Nella verifica dei protocolli di sicurezza ci sono due importanti approcci che sono conosciuti sotto il nome di approccio simbolico e computazionale, rispettivamente. Nell'approccio simbolico i messaggi sono termini di un'algebra e le primitive crittografiche sono idealmente sicure; nell'approccio computazionale i messaggi sono sequenze di bit e le primitive crittografiche sono sicure con elevata probabilit\ue0. Questo significa, per esempio, che nell'approccio simbolico solo chi conosce la chiave di decifratura pu\uf2 decifrare un messaggio cifrato, mentre nell'approccio computazionale la probabilit\ue0 di decifrare un testo cifrato senza conoscere la chiave di decifratura \ue8 trascurabile. Di solito, i protocolli crittografici sono il risultato dell'interazione di molte componenti: alcune sono basate su primitive crittografiche, altre su altri principi. In generale, quello che risulta \ue8 un sistema complesso che vorremmo poter analizzare in modo modulare invece che doverlo studiare come un singolo sistema. Una situazione simile pu\uf2 essere trovata nel contesto dei sistemi distribuiti, dove ci sono molti componenti probabilistici che interagiscono tra loro implementando un algoritmo distribuito. In questo contesto l'analisi della correttezza di un sistema complesso \ue8 molto rigorosa ed \ue8 basata su strumenti che derivano dalla teoria dell'informazione, strumenti come il metodo di simulazione che permette di decomporre grossi problemi in problemi pi\uf9 piccoli e di verificare i sistemi in modo gerarchico e composizionale. Il metodo di simulazione consiste nello stabilire delle relazioni tra gli stati di due automi, chiamate relazioni di simulazione, e nel verificare che tali relazioni soddisfano delle condizioni di passo appropriate, come che ogni transizione del sistema simulato pu\uf2 essere imitata dal sistema simulante nel rispetto della relazione data. Usando un approccio composizionale possiamo studiare le propriet\ue0 di ogni singolo sotto-problema indipendentemente dagli altri per poi derivare le propriet\ue0 del sistema complessivo. Inoltre, la verifica gerarchica ci permette di definire molti raffinamenti intermedi tra la specifica e l'implementazione. Spesso la verifica gerarchica e composizionale \ue8 pi\uf9 semplice e chiara che l'intera verifica fatta in una volta sola. In questa tesi introduciamo una nuova relazione di simulazione, che chiamiamo simulazione polinomialmente accurata o simulazione approssimata, che \ue8 composizionale e che permette di usare l\u2019approccio gerarchico nelle nostre analisi. Le simulazioni polinomialmente accurate estendono le relazioni di simulazione definite nel contesto dei sistemi distribuiti sia nel caso forte sia in quello debole tenendo conto delle lunghezze delle esecuzioni e delle propriet\ue0 computazionali delle primitive crittografiche. Oltre alle simulazioni polinomialmente accurate, forniamo altri strumenti che possono semplificare l\u2019analisi dei protocolli crittografici: il primo \ue8 il concetto di automa condizionale che permette di rimuovere eventi che occorrono con probabilit\ue0 trascurabile in modo sicuro. Data una macchina che \ue8 attaccabile con probabilit\ue0 trascurabile, se costruiamo un automa che \ue8 condizionale all'assenza di questi attacchi, allora esiste una simulazione tra i due. Questo ci permette, tra l'altro, di lavorare con le relazioni di simulazione tutto il tempo e in particolare possiamo anche dimostrare in modo composizionale che l'eliminazione di eventi trascurabili \ue8 sicura. Questa propriet\ue0 \ue8 giustificata dal teorema dell\u2019automa condizionale che afferma che gli eventi sono trascurabili se e solo se la relazione identit\ue0 \ue8 una simulazione approssimata dall\u2019automa alla sua controparte condizionale. Un altro strumento \ue8 il teorema della corrispondenza delle esecuzioni, che estende quello del contesto dei sistemi distribuiti, che giustifica l\u2019approccio gerarchico. Infatti, il teorema afferma che se abbiamo molti automi e una catena di simulazioni tra di essi, allora con elevata probabilit\ue0 ogni esecuzione del primo automa della catena \ue8 in relazione con un\u2019esecuzione dell'ultimo automa della catena. In altre parole, abbiamo che la probabilit\ue0 che l'ultimo automa non sia in grado di simulare un\u2019esecuzione del primo \ue8 trascurabile. Infine, usiamo il framework delle simulazioni polinomialmente accurate per fornire delle famiglie di automi che implementano le primitive crittografiche comunemente usate e per dimostrare che l'approccio simbolico \ue8 corretto rispetto all\u2019approccio computazionale.Two important approaches to the verification of security protocols are known under the general names of symbolic and computational, respectively. In the symbolic approach messages are terms of an algebra and the cryptographic primitives are ideally secure; in the computational approach messages are bitstrings and the cryptographic primitives are secure with overwhelming probability. This means, for example, that in the symbolic approach only who knows the decryption key can decrypt a ciphertext, while in the computational approach the probability to decrypt a ciphertext without knowing the decryption key is negligible. Usually, the cryptographic protocols are the outcome of the interaction of several components: some of them are based on cryptographic primitives, other components on other principles. In general, the result is a complex system that we would like to analyse in a modular way instead of studying it as a single system. A similar situation can be found in the context of distributed systems, where there are several probabilistic components that interact with each other implementing a distributed algorithm. In this context, the analysis of the correctness of a complex system is very rigorous and it is based on tools from information theory such as the simulation method that allows us to decompose large problems into smaller problems and to verify systems hierarchically and compositionally. The simulation method consists of establishing relations between the states of two automata, called simulation relations, and to verify that such relations satisfy appropriate step conditions: each transition of the simulated system can be matched by the simulating system up to the given relation. Using a compositional approach we can study the properties of each small problem independently from the each other, deriving the properties of the overall system. Furthermore, the hierarchical verification allows us to build several intermediate refinements between specification and implementation. Often hierarchical and compositional verification is simpler and cleaner than direct one-step verification, since each refinement may focus on specific homogeneous aspects of the implementation. In this thesis we introduce a new simulation relation, that we call polynomially accurate simulation, or approximated simulation, that is compositional and that allows us to adopt the hierarchical approach in our analyses. The polynomially accurate simulations extend the simulation relations of the distributed systems context in both strong and weak cases taking into account the lengths of the computations and of the computational properties of the cryptographic primitives. Besides the polynomially accurate simulations, we provide other tools that can simplify the analysis of cryptographic protocols: the first one is the concept of conditional automaton, that permits to safely remove events that occur with negligible probability. Starting from a machine that is attackable with negligible probability, if we build an automaton that is conditional to the absence of these attacks, then there exists a simulation. And this allows us to work with the simulation relations all the time and in particular we can also prove in a compositional way that the elimination of negligible events from an automaton is safe. This property is justified by the conditional automaton theorem that states that events are negligible if and only if the identity relation is an approximated simulation from the automaton and its conditional counterpart. Another tool is the execution correspondence theorem, that extends the one of the distributed systems context, that allows us to use the hierarchical approach. In fact, the theorem states that if we have several automata and a chain of simulations between them, then with overwhelming probability each execution of the first automaton is related to an execution of the last automaton. In other words, we have that the probability that the last automaton is not able to simulate an execution of the first one is negligible. Finally, we use the polynomially accurate simulation framework to provide families of automata that implement commonly used cryptographic primitives and to prove that the symbolic approach is sound with respect to the computational approach