Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

Integration of analysis techniques in security and fault-tolerance

This thesis focuses on the study of integration of formal methodologies in security protocol analysis and fault-tolerance analysis. The research is developed in two different directions: interdisciplinary and intra-disciplinary. In the former, we look for a beneficial interaction between strategies of analysis in security protocols and fault-tolerance; in the latter, we search for connections among different approaches of analysis within the security area. In the following we summarize the main results of the research

A Temporal Logic for Strategic Hyperproperties

Hyperproperties are commonly used in computer security to define information-flow policies and other requirements that reason about the relationship between multiple computations. In this paper, we study a novel class of hyperproperties where the individual computation paths are chosen by the strategic choices of a coalition of agents in a multi-agent system. We introduce HyperATL^*, an extension of computation tree logic with path variables and strategy quantifiers. HyperATL^* can express strategic hyperproperties, such as that the scheduler in a concurrent system has a strategy to avoid information leakage. HyperATL^* is particularly useful to specify asynchronous hyperproperties, i.e., hyperproperties where the speed of the execution on the different computation paths depends on the choices of the scheduler. Unlike other recent logics for the specification of asynchronous hyperproperties, our logic is the first to admit decidable model checking for the full logic. We present a model checking algorithm for HyperATL^* based on alternating word automata, and show that our algorithm is asymptotically optimal by providing a matching lower bound. We have implemented a prototype model checker for a fragment of HyperATL^*, able to check various security properties on small programs

Contingent payments on a public ledger: models and reductions for automated verification

International audienceWe study protocols that rely on a public ledger infrastructure, concentrating on protocols for zero-knowledge contingent payment, whose security properties combine diverse notions of fairness and privacy. We argue that rigorous models are required for capturing the ledger semantics, the protocol-ledger interaction, the cryptographic primitives and, ultimately, the security properties one would like to achieve.Our focus is on a particular level of abstraction, where network messages are represented by a term algebra, protocol execution by state transition systems (e.g. multiset rewrite rules) and where the properties of interest can be analyzed with automated verification tools. We propose models for: (1) the rules guiding the ledger execution, taking the coin functionality of public ledgers such as Bitcoin as an example; (2) the security properties expected from ledger-based zero-knowledge contingent payment protocols; (3) two different security protocols that aim at achieving these properties relying on different ledger infrastructures; (4) reductions that allow simpler term algebras for homomorphic cryptographic schemes.Altogether, these models allow us to derive a first automated verification for ledger-based zero-knowledge contingent payment using the Tamarin prover. Furthermore , our models help in clarifying certain underlying assumptions, security and efficiency tradeoffs that should be taken into account when deploying protocols on the blockchain

Contingent payments on a public ledger: models and reductions for automated verification

International audienceWe study protocols that rely on a public ledger infrastructure, concentrating on protocols for zero-knowledge contingent payment, whose security properties combine diverse notions of fairness and privacy. We argue that rigorous models are required for capturing the ledger semantics, the protocol-ledger interaction, the cryptographic primitives and, ultimately, the security properties one would like to achieve.Our focus is on a particular level of abstraction, where network messages are represented by a term algebra, protocol execution by state transition systems (e.g. multiset rewrite rules) and where the properties of interest can be analyzed with automated verification tools. We propose models for: (1) the rules guiding the ledger execution, taking the coin functionality of public ledgers such as Bitcoin as an example; (2) the security properties expected from ledger-based zero-knowledge contingent payment protocols; (3) two different security protocols that aim at achieving these properties relying on different ledger infrastructures; (4) reductions that allow simpler term algebras for homomorphic cryptographic schemes.Altogether, these models allow us to derive a first automated verification for ledger-based zero-knowledge contingent payment using the Tamarin prover. Furthermore , our models help in clarifying certain underlying assumptions, security and efficiency tradeoffs that should be taken into account when deploying protocols on the blockchain

Formal Verification of Differential Privacy for Interactive Systems

Differential privacy is a promising approach to privacy preserving data analysis with a well-developed theory for functions. Despite recent work on implementing systems that aim to provide differential privacy, the problem of formally verifying that these systems have differential privacy has not been adequately addressed. This paper presents the first results towards automated verification of source code for differentially private interactive systems. We develop a formal probabilistic automaton model of differential privacy for systems by adapting prior work on differential privacy for functions. The main technical result of the paper is a sound proof technique based on a form of probabilistic bisimulation relation for proving that a system modeled as a probabilistic automaton satisfies differential privacy. The novelty lies in the way we track quantitative privacy leakage bounds using a relation family instead of a single relation. We illustrate the proof technique on a representative automaton motivated by PINQ, an implemented system that is intended to provide differential privacy. To make our proof technique easier to apply to realistic systems, we prove a form of refinement theorem and apply it to show that a refinement of the abstract PINQ automaton also satisfies our differential privacy definition. Finally, we begin the process of automating our proof technique by providing an algorithm for mechanically checking a restricted class of relations from the proof technique.Comment: 65 pages with 1 figur

Principled Flow Tracking in IoT and Low-Level Applications

Significant fractions of our lives are spent digitally, connected to and dependent on Internet-based applications, be it through the Web, mobile, or IoT. All such applications have access to and are entrusted with private user data, such as location, photos, browsing habits, private feed from social networks, or bank details.In this thesis, we focus on IoT and Web(Assembly) apps. We demonstrate IoT apps to be vulnerable to attacks by malicious app makers who are able to bypass the sandboxing mechanisms enforced by the platform to stealthy exfiltrate user data. We further give examples of carefully crafted WebAssembly code abusing the semantics to leak user data.We are interested in applying language-based technologies to ensure application security due to the formal guarantees they provide. Such technologies analyze the underlying program and track how the information flows in an application, with the goal of either statically proving its security, or preventing insecurities from happening at runtime. As such, for protecting against the attacks on IoT apps, we develop both static and dynamic methods, while for securing WebAssembly apps we describe a hybrid approach, combining both.While language-based technologies provide strong security guarantees, they are still to see a widespread adoption outside the academic community where they emerged.In this direction, we outline six design principles to assist the developer in choosing the right security characterization and enforcement mechanism for their system.We further investigate the relative expressiveness of two static enforcement mechanisms which pursue fine- and coarse-grained approaches for tracking the flow of sensitive information in a system.\ua0Finally, we provide the developer with an automatic method for reducing the manual burden associated with some of the language-based enforcements

Modularity in answer set programs

Answer set programming (ASP) is an approach to rule-based constraint programming allowing flexible knowledge representation in variety of application areas. The declarative nature of ASP is reflected in problem solving. First, a programmer writes down a logic program the answer sets of which correspond to the solutions of the problem. The answer sets of the program are then computed using a special purpose search engine, an ASP solver. The development of efficient ASP solvers has enabled the use of answer set programming in various application domains such as planning, product configuration, computer aided verification, and bioinformatics. The topic of this thesis is modularity in answer set programming. While modern programming languages typically provide means to exploit modularity in a number of ways to govern the complexity of programs and their development process, relatively little attention has been paid to modularity in ASP. When designing a module architecture for ASP, it is essential to establish full compositionality of the semantics with respect to the module system. A balance is sought between introducing restrictions that guarantee the compositionality of the semantics and enforce a good programming style in ASP, and avoiding restrictions on the module hierarchy for the sake of flexibility of knowledge representation. To justify a replacement of a module with another, that is, to be able to guarantee that changes made on the level of modules do not alter the semantics of the program when seen as an entity, a notion of equivalence for modules is provided. In close connection with the development of the compositional module architecture, a transformation from verification of equivalence to search for answer sets is developed. The translation-based approach makes it unnecessary to develop a dedicated tool for the equivalence verification task by allowing the direct use of existing ASP solvers. Translations and transformations between different problems, program classes, and formalisms are another central theme in the thesis. To guarantee efficiency and soundness of the translation-based approach, certain syntactical and semantical properties of transformations are desirable, in terms of translation time, solution correspondence between the original and the transformed problem, and locality/globality of a particular transformation. In certain cases a more refined notion of minimality than that inherent in ASP can make program encodings more intuitive. Lifschitz' parallel and prioritized circumscription offer a solution in which certain atoms are allowed to vary or to have fixed values while others are falsified as far as possible according to priority classes. In this thesis a linear and faithful transformation embedding parallel and prioritized circumscription into ASP is provided. This enhances the knowledge representation capabilities of answer set programming by allowing the use of existing ASP solvers for computing parallel and prioritized circumscription

Deductive Verification of Concurrent Programs and its Application to Secure Information Flow for Java

Formal verification of concurrent programs still poses a major challenge in computer science. Our approach is an adaptation of the modular rely/guarantee methodology in dynamic logic. Besides functional properties, we investigate language-based security. Our verification approach extends naturally to multi-threaded Java and we present an implementation in the KeY verification system. We propose natural extensions to JML regarding both confidentiality properties and multi-threaded programs

Implementation-level analysis of cryptographic protocols and their applications to e-voting systems

Formal verification of security properties of both cryptographic operations, such as encryption, and protocols based on them, such as TLS, has been the goal of a substantial research effort in the last three decades. One fundamental limitation in the verification of these security properties is that analyses are typically carried out at the design level and hence they do not provide reliable guarantees on the implementations of these operations/protocols. To overcome this limitation, in this thesis we aim at establishing formally justified cryptographic guarantees directly at the implementation level for systems that are coded in Java and use cryptography. Our approach is based on a general framework for the cryptographic verification of Java programs (the CVJ framework) which formally links cryptographic indistinguishability properties and noninterference properties. In this way, it enables existing tools that can check standard noninterference properties, but a priori cannot deal with cryptography, to also establish cryptographic privacy properties for Java systems. The CVJ framework is stated and proven for a Java-like formal language which however does not cover all the data types and features commonly used in Java programs. Moreover, the framework originally supports only one cryptographic operation, namely public-key encryption. The first contribution of this thesis is hence to extend and to instantiate the CVJ framework in order to make it more widely applicable. We extend the underlying formal language with some features of Java which have not been captured yet, such as concurrency, and we restate and prove all the results of the framework to carry them over into this extended language. We then further instantiate the framework with additional cryptographic operations: digital signatures and public-key encryption, both now also including a public-key infrastructure, (private) symmetric encryption, and nonce generation. The methods and techniques developed within the CVJ framework are relevant and applicable independently of any specific tool employed. However, to illustrate the usefulness of this approach, we apply the framework along with two verification tools for Java programs, namely the fully automated static checker Joana and the interactive theorem prover KeY, to establish strong cryptographic privacy properties for systems which use cryptography, such as client-server applications and e-voting systems. In this context, the second major contribution of this thesis is the design, the implementation, and the deployment of a novel remote voting system called sElect (secure/simple elections). sElect is designed to be particularly simple and lightweight in terms of its structure, the cryptography it uses, and the user experience. One of its unique features is a fully automated procedure which does not require any user interaction and it is triggered as soon as voters look at the election result, allowing them to verify that their vote has been properly counted. The component of sElect which provides vote privacy is implemented in Java such that we can establish cryptographic guarantees directly on its implementation: by combining the techniques of the CVJ framework with a hybrid approach for proving noninterference, we are able to show that the Java implementation ensures strong cryptographic privacy of the votes cast with our proposed voting system. sElect is therefore the first full-fledged e-voting system with strong cryptographic security guarantees not only at the design level, but also on its implementation