Complexity and Unwinding for Intransitive Noninterference

The paper considers several definitions of information flow security for intransitive policies from the point of view of the complexity of verifying whether a finite-state system is secure. The results are as follows. Checking (i) P-security (Goguen and Meseguer), (ii) IP-security (Haigh and Young), and (iii) TA-security (van der Meyden) are all in PTIME, while checking TO-security (van der Meyden) is undecidable, as is checking ITO-security (van der Meyden). The most important ingredients in the proofs of the PTIME upper bounds are new characterizations of the respective security notions, which also lead to new unwinding proof techniques that are shown to be sound and complete for these notions of security, and enable the algorithms to return simple counter-examples demonstrating insecurity. Our results for IP-security improve a previous doubly exponential bound of Hadj-Alouane et al

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

Opacity with Orwellian Observers and Intransitive Non-interference

Opacity is a general behavioural security scheme flexible enough to account for several specific properties. Some secret set of behaviors of a system is opaque if a passive attacker can never tell whether the observed behavior is a secret one or not. Instead of considering the case of static observability where the set of observable events is fixed off line or dynamic observability where the set of observable events changes over time depending on the history of the trace, we consider Orwellian partial observability where unobservable events are not revealed unless a downgrading event occurs in the future of the trace. We show how to verify that some regular secret is opaque for a regular language L w.r.t. an Orwellian projection while it has been proved undecidable even for a regular language L w.r.t. a general Orwellian observation function. We finally illustrate relevancy of our results by proving the equivalence between the opacity property of regular secrets w.r.t. Orwellian projection and the intransitive non-interference property

A Verified Information-Flow Architecture

SAFE is a clean-slate design for a highly secure computer system, with pervasive mechanisms for tracking and limiting information flows. At the lowest level, the SAFE hardware supports fine-grained programmable tags, with efficient and flexible propagation and combination of tags as instructions are executed. The operating system virtualizes these generic facilities to present an information-flow abstract machine that allows user programs to label sensitive data with rich confidentiality policies. We present a formal, machine-checked model of the key hardware and software mechanisms used to dynamically control information flow in SAFE and an end-to-end proof of noninterference for this model. We use a refinement proof methodology to propagate the noninterference property of the abstract machine down to the concrete machine level. We use an intermediate layer in the refinement chain that factors out the details of the information-flow control policy and devise a code generator for compiling such information-flow policies into low-level monitor code. Finally, we verify the correctness of this generator using a dedicated Hoare logic that abstracts from low-level machine instructions into a reusable set of verified structured code generators

Verifying Noninterference in a Cyber-Physical System the Advanced Electric Power Grid

The advanced electric power grid is a complex real-time system having both cyber and physical components. While each component may function correctly, independently, their composition may yield incorrectness due to interference. One specific type of interference is in the frequency domain, essentially, violations of the Nyquist rate. The challenge is to encode these signal processing problem characteristics into a form that can be model checked. To verify the correctness of the cyber-physical composition using model-checking techniques requires that a model be constructed that can represent frequency interference. In this paper, RT-PROMELA was used to construct the model, which was checked in RT-SPIN. In order to reduce the state explosion problem, the model was decomposed into multiple sub-models, each with a smaller state space that can be checked individually, and then the proofs checked for noninterference. Cooperation among multiple clock variables due to their lack of notion of urgency and their asynchronous interactions, are also addressed

Verifying That a Compiler Preserves Concurrent Value-Dependent Information-Flow Security

It is common to prove by reasoning over source code that programs do not leak sensitive data. But doing so leaves a gap between reasoning and reality that can only be filled by accounting for the behaviour of the compiler. This task is complicated when programs enforce value-dependent information-flow security properties (in which classification of locations can vary depending on values in other locations) and complicated further when programs exploit shared-variable concurrency. Prior work has formally defined a notion of concurrency-aware refinement for preserving value-dependent security properties. However, that notion is considerably more complex than standard refinement definitions typically applied in the verification of semantics preservation by compilers. To date it remains unclear whether it can be applied to a realistic compiler, because there exist no general decomposition principles for separating it into smaller, more familiar, proof obligations. In this work, we provide such a decomposition principle, which we show can almost halve the complexity of proving secure refinement. Further, we demonstrate its applicability to secure compilation, by proving in Isabelle/HOL the preservation of value-dependent security by a proof-of-concept compiler from an imperative While language to a generic RISC-style assembly language, for programs with shared-memory concurrency mediated by locking primitives. Finally, we execute our compiler in Isabelle on a While language model of the Cross Domain Desktop Compositor, demonstrating to our knowledge the first use of a compiler verification result to carry an information-flow security property down to the assembly-level model of a non-trivial concurrent program

Compositional closure for Bayes Risk in probabilistic noninterference

We give a sequential model for noninterference security including probability (but not demonic choice), thus supporting reasoning about the likelihood that high-security values might be revealed by observations of low-security activity. Our novel methodological contribution is the definition of a refinement order and its use to compare security measures between specifications and (their supposed) implementations. This contrasts with the more common practice of evaluating the security of individual programs in isolation. The appropriateness of our model and order is supported by our showing that our refinement order is the greatest compositional relation --the compositional closure-- with respect to our semantics and an "elementary" order based on Bayes Risk --- a security measure already in widespread use. We also relate refinement to other measures such as Shannon Entropy. By applying the approach to a non-trivial example, the anonymous-majority Three-Judges protocol, we demonstrate by example that correctness arguments can be simplified by the sort of layered developments --through levels of increasing detail-- that are allowed and encouraged by compositional semantics