Precisely Measuring Quantitative Information Flow: 10K Lines of Code and Beyond

Val, Celina G.; Enescu, Michael A.; Bayless, Sam; Aiello, William; Hu, Alan J.

doi:10.1109/eurosp.2016.15

Cited by 15 publications

(17 citation statements)

References 26 publications

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“…Despite given those evidences about the hardness of calculating QIF, for this decade, precise QIF analysis gathers much attention of the researchers. In [15], Klebanov [25] reported a method that can scale to programs of 10,000 lines of code but still based on SAT solver and symbolic execution. However, there is still a gap between such improvements and practical use, and researchers also work on approximating QIF.…”

Section: Examplementioning

confidence: 99%

Quantifying Dynamic Leakage - Complexity Analysis and Model Counting-based Calculation -

Chu

Hashimoto

Seki

2019

IEICE Trans. Inf. & Syst.

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A program is non-interferent if it leaks no secret information to an observable output. However, non-interference is too strict in many practical cases and quantitative information flow (QIF) has been proposed and studied in depth. Originally, QIF is defined as the average of leakage amount of secret information over all executions of a program. However, a vulnerable program that has executions leaking the whole secret but has the small average leakage could be considered as secure. This counter-intuition raises a need for a new definition of information leakage of a particular run, i.e., dynamic leakage. As discussed in [5], entropy-based definitions do not work well for quantifying information leakage dynamically; Belief-based definition on the other hand is appropriate for deterministic programs, however, it is not appropriate for probabilistic ones. In this paper, we propose new simple notions of dynamic leakage based on entropy which are compatible with existing QIF definitions for deterministic programs, and yet reasonable for probabilistic programs in the sense of [5]. We also investigated the complexity of computing the proposed dynamic leakage for three classes of Boolean programs. We also implemented a tool for QIF calculation using model counting tools for Boolean formulae. Experimental results on popular benchmarks of QIF research show the flexibility of our framework. Finally, we discuss the improvement of performance and scalability of the proposed method as well as an extension to more general cases.According to [5], we arrange three criteria that a 'good' definition of dynamic leakage should satisfy, namely, the measure should be (R1) non-negative, (R2) independent of a secret value to prevent a side channel and (R3) compatible with existing notions to keep the consistency within QIF as a whole (both dynamic leakage and normal QIF). Based on those criteria, we come up with two notions of dynamic leakage QIF1 and QIF2, where both of them satisfy all (R1), (R2) and (R3). QIF1, motivated by entropy-based approach, takes the difference between the initial and remaining self-information of the secret before and after observing output as dynamic leakage. On the other hand, QIF2 models that of the joint probability between secret and output. Because both of them are useful in different scenarios, we studied these two models in parallel in the theoretical part of the paper. We call the problems of computing QIF1 and QIF2 for Boolean programs CompQIF1 and CompQIF2, respectively. For example, we show that even for deterministic loop-free programs with uniformly distributed input, both CompQIF1 and CompQIF2 are P-hard. Next, we assume that secret inputs of a program are uniformly distributed and consider the following method of computing QIF1 and QIF2 (only for deterministic programs for QIF2 by the technical reason mentioned in Section 4): (1) translate a program into a Boolean formula that represents relationship among values of variables during a program execution, (2) augment additional constraints that ...

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Section: Examplementioning

confidence: 99%

Quantifying Dynamic Leakage - Complexity Analysis and Model Counting-based Calculation -

Chu

Hashimoto

Seki

2019

IEICE Trans. Inf. & Syst.

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“…They explore both exhaustive enumeration and the existing DSHARP and sharpSAT tools, but only counting distinct values of the output variables. Val et al [36] integrate a symbolic execution tool more closely with a SAT solver by using techniques from SAT solving to prune the symbolic execution search space, and then perform exact model counting restricted to an output variable.…”

Section: A Exact Model Countingmentioning

confidence: 99%

Bit-Vector Model Counting Using Statistical Estimation

Kim

McCamant

2018

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Approximate model counting for bit-vector SMT formulas (generalizing #SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms.

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“…Recently, QIF computation based on program analysis and model counting has effectively analyzed codebases of tens of thousands of lines of C code [29]. This technique proceeds as follows.…”

Section: Introductionmentioning

confidence: 99%

“…The technique has been shown to be able to help detect and confirm bugs in software [24,22,25], and to signal to a developer that there may be bugs in a particular part of the software. Indeed, QIF-based techniques, while not foolproof, can use the a large information flow to a particular part of the program as a hint to a developer in order to narrow down where to look for bugs [29]. However, the model counting step of the procedure is computationally very expensive, since it is #P -complete [30].…”

Section: Introductionmentioning

confidence: 99%

Scalable Approximation of Quantitative Information Flow in Programs

Biondi

Enescu²,

Heuser³

et al. 2017

Lecture Notes in Computer Science

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Quantitative information flow measurement techniques have been proven to be successful in detecting leakage of confidential information from programs. Modern approaches are based on formal methods, relying on program analysis to produce a SAT formula representing the program's behavior, and model counting to measure the possible information flow. However, while program analysis scales to large codebases like the OpenSSL project, the formulas produced are too complex for analysis with precise model counting. In this paper we use the approximate model counter ApproxMC2 to quantify information flow. We show that ApproxMC2 is able to provide a large performance increase for a very small loss of precision, allowing the analysis of SAT formulas produced from complex code. We call the resulting technique ApproxFlow and test it on a large set of benchmarks against the state of the art. Finally, we show that ApproxFlow can evaluate the leakage incurred by the Heartbleed OpenSSL bug, contrarily to the state of the art.

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Precisely Measuring Quantitative Information Flow: 10K Lines of Code and Beyond

Cited by 15 publications

References 26 publications

Quantifying Dynamic Leakage - Complexity Analysis and Model Counting-based Calculation -

Quantifying Dynamic Leakage - Complexity Analysis and Model Counting-based Calculation -

Bit-Vector Model Counting Using Statistical Estimation

Scalable Approximation of Quantitative Information Flow in Programs

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