Scalable Approximation of Quantitative Information Flow in Programs

As many people use internet through the various programs of PC and mobile devices, the possibility of private data leak is increasing. A program should be used after checking security of information flow. Security analysis of information flow is a method that analyzes security of information flow in program. If the information flow is secure, there is no leakage of personal information. If the information flow not secure, there may be a leakage of personal information. This paper proposes a method of analyzing information flow that facilitates SAT solver. The method translates a program that includes variables where security level is set into propositional formula representing control and information flow. The satisfiability of the formula translated is determined by using SAT solver. The security of program is represented through the result. Counter-example is generated if the program is not secure.

Quantitative Information Flow (QIF) and Differential Privacy (DP) are both concerned with the protection of sensitive information, but they are rather different approaches. In particular, QIF considers the expected probability of a successful attack, while DP (in both its standard and local versions) is a max-case measure, in the sense that it is compromised by the existence of a possible attack, regardless of its probability. Comparing systems is a fundamental task in these areas: one wishes to guarantee that replacing a system A by a system B is a safe operation that is the privacy of B is no worse than that of A. In QIF, a refinement order provides strong such guarantees, while, in DP, mechanisms are typically compared w.r.t. the privacy parameter ε in their definition. In this paper, we explore a variety of refinement orders, inspired by the one of QIF, providing precise guarantees for max-case leakage. We study simple structural ways of characterising them, the relation between them, efficient methods for verifying them and their lattice properties. Moreover, we apply these orders in the task of comparing DP mechanisms, raising the question of whether the order based on ε provides strong privacy guarantees. We show that, while it is often the case for mechanisms of the same “family” (geometric, randomised response, etc.), it rarely holds across different families.

Differential privacy is a notion that has emerged in the community of statistical databases, as a response to the problem of protecting the privacy of the database's participants when performing statistical queries. The idea is that a randomized query satisfies differential privacy if the likelihood of obtaining a certain answer for a database $x$ is not too different from the likelihood of obtaining the same answer on adjacent databases, i.e. databases which differ from $x$ for only one individual. Information flow is an area of Security concerned with the problem of controlling the leakage of confidential information in programs and protocols. Nowadays, one of the most established approaches to quantify and to reason about leakage is based on the R\'enyi min entropy version of information theory. In this paper, we analyze critically the notion of differential privacy in light of the conceptual framework provided by the R\'enyi min information theory. We show that there is a close relation between differential privacy and leakage, due to the graph symmetries induced by the adjacency relation. Furthermore, we consider the utility of the randomized answer, which measures its expected degree of accuracy. We focus on certain kinds of utility functions called "binary", which have a close correspondence with the R\'enyi min mutual information. Again, it turns out that there can be a tight correspondence between differential privacy and utility, depending on the symmetries induced by the adjacency relation and by the query. Depending on these symmetries we can also build an optimal-utility randomization mechanism while preserving the required level of differential privacy. Our main contribution is a study of the kind of structures that can be induced by the adjacency relation and the query, and how to use them to derive bounds on the leakage and achieve the optimal utility.

This paper uses Shannon's information theory to give a quantitative definition of information flow in systems that transform inputs to outputs. For deterministic systems, the definition is shown to specialize to a simpler form when the information source and the known inputs jointly determine all inputs uniquely. For this special case, the definition is related to the classical security condition of non-interference and an equivalence is established between non-interference and independence of random variables. Quantitative information flow for deterministic systems is then presented in relational form. With this presentation, it is shown how relational parametricity can be used to derive upper and lower bounds on information flows through families of functions defined in the second-order lambda calculus.

Current tools for analysing information flow in programs build upon ideas going back to Denning’s work from the 70’s. These systems enforce an imperfect notion of information flow which has become known as termination-insensitive noninterference. Under this version of noninterference, information leaks are permitted if they are transmitted purely by the program’s termination behaviour (i.e., whether it terminates or not). This imperfection is the price to pay for having a security condition which is relatively liberal (e.g. allowing while-loops whose termination may depend on the value of a secret) and easy to check. But what is the price exactly? We argue that, in the presence of output, the price is higher than the “one bit” often claimed informally in the literature, and effectively such programs can leak all of their secrets. In this paper we develop a definition of termination-insensitive noninterference suitable for reasoning about programs with outputs. We show that the definition generalises “batch-job” style definitions from the literature and that it is indeed satisfied by a Denning-style program analysis with output. Although more than a bit of information can be leaked by programs satisfying this condition, we show that the best an attacker can do is a brute-force attack, which means that the attacker cannot reliably (in a technical sense) learn the secret in polynomial time in the size of the secret. If we further assume that secrets are uniformly distributed, we show that the advantage the attacker gains when guessing the secret after observing a polynomial amount of output is negligible in the size of the secret.

Dynamic information flow analysis (DIFA) was devised to enable the flow of information among variables in an executing program to be monitored and possibly regulated. It is related to techniques like dynamic slicing and dynamic impact analysis . To better understand the basis for DIFA, we conducted an empirical study in which we measured the strength of information flows identified by DIFA, using information theoretic and correlation-based methods. The results indicate that in most cases the occurrence of a chain of dynamic program dependences between two variables does not indicate a measurable information flow between them. We also explored the relationship between the strength of an information flow and the length of the corresponding dependence chain, and we obtained results indicating that no consistent relationship exists between the length of an information flow and its strength. Finally, we investigated whether data dependence and control dependence makes equal or unequal contributions to flow strength. The results indicate that flows due to data dependences alone are stronger, on average, than flows due to control dependences alone. We present the details of our study and consider the implications of the results for applications of DIFA and related techniques.

We, in this paper, try to represent information flow of program on the basis of slices. It is referred to slice-based information flow graph(SIFG). SIFG captures the information flow among data tokens. We can find the elementary characteristics of the information flow of program by using SIFG and increase the understanding about program.

The field of Quantitative Information Flow (QIF) is concerned with quantifying information leakage in systems. This work generalises the QIF framework to the setting, having as foundations the recently developed g-leakage framework. Next, some recent results of the field of statistical decision are presented and translated in terms of the quantum g-leakage framework, including a recently developed generalisation of the Coriasceous Theorem, an important result for QIF.

#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of satisfiability modulo theories (SMT) there is a growing need for model counting solvers, coming from several application domains (quantitative information flow, static analysis of probabilistic programs). In this paper, we show a reduction from an approximate version of #SMT to SMT. We focus on the theories of integer arithmetic and linear real arithmetic. We propose model counting algorithms that provide approximate solutions with formal bounds on the approximation error. They run in polynomial time and make a polynomial number of queries to the SMT solver for the underlying theory, exploiting “for free” the sophisticated heuristics implemented within modern SMT solvers. We have implemented the algorithms and used them to solve the value problem for a model of loop-free probabilistic programs with nondeterminism.

Information Flow Tracking (IFT) is an established formal method for proving security properties related to confidentiality, integrity, and isolation. It has seen promise in identifying security vulnerabilities resulting from design flaws, timing channels, and hardware Trojans for secure hardware design. However, existing IFT methods tend to take a qualitative approach and only enforce binary security properties, requiring strict non-interference for the properties to hold while real systems usually allow a small amount of information flows to enable desirable interactions. Consequently, existing methods are inadequate for reasoning about quantitative security properties or measuring the security of a design in order to assess the severity of a security vulnerability. In this work, we propose two multi-flow solutions - multiple verifications for replicating existing IFT model and multi-flow IFT method. The proposed multi-flow IFT method provides more insight into simultaneous information flow behaviors and allows for proof of quantitative information flow security properties, such as diffusion, randomization, and boundaries on the amount of simultaneous information flows. Experimental results show that our method can be used to prove a new type of information flow security property with verification performance benefits.

We present a method based on abstract interpretation to check secure information flow in programs with dynamic structures where input and output channels are associated with security levels. In the concrete operational semantics each value is annotated by a security level dynamically taking into account both the explicit and the implicit information flows. We define a collecting semantics which associates with each program point the set of concrete states of the machine when the point is reached. The abstract domains are obtained from the concrete ones by keeping the security levels and forgetting the actual values. Using this framework, we define an abstract semantics, called instruction-level security typing, that allows us to certify a larger set of programs with respect to the typing approaches to check secure information flow. An efficient implementation is shown, operating a fixpoint iteration similar to that of the Java bytecode verification.

We present a new technique for determining how much information about a program's secret inputs is revealed by its public outputs. In contrast to previous techniques based on reachability from secret inputs (tainting), it achieves a more precise quantitative result by computing a maximum flow of information between the inputs and outputs. The technique uses static control-flow regions to soundly account for implicit flows via branches and pointer operations, but operates dynamically by observing one or more program executions and giving numeric flow bounds specific to them (e.g., 17 bits). The maximum flow in a network also gives a minimum cut (a set of edges that separate the secret input from the output), which can be used to efficiently check that the same policy is satisfied on future executions. We performed case studies on 5 real C, C++, and Objective C programs, 3 of which had more than 250K lines of code. The tool checked multiple security policies, including one that was violated by a previously unknown bug.

We show how static analysis for secure information flow can be expressed and proved correct entirely within the framework of abstract interpretation. The key idea is to define a Galois connection that directly approximates the hyperproperty of interest. To enable use of such Galois connections, we introduce a fixpoint characterisation of hypercollecting semantics, i.e. a "set of set" transformer. This makes it possible to systematically derive static analyses for hyperproperties entirely within the calculational framework of abstract interpretation. We evaluate this technique by deriving example static analyses. For qualitative information flow, we derive a dependence analysis similar to the logic of Amtoft and Banerjee (SAS'04) and the type system of Hunt and Sands (POPL'06). For quantitative information flow, we derive a novel cardinality analysis that bounds the leakage conveyed by a program instead of simply deciding whether it exists. This encompasses problems that are hypersafety but not k-safety. We put the framework to use and introduce variations that achieve precision rivalling the most recent and precise static analyses for information flow.

Privacy in elections: How small is “small”?

Satisfiability Modulo Theories (SMT) is a decision problem for logical formulas over one or more first-order theories. In this paper, we study the problem of finding all solutions of an SMT problem with respect to a set of Boolean variables, henceforth All-SMT. First, we show how an All-SMT solver can benefit various domains of application: Bounded Model Checking, Automated Test Generation, Reliability analysis, and Quantitative Information Flow. Secondly, we then propose algorithms to design an All-SMT solver on top of an existing SMT solver, and implement it into a prototype tool, called aZ3. Thirdly, we create a set of benchmarks for All-SMT in the theory of linear integer arithmetic QF_LIA and the theory of bit vectors with arrays and uninterpreted functions QF_AUFBV. We compare aZ3 against Math SAT, the only existing All-SMT solver, on our benchmarks. Experimental results show that aZ3 is more precise than Math SAT.