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Section: New Results
Privacy and Security
Participants : Axel Legay, Fabrizio Biondi, Jean Quilbeuf, Thomas Given-Wilson.
Information-Theoretical Quantification of Security Properties
This part of the work was not foreseen at the beginning of the action. It concerns security aspects, and more precisely quantifying privacy of data. This aspect is in fact central for SoS and all our algorithms developed for Tasks 4 and 5 should be adapted to solve a series of problems linked to privacy in interconnected object and dynamical environment. For now, we only studied the foundations.
Information theory provides a powerful quantitative approach to measuring security and privacy properties of systems. By measuring the information leakage of a system security properties can be quantified, validated, or falsified. When security concerns are non-binary, information theoretic measures can quantify exactly how much information is leaked. The knowledge of such informations is strategic in the developments of component-based systems.
The quantitative information-theoretical approach to security models the correlation between the secret information of the system and the output that the system produces. Such output can be observed by the attacker, and the attacker tries to infer the value of the secret by combining this information with its knowledge of the system.
Armed with the produced output and the source code of the system, the attacker tries to infer the value of the secret. The quantitative analysis we implement computes with arbitrary precision the number of bits of the secret that the attacker will expectedly infer. This expected number of bits is the information leakage of the system.
The quantitative approach generalizes the qualitative approach and thus provides superior analysis. In particular, a system respects non-interference if and only if its leakage is equal to zero. In practice very few systems respect non-interference, and for those who don’t it is imperative to be able to distinguish between the ones leaking a very small amount of bits and the ones leaking a significant amount of bits, since only the latter are considered to pose a security vulnerability to the system.
Since black box security analyzes are immediately invalidated whenever an attacker gains information about the source code of the system, we assume that the attacker has a white box view of the system, meaning that it has access to the system’s source code. This approach is also consistent with the fact that many security protocol implementations are in fact open source.
The scope of modern software projects is too large to be analyzed manually. For this reason we provide tools that can support the analyst and locate security vulnerabilities in large codebases and projects. We work with a variety of tools, including commercial software analysis tools being adapted with our techniques, and tools such as QUAIL developed here by our team.
We applied the leakage analysis provided by QUAIL to several case studies. Our case studies (voting protocol and smart grid coordination) have in common that a publicly disclosed information is computed from the secret of every participant in the model. In the voting example, the vote of a given voter is secret, but the number of votes for each candidates is public. Similarly, in the smart grid example, the consumption of one of the houses is secret, but the consumption of a whole quarter can be deduced. Qualitative analyses are either too restrictive or too permissive on these types of systems. For instance, non-interference will reject them as the public information depends on the secret. Declassification approaches will accept them, even if the number of voters or consumers is 2, in which case the secret can be deduced.
The development of better tools for quantitative security builds upon both theoretical developments in information theory, and development of the tools themselves. These often progress in parallel with each supporting the findings of the other, and increasing the demands and understanding upon each other.
Papers:
- [3] (J; submitted)
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The quantification of information leakage provides a quantitative evaluation of the security of a system. We propose the usage of Markovian processes to model deterministic and probabilistic systems. By using a methodology generalizing the lattice of information approach we model refined attackers capable to observe the internal behavior of the system, and quantify the information leakage of such systems. We also use our method to obtain an algorithm for the computation of channel capacity from our Markovian models. Finally, we show how to use the method to analyze timed and non-timed attacks on the Onion Routing protocol.
- [46] (C)
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Quantitative security analysis evaluates and compares how effectively a system protects its secret data. We introduce QUAIL, the first tool able to perform an arbitrary-precision quantitative analysis of the security of a system depending on private information. QUAIL builds a Markov Chain model of the system's behavior as observed by an attacker, and computes the correlation between the system's observable output and the behavior depending on the private information, obtaining the expected amount of bits of the secret that the attacker will infer by observing the system. QUAIL is able to evaluate the safety of randomized protocols depending on secret data, allowing to verify a security protocol's effectiveness. We experiment with a few examples and show that QUAIL's security analysis is more accurate and revealing than results of other tools.
- [40] (C; submitted)
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Quantitative security techniques have been proven effective to measure the security of systems against various types of attackers. However, such techniques are based on computing exponentially large channel matrices or Markov chains, making them impractical for large programs. We propose a different approach based on abstract trace analysis. By analyzing directly sets of execution traces of the program and computing security measures on the results, we are able to scale down the exponential cost of the problem. Also, we are able to appy statistical simulation techniques, allowing us to obtain significant results even without exploring the full space of traces. We have implemented the resulting algorithms in the QUAIL tool. We compare their effectiveness against the state of the art LeakWatch tool on two case studies: privacy of user consumption in smart grid systems and anonymity of voters in different voting schemes.
- [12] (C)
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In an election, it is imperative that the vote of the single voters remain anonymous and undisclosed. Alas, modern anonymity approaches acknowledge that there is an unavoidable leak of anonymity just by publishing data related to the secret, like the election's result. Information theory is applied to quantify this leak and ascertain that it remains below an acceptable threshold. We apply modern quantitative anonymity analysis techniques via the state-of-the-art QUAIL tool to the voting scenario. We consider different voting typologies and establish which are more effective in protecting the voter's privacy. We further demonstrate the effectiveness of the protocols in protecting the privacy of the single voters, deriving an important desirable property of protocols depending on composite secrets.
- [13] (C)
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In recent years, quantitative security techniques have been providing effective measures of the security of a system against an attacker. Such techniques usually assume that the system produces a finite amount of observations based on a finite amount of secret bits and terminates, and the attack is based on these observations. By modeling systems with Markov chains, we are able to measure the effectiveness of attacks on non-terminating systems. Such systems do not necessarily produce a finite amount of output and are not necessarily based on a finite amount of secret bits. We provide characterizations and algorithms to define meaningful measures of security for non-terminating systems, and to compute them when possible. We also study the bounded versions of the problems, and show examples of non-terminating programs and how their effectiveness in protecting their secret can be measured.