Almost Perfect Privacy for Additive Gaussian Privacy Filters

We study the maximal mutual information about a random variable $Y$ (representing non-private information) displayed through an additive Gaussian channel when guaranteeing that only $\epsilon$ bits of information is leaked about a random variable $X$ (representing private information) that is correlated with $Y$. Denoting this quantity by $g_\epsilon(X,Y)$, we show that for perfect privacy, i.e., $\epsilon=0$, one has $g_0(X,Y)=0$ for any pair of absolutely continuous random variables $(X,Y)$ and then derive a second-order approximation for $g_\epsilon(X,Y)$ for small $\epsilon$. This approximation is shown to be related to the strong data processing inequality for mutual information under suitable conditions on the joint distribution $P_{XY}$. Next, motivated by an operational interpretation of data privacy, we formulate the privacy-utility tradeoff in the same setup using estimation-theoretic quantities and obtain explicit bounds for this tradeoff when $\epsilon$ is sufficiently small using the approximation formula derived for $g_\epsilon(X,Y)$.Comment: 20 pages. To appear in Springer-Verla

Unconditionally secure ciphers with a short key for a source with unknown statistics

We consider the problem of constructing an unconditionally secure cipher with a short key for the case where the probability distribution of encrypted messages is unknown. Note that unconditional security means that an adversary with no computational constraints can obtain only a negligible amount of information ("leakage") about an encrypted message (without knowing the key). Here we consider the case of a priori (partially) unknown message source statistics. More specifically, the message source probability distribution belongs to a given family of distributions. We propose an unconditionally secure cipher for this case. As an example, one can consider constructing a single cipher for texts written in any of the languages of the European Union. That is, the message to be encrypted could be written in any of these languages

Using data compression and randomization to build an unconditionally secure short key cipher

We consider the problem of constructing an unconditionally secure cipher for the case when the key length is less than the length of the encrypted message. (Unconditional security means that a computationally unbounded adversary cannot obtain information about the encrypted message without the key.) In this article, we propose data compression and randomization techniques combined with entropically-secure encryption. The resulting cipher can be used for encryption in such a way that the key length does not depend on the entropy or the length of the encrypted message; instead, it is determined by the required security level

Privacy-Protection in Cooperative Distributed Systems

The new form of digital computational capabilities and internet connectivity are promptly grow. This introduced a new form of computation that is emerging rapidly with cloud computing, mobile computing, wearable computing and the Internet-of-Things. All can be characterized as a class of “Cooperative Distributed Systems” (CDS) in open environment. A major drive of the growth involves massive number of people and organization, that has been engaged within their all daily life aspects and businesses activities. In this context, users’ privacy protection for a becoming crucial and essential requirement beyond the traditional approaches. This requires a formal treatment of “privacy concern” as a fundamental computation concept in CDS paradigm. The objective is to develop a model for “privacy protection” as base to build a CDS based framework and platform in which various applications allow users to enjoy the comprehensive services in open environments while protecting their privacy seamlessly. The practicality aspects of the framework have been measured from two main aspects, which are the Efficacy aspect and Feasibility. To this end, formal foundations and model of privacy concern have been treated in the context of information management. This served as a base for a practical privacy protection management framework for CDS. It includes a privacy-aware agent model and privacy-based platform for CDS with the ability to support interaction-based privacy protection. The practical aspects of the proposed models have been demonstrated by developing an Interaction-based CDS platform

Information-theoretic metrics for security and privacy

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.Cataloged from PDF version of thesis.Includes bibliographical references (pages 143-150).In this thesis, we study problems in cryptography, privacy and estimation through the information-theoretic lens. We introduce information-theoretic metrics and associated results that shed light on the fundamental limits of what can be learned from noisy data. These metrics and results, in turn, are used to evaluate and design both symmetric-key encryption schemes and privacy-assuring mappings with provable information-theoretic security guarantees. We start by studying information-theoretic properties of symmetric-key encryption in the "small key" regime (i.e. when the key rate is smaller than the entropy rate of the message source). It is well known that security against computationally unbounded adversaries in such settings can only be achieved when the communicating parties share a key that is at least as long as the secret message (i.e. plaintext) being communicated, which is infeasible in practice. Nevertheless, even with short keys, we show that a certain level of security can be guaranteed, albeit not perfect secrecy. In order to quantify exactly how much security can be provided with short keys, we propose a new security metric, called symbol secrecy, that measures how much an adversary that observes only the encrypted message learns about individual symbols of the plaintext. Unlike most traditional rate-based information-theoretic metrics for security, symbol secrecy is non-asymptotic. Furthermore, we demonstrate how fundamental symbol secrecy performance bounds can be achieved through standard code constructions (e.g. Reed-Solomon codes). While much of information-theoretic security has considered the hiding of the plaintext, cryptographic metrics of security seek to hide functions thereof. Consequently, we extend the definition of symbol secrecy to quantify the information leaked about certain classes of functions of the plaintext. This analysis leads to a more general question: can security claims based on information metrics be translated into guarantees on what an adversary can reliably infer from the output of a security system? On the one hand, information metrics usually quantify how far the probability distribution between the secret and the disclosed information is from the ideal case where independence is achieved. On the other hand, estimation guarantees seek to assure that an adversary cannot significantly improve his estimate of the secret given the information disclosed by the system. We answer this question in the positive, and present formulations based on rate-distortion theory that allow security bounds given in terms of information metrics to be transformed into bounds on how well an adversary can estimate functions of secret variable. We do this by solving a convex program that minimizes the average estimation error over all possible distributions that satisfy the bound on the information metric. Using this approach, we are able to derive a set of general sharp bounds on how well certain classes of functions of a hidden variable can(not) be estimated from a noisy observation in terms of different information metrics. These bounds provide converse (negative) results: If an information metric is small, then any non-trivial function of the hidden variable cannot be estimated with probability of error or mean-squared error smaller than a certain threshold. The main tool used to derive the converse bounds is a set of statistics known as the Principal Inertia Components (PICs). The PICs provide a fine-grained decomposition of the dependence between two random variables. Since there are well-studied statistical methods for estimating the PICs, we can then determine the (im)possibility of estimating large classes of functions by using the bounds derived in this thesis and standard statistical tests. The PICs are of independent interest, and are applicable to problems in information theory, statistics, learning theory, and beyond. In the security and privacy setting, the PICs fulfill the dual goal of providing (i) a measure of (in)dependence between the secret and disclosed information of a security system, and (ii) a complete characterization of the functions of the secret information that can or cannot be reliably inferred given the disclosed information. We study the information-theoretic properties of the PICs, and show how they characterize the fundamental limits of perfect privacy. The results presented in this thesis are applicable to estimation, security and privacy. For estimation and statistical learning theory, they shed light on the fundamental limits of learning from noisy data, and can help guide the design of practical learning algorithms. Furthermore, as illustrated in this thesis, the proposed converse bounds are particularly useful for creating security and privacy metrics, and characterize the inherent trade-off between privacy and utility in statistical data disclosure problems. The study of security systems through the information-theoretic lens adds a new dimension for understanding and quantifying security against very powerful adversaries. Furthermore, the framework and metrics discussed here provide practical insight on how to design and improve security systems using well-known coding and optimization techniques. We conclude the thesis by presenting several promising future research directions.by Flavio du Pin Calmon.Ph. D