Impossibility of unconditionally secure scalar products

The ability to perform scalar products of two vectors, each known to a different party, is a central problem in privacy preserving data mining and other multi-party computation problems. Ongoing search for both efficient and secure scalar product protocols has revealed that this task is not easy. In this paper we show that, indeed, scalar products can never be made secure in the information theoretical sense. We show that any attempt to make unconditionally secure scalar products will inevitably allow one of the parties to learn the other parties input vector with high probability. On the other hand, we show that under various assumptions, such as the existence of a trusted third party or the difficulty of discrete logarithms, both efficient and secure scalar products do exist. We proposed two new protocols for secure scalar products and compare their performance with existing secure scalar products

Distributed Constraint Optimization:Privacy Guarantees and Stochastic Uncertainty

Distributed Constraint Satisfaction (DisCSP) and Distributed Constraint Optimization (DCOP) are formal frameworks that can be used to model a variety of problems in which multiple decision-makers cooperate towards a common goal: from computing an equilibrium of a game, to vehicle routing problems, to combinatorial auctions. In this thesis, we independently address two important issues in such multi-agent problems: 1) how to provide strong guarantees on the protection of the privacy of the participants, and 2) how to anticipate future, uncontrollable events. On the privacy front, our contributions depart from previous work in two ways. First, we consider not only constraint privacy (the agents' private costs) and decision privacy (keeping the complete solution secret), but also two other types of privacy that have been largely overlooked in the literature: agent privacy, which has to do with protecting the identities of the participants, and topology privacy, which covers information about the agents' co-dependencies. Second, while previous work focused mainly on quantitatively measuring and reducing privacy loss, our algorithms provide stronger, qualitative guarantees on what information will remain secret. Our experiments show that it is possible to provide such privacy guarantees, while still scaling to much larger problems than the previous state of the art. When it comes to reasoning under uncertainty, we propose an extension to the DCOP framework, called DCOP under Stochastic Uncertainty (StochDCOP), which includes uncontrollable, random variables with known probability distributions that model uncertain, future events. The problem becomes one of making "optimal" offline decisions, before the true values of the random variables can be observed. We consider three possible concepts of optimality: minimizing the expected cost, minimizing the worst-case cost, or maximizing the probability of a-posteriori optimality. We propose a new family of StochDCOP algorithms, exploring the tradeoffs between solution quality, computational and message complexity, and privacy. In particular, we show how discovering and reasoning about co-dependencies on common random variables can yield higher-quality solutions

Elsevier Editorial System(tm) for Data & Knowledge Engineering Title: Impossibility of Unconditionally Secure Scalar Products Impossibility of Unconditionally Secure Scalar Products

Abstract The ability to perform scalar products of two vectors, each known to a different party, is a central problem in privacy preserving data mining and other multi party computation problems. Ongoing search for both efficient and secure scalar product protocols has revealed that this task is not easy. In this paper we show that, indeed, scalar products can never be made secure in the information theoretical sense. We show that any attempt to make unconditionally secure scalar products will always allow one of the parties to learn the other parties input vector with high probability. On the other hand, we show that under various assumptions, such as the existence of a trusted third party, both efficient and secure scalar products do exist