Secure multi-party computation (MPC) is a central area of research in cryptography. Its goal is to allow a set of players to jointly compute a function on their inputs while protecting and preserving the privacy of each player's input.;Motivated by the huge growth of data available and the rise of global privacy concerns of entities using this data, we study the feasibility of using secure computation techniques on large scale data sets to address these concerns.;An important limitation of generic secure computation protocols is that they require at least linear time complexity. This seems to rule out applications involving big amounts of data. On the other hand, specific applications may have particular properties that allow for ad-hoc secure protocols overcoming the linear time barrier. In addition, in some settings the full level of security guaranteed by MPC protocols may not be required, and some controlled amount of privacy leakage can be acceptable.;Towards this end, we first take a theoretical point of view, and study whether sublinear time RAM programs can be computed securely with sublinear time complexity in the two party setting. We then take a more practical approach, and study the specific scenario of private database querying, where both the server's data and the client's query need to be protected. In this last setting we provide two private database management systems achieving different levels of efficiency, functionality, and security. These three results provide an overview of this three-dimensional trade-off space.;For the above systems, we describe formal security definitions and stablish mathematical proofs of security. We also take a practical approach roviding an implementation of the systems and experimental analysis of their efficiency.
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