Gathering and processing sensitive data is a difficult task. In fact, there is no common recipe for building the necessary information systems. In this paper, we present a provably secure and efficient general-purpose computation system to address this problem. Our solution--SHAREMIND--is a virtual machine for privacy-preserving data processing that relies on share computing techniques. This is a standard way for securely evaluating functions in a multi-party computation environment. The novelty of our solution is in the choice of the secret sharing scheme and the design of the protocol suite. We have made many practical decisions to make large-scale share computing feasible in practice. The protocols of SHAREMIND are information-theoretically secure in the honest-but-curious model with three computing participants. Although the honest-but-curious model does not tolerate malicious participants, it still provides significantly increased privacy preservation when compared to standard cen...