Data privacy is a major threat to the widespread deployment of data grids in domains such as health care and finance. We propose a novel technique for obtaining knowledge - by way of a data mining model - from a data grid, while ensuring that the privacy is cryptographically secure. To the best of our knowledge, all previous approaches for solving this problem fail in the presence of malicious participants. In this paper we present an algorithm which, in addition to being secure against malicious members, is asynchronous, involves no global communication patterns, and dynamically adjusts to new data or newly added resources. As far as we know, this is the first privacy-preserving data mining algorithm to possess these features in the presence of malicious participants. Simulations of thousands of resources prove that our algorithm quickly converges to the correct result. The simulations also prove that the effect of the privacy parameter on the convergence time is logarithmic.