Achieving full security in privacy-preserving data mining

In privacy-preserving data mining, a number of parties would like to jointly learn a function of their private data sets in a way that no information about their inputs, beyond the output itself, is revealed as a result of such computation. Yang et al. 2010 showed that several popular data mining algorithms can be reduced to three basic operations, secure implementation of which - termed Secure Product of Summations (SPoS), Secure Ratios of Summations (SRoS), and Secure Comparison of Summations (SCoS) - would lead to privacy-preserving data mining solutions. The authors showed that prior privacy-preserving data mining solutions are unsatisfactory in presence of participants'collusion and they gave new implementation of these operations that were designed to sustain the collusion. In this work, we show that unfortunately the protocols of Yang et al. leak a significant amount of private information and are not secure even if no collusion takes place. We then show how these operations can be securely and efficiently realized in the same and stronger security models, which leads to fully secure solutions for many data mining algorithms.