In today’s ever-increasingly digital world, the concept of data privacy has become more and more important. Researchers have developed many privacy-preserving technologies, particularly in the area of data mining and data sharing. These technologies can compute exact data mining models from private data without revealing private data, but are generally slow. We therefore present a framework for implementing efficient privacy-preserving secure approximations of data mining tasks. In particular, we implement two sketching protocols for the scalar (dot) product of two vectors which can be used as sub-protocols in larger data mining tasks. These protocols can lead to approximations which have high accuracy, low data leakage, and one to two orders of magnitude improvement in efficiency. We show these accuracy and efficiency results through extensive experimentation. We also analyze the security properties of these approximations under a security definition which, in contrast to previous definitions, allows for very efficient approximation protocols.