Privacy-preserving support vector machine (SVM) classifiers are proposed for vertically and horizontally partitioned data. Vertically partitioned data represent instances where distinct entities hold different groups of input space features for the same individuals, but are not willing to share their data or make it public. Horizontally partitioned data represent instances where all entities hold the same features for different groups of individuals and also are not willing to share their data or make it public. By using a random kernel formulation we are able to construct a secure privacy-preserving kernel classifier for both instances using all the data but without any entity revealing its privately held data. Classification accuracy is better than an SVM classifier without sharing data, and comparable to an SVM classifier where all the data is made public.