Training sophisticated machine learning models usually requires many training samples. Especially in healthcare settings these samples can be very expensive, meaning that one institution alone usually does not have enough. Merging privacy-sensitive data from different sources is usually restricted by data security and data protection measures. This can lead to approaches that reduce data quality by putting noise onto the variables (e.g., in epsilon-differential privacy) or omitting certain values (e.g., for k-anonymity). Other measures based on cryptographic methods can lead to very time-consuming computations, which is especially problematic for larger multi-omics data. We address this problem by introducing ESCAPED, which stands for Efficient SeCure And PrivatE Dot product framework. ESCAPED enables the computation of the dot product of vectors from multiple sources on a third-party, which later trains kernel-based machine learning algorithms, while neither sacrificing privacy nor adding noise. We have evaluated our framework on drug resistance prediction for HIV-infected people and multi-omics dimensionality reduction and clustering problems in precision medicine. In terms of execution time, our framework significantly outperforms the best-fitting existing approaches without sacrificing the performance of the algorithm. Even though we only present the benefit for kernel-based algorithms, our framework can open up new research opportunities for further machine learning models that require the dot product of vectors from multiple sources.