Since Fully Homomorphic Encryption (FHE) is still unpractical, one alternative to guarantee privacy while outsourcing data processing to the cloud is to develop homomorphic versions of algorithms to be executed over encrypted data using a leveled or somewhat homomorphic encryption (LHE or SHE). In this work, we propose a homomorphic version of Principal Component Analysis, an algorithm for dimensionality reduction of a dataset, maintaining the information related to the variance of the original data as much as possible. PCA is used very often as a pre-processing step in machine learning tasks.