Multi-factor authentication (MFA) is an approach to user validation that requires the presentation of two or more authentication factors. Given the popularity of cloud systems, MFA systems become vital in authenticating users. However, MFA approaches are highly intrusive and expose users' sensitive information to untrusted cloud servers that can keep physically identifying elements of users, long after the user ends the relationship with the cloud. To address these concerns in this work, we present a privacy-preserving multi-factor authentication system utilizing the features of big data called MACA. In MACA, the first factor is a password while the second factor is a hybrid profile of user behavior. The hybrid profile is based on users' integrated behavior, which includes both host-based characteristics and network flow-based features. MACA is the first MFA that considers both user privacy and usability combining big data features (26 total configurable features). Furthermore, we adopt fuzzy hashing and fully homomorphic encryption (FHE) to protect users' sensitive profiles and to handle the varying nature of the user profiles. We evaluate the performance of our proposed approach through experiments with several public datasets. Our results show that our proposed system can successfully validate legitimate users while detecting impostors.