Nowadays, data privacy plays a key role in the context of the Cloud services, Artificial Intelligence applications, Internet of Things and other applications. Among all the different approaches in the field of information security and cryptography for preserving the privacy and the secrecy of data, one of the most promising is Fully Homomorphic Encryption (FHE). In fact, FHE enables users to perform computations directly on encrypted data without having to first decrypt it, ensuring the property of data confidentiality and preventing the exposure of sensitive information. This thesis presents a use case application for FHE, more specifically, a homomorphic implementation of the currently most used hash function, SHA256.