Nowadays, data privacy plays a key role in the context of the Cloud services,Artificial Intelligence, Internet of Things and other applications. Among all thedifferent approaches in the field of information security and cryptography for preserving the privacy and the secrecy of data, one of the most promising is FullyHomomorphic Encryption (FHE). In fact, FHE enables users to perform computations directly on encrypted data without having to first decrypt it, ensuringconfidentiality 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.The initial part of this thesis is focused on the study of FHE, initially going oversome basic fundamentals of cryptography, and then introducing various Homomorphic Encryption schemes, culminating in the FHE scheme called TFHE (FullyHomomorphic Encryption over the Torus).In the second part of this thesis we present our implementation of SHA256 thatoperates homomorphically on encrypted input. We then integrate this work in thecontext of a client-server architecture where the server can compute the hash function without knowing the input giving by the client. We develop this applicationusing the ZAMA Concrete compiler based on the TFHE scheme.Given the continuous progress in the development of FHE applications, we believethat a homomorphic version of SHA256 might be extremely helpful as a foundationfor future complex applications, aiming to increase users’ privacy.