Homomorphic encryption is a recent technique that enables computation on encrypted data. The subject of this internship is the TFHE cryptosystem and, in particular, its functional bootstrapping method. This method enables us to evaluate a function on an encrypted message while reducing the ciphertext noise. If we denote [x] the encryption of message x and consider a function f, functional bootstrapping enables us to calculate [f (x)] with the latter ciphertext having less noise than [x]. Note that f can be the identity function, and in this case, we obtain a new encryption of x, but with a smaller noise (regular bootstrapping). In this internship, we will use the tree-based method, a method that generalizes functional bootstrapping with several encrypted inputs. These inputs will be two or more ciphertexts of size 4 bits. The aim is to build a set of universal instructions using this method. For instance, we would like to have efficient operators to perform XOR, AND, additions, etc. of several ciphertexts. During the internship, the student will propose a small instruction set and analyze it with respect to its homomorphic execution (parameter settings, functional bootstrapping approach, noise analysis, etc.). The work will also include prototyping in C++ with TFHElib and experimental evaluation of the resulting performances. Particular attention will also be given to conditional assignment instructions.