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In this thesis, we study fully homomorphic encryption, a cryptographic technique that allows computations to be performed directly on encrypted data, without requiring prior decryption. This field has experienced remarkable growth over the past fifteen years, with the emergence of increasingly efficient encryption schemes. Nevertheless, homomorphic computations remain significantly more costly than their classical counterparts, which still hinders their adoption in practical applications.In this work, we focus on one of the most promising schemes: TFHE. We propose new techniques aimed at accelerating homomorphic computations for various use cases. By leveraging an innovative message encoding strategy, we begin by designing more efficient algorithms for the homomorphic evaluation of Boolean functions.Next, we address the problem of transciphering, an approach that seeks to reduce bandwidth consumption during the transmission of homomorphically encrypted data. This requires the evaluation of a symmetric encryption algorithm within the homomorphic domain. Still relying on our encoding technique, we develop a homomorphic implementation of the standard AES encryption scheme that outperforms state-of-the-art implementations, and present our contribution to the design of a stream cipher specifically optimized for transciphering.We continue with a contribution that extends the capabilities of TFHE by enabling it to operate over larger message spaces. This improvement is made possible by a new algorithm for evaluating look-up tables in these extended spaces.Finally, we propose a conceptually simple and practical method for generating parameter sets that ensure security, correctness, and efficiency, thereby facilitating the use of TFHE in real-world applications.