In this work, we first propose a new functional bootstrapping with TFHE for evaluating any function of domain and codomain the real torus T by using a small number of bootstrappings. This result improves some aspects of previous approaches: like them, we allow for evaluating any functions, but with better precision. In addition, we develop more efficient multiplication and addition over ciphertexts building on the digit-decomposition approach of [GBA21]. As a practical application, our results

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... ead to an efficient implementation of ReLU, one of the most used activation functions in deep learning. The paper is concluded by extensive experimental results comparing each building block as well as their practical relevance and trade-offs.