The paper proposes a new framework for homomorphically evaluating Boolean functions using the Torus Fully Homomorphic Encryption (TFHE) scheme. This approach allows for the evaluation of more complex Boolean functions with multiple inputs using a single bootstrapping operation, significantly reducing the number of bootstrapping operations required compared to previous methods. The authors introduce an intermediate homomorphic layer that encodes bits into a small ring \(\mathbb{Z}_p\), enabling the evaluation of Boolean functions with one cheap homomorphic sum followed by one bootstrapping. They define the concept of \(\mu\)-encodings and provide algorithms to find valid sets of encodings for a given Boolean function. The framework is applied to various cryptographic primitives, including the AES cipher, achieving significant performance improvements over state-of-the-art implementations. The paper also discusses the theoretical foundations of the approach, including the properties of \(\mu\)-encodings and the construction of gadgets for evaluating Boolean functions.The paper proposes a new framework for homomorphically evaluating Boolean functions using the Torus Fully Homomorphic Encryption (TFHE) scheme. This approach allows for the evaluation of more complex Boolean functions with multiple inputs using a single bootstrapping operation, significantly reducing the number of bootstrapping operations required compared to previous methods. The authors introduce an intermediate homomorphic layer that encodes bits into a small ring \(\mathbb{Z}_p\), enabling the evaluation of Boolean functions with one cheap homomorphic sum followed by one bootstrapping. They define the concept of \(\mu\)-encodings and provide algorithms to find valid sets of encodings for a given Boolean function. The framework is applied to various cryptographic primitives, including the AES cipher, achieving significant performance improvements over state-of-the-art implementations. The paper also discusses the theoretical foundations of the approach, including the properties of \(\mu\)-encodings and the construction of gadgets for evaluating Boolean functions.