In 2019, Antoine Joux proposed a FHE based on Fermat numbers, with an aim to express all cryptographic functions in simple operations on the ciphertext components and their binary decompositions. We use recent results on sub-Gaussian variables to find better bounds on the errors in the cryptosystem leading to smaller parameters. We also adapt the concept of k-bit encryption and functional bootstrapping proposed by Gao to the FHE. With this variant, we can extract the XOR and AND gates (and all other basic gates) in a single bit extraction. For larger values of k, we also discuss possibilities of evaluating commonly used activation functions in neural networks using this mechanism.

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https://uvsq-fr.zoom.us/j/96588261994?pwd=YVZLYm04R2dUOFQvS25lb2QzVm9Ydz09

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