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TFHE is a practical fully homomorphic encryption scheme (FHE) capable of computing any boolean gate or non-linear function. The scheme was originally designed to work for the single key setting. To implement realistic application scenarios, it is necessary to extend it to handle multiple users. In this paper, we introduce a new approach to generate TFHE bootstrapping keys for (predefined) multiple users. Hence, a fixed number of users can enjoy the same level of efficiency as in the single key setting, keeping their individual input privacy. Our construction relies on a novel algorithm called homomorphic indicator, which can be of independent interest. We provide a detailed analysis of the noise growth and a set of secure parameters suitable to be used in practice. Moreover, we compare the complexity of our technique with other state-of-the-art constructions and show which method performs better depending on the parameter sets. We also provide a prototype implementation of our technique. To the best of our knowledge, this is the first implementation of TFHE in the multiparty setting.

Efficient TFHE Bootstrapping in the Multiparty Setting