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原文摘要

Gate bootstrapping (GB) is a widely used technique in FHEW-like fully homomorphic encryption schemes, such as TFHE,for evaluating Boolean gates while simultaneously reducing the noise of the resulting ciphertext. However, the computational cost of GB is typically dominated by an expensive blind rotation (BR). [8] proposed a gate bootstrapping framework in which XOR gates can be evaluated simply by adding the two input ciphertexts, resulting in what they call freeXOR. To obtain a functionally complete set of operations, they further designed a GB procedure for evaluating AND gates using two lightweight blind rotations. In this work, we propose a similar gate bootstrapping framework that supports free evaluation of XOR gates while evaluating all symmetric binary Boolean gates, i.e., the 8 gates whose output is identical for the inputs (0,1)and (1,0), using two blind rotations. In addition to providing broader gate support, our construction is substantially simpler than that of [8], both conceptually and in terms of implementation. As a proof of concept, we implemented our approach and compared it with standard TFHE, measuring speedups of about 30% for AES and 34% for SHA.