Free-XOR TFHE via Lazy Bootstrapping

Ali Ajorian, Osman Biçer · 2026 · arXiv

DOI: 10.48550/arXiv.2610.29983 · open-access PDF

Abstract

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). \cite{chen2024free} proposed a gate bootstrapping framework in which $\txor$ gates can be evaluated simply by adding the two input ciphertexts, resulting in what they call \textit{free-XOR}. To obtain a functionally complete set of operations, they further designed a GB procedure for eva

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