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Free-XOR TFHE via Lazy Bootstrapping

Ali Ajorian, Osman Biçer · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29983 · cited by 0 works (OpenAlex) · open-access PDF

Portuguese

Port bootstrapping (GB) é uma técnica amplamente utilizada em esquemas de criptografia totalmente homomórficos como o FHEW, como o TFHE, para avaliar portas booleanas ao mesmo tempo que reduz o ruído do texto cifrado resultante. No entanto, o custo computacional do GB é tipicamente dominado por um conjunto funcional completo de operações cegas (BR). \citechen{2024free} propôs um quadro de bootstrapping de portas no qual portas $\txor$ podem ser avaliadas simplesmente adicionando os dois textos cifrados de entrada, resultando no que eles chamam \textit{free-XOR}. Para obter um conjunto funcional completo de operações, eles projetaram um procedimento GB para avaliar portas $\tand$ usando duas rotações cegas ligeiras. Neste trabalho, propomos um

Machine translation (Meta M2M100); the English original follows.

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 evaluating $\tand$ gates using two lightweight blind rotations. In this work, we propose a similar gate bootstrapping framework that supports free evaluation of $\txor$ gates while evaluating \textit{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 \cite{chen2024free}, both conceptually and in terms of implementation.

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Topics: Bootstrapping (finance), Computer science, Algorithm, Set (abstract data type), Boolean circuit, Boolean function

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