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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

Chinese

门 bootstrapping (GB) 是一种在 FHEW 类似的完全同形加密系统中广泛使用的技术,例如 TFHE,用于评估布尔式门,同时同时减少所产生的加密文本的噪音。然而,GB 的计算成本通常由昂贵的盲旋转(BR)主导。 \citechen{2024free} 提出了一个门 bootstrapping 框架,其中 $\txor$ 门可以简单地通过添加两个输入加密文本来评估,从而产生了他们称之为 \textit{free-XOR} 的计算成本。 为了获得功能齐全的操作,他们进一步设计了一种 GB 程序来评估 $\tand$ 门使用两种轻重的盲旋旋转。 在这项工作中,我们提出了一个类似的 bootstrapping 框

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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