任意单/二元整数函数的有效同态求值及其应用

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE
Daisuke MAEDA, Koki MORIMURA, Shintaro NARISADA, Kazuhide FUKUSHIMA, Takashi NISHIDE
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引用次数: 2

摘要

我们提出了如何同态求任意单变量和双变量整数函数,如除法。Okada等人(WISTP'18)先前提出的一项工作使用多项式评估,使得该方案仍然与BFV和BGV方案中的SIMD操作兼容,并使用输入域𝕫257实现。然而,Okada等人的方案需要输入域大小中明文-密文相乘和密文-密文相加的二次次数,尽管这些操作比密文-密文相乘更轻量级,但二次复杂度使得处理更大的输入相当低效。在这项工作中,我们首先改进了先前的工作,并提出了一种新的方法,利用打包方法来处理更大的输入域大小,而不是启用SIMD操作,从而可以以一种合理有效的方式处理更大的输入域大小,例如𝕫215。此外,我们还展示了如何将输入域大小略微扩展到𝕫216,开销相对适中。此外,我们还展示了另一种处理较大输入域大小的方法,即使用两个密文加密一个整数明文,并将我们的技术应用于单变量/二元函数求值。我们在PALISADE中实现了Okada等人的先前工作、我们改进的Okada等人的改进版本和我们的新方案,输入域为𝕫215,并确认了先前工作和我们改进的先前工作的估计运行时间分别约为117天和59天,而我们的新方案可以在307秒内计算完成。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficient Homomorphic Evaluation of Arbitrary Uni/Bivariate Integer Functions and Their Applications
We propose how to homomorphically evaluate arbitrary univariate and bivariate integer functions such as division. A prior work proposed by Okada et al. (WISTP'18) uses polynomial evaluations such that the scheme is still compatible with the SIMD operations in BFV and BGV schemes, and is implemented with the input domain 𝕫257. However, the scheme of Okada et al. requires the quadratic numbers of plaintext-ciphertext multiplications and ciphertext-ciphertext additions in the input domain size, and although these operations are more lightweight than the ciphertext-ciphertext multiplication, the quadratic complexity makes handling larger inputs quite inefficient. In this work, first we improve the prior work and also propose a new approach that exploits the packing method to handle the larger input domain size instead of enabling the SIMD operation, thus making it possible to work with the larger input domain size, e.g., 𝕫215 in a reasonably efficient way. In addition, we show how to slightly extend the input domain size to 𝕫216 with a relatively moderate overhead. Further we show another approach to handling the larger input domain size by using two ciphertexts to encrypt one integer plaintext and applying our techniques for uni/bivariate function evaluation. We implement the prior work of Okada et al., our improved version of Okada et al., and our new scheme in PALISADE with the input domain 𝕫215, and confirm that the estimated run-times of the prior work and our improved version of the prior work are still about 117 days and 59 days respectively while our new scheme can be computed in 307 seconds.
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来源期刊
CiteScore
1.10
自引率
20.00%
发文量
137
审稿时长
3.9 months
期刊介绍: Includes reports on research, developments, and examinations performed by the Society''s members for the specific fields shown in the category list such as detailed below, the contents of which may advance the development of science and industry: (1) Reports on new theories, experiments with new contents, or extensions of and supplements to conventional theories and experiments. (2) Reports on development of measurement technology and various applied technologies. (3) Reports on the planning, design, manufacture, testing, or operation of facilities, machinery, parts, materials, etc. (4) Presentation of new methods, suggestion of new angles, ideas, systematization, software, or any new facts regarding the above.
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