Fully homomorphic encryption (FHE) enables a simple, attractive framework for secure search. Compared to other secure search systems, no costly setup procedure is necessary; it is sufficient for the client merely to upload the encrypted database to the server. Confidentiality is provided because the server works only on the encrypted query and records. While the search functionality is enabled by the full homomorphism of the encryption scheme. For this reason, researchers have been paying increasing attention to this problem. Since Akavia et al. (CCS 2018) presented a framework for secure search on FHE encrypted data and gave a working implementation called SPiRiT, several more efficient realizations have been proposed. In this paper, we identify the main bottlenecks of this framework and show how to significantly improve the performance of FHE-base secure search. In particular, 1. To retrieve $\ell$ matching items, the existing framework needs to repeat the protocol $\ell$ times sequentially. In our new framework, all matching items are retrieved in parallel in a single protocol execution. 2. The most recent work by Wren et al. (CCS 2020) requires $O(n)$ multiplications to compute the first matching index. Our solution requires no homomorphic multiplication, instead using only additions and scalar multiplications to encode all matching indices. 3. Our implementation and experiments show that to fetch 16 matching records, our system gives an 1800X speed-up over the state of the art in fetching the query results resulting in a 26X speed-up for the full search functionality.

中文翻译：

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用于同态加密搜索的压缩遗忘编码

全同态加密 (FHE) 为安全搜索提供了一个简单、有吸引力的框架。与其他安全搜索系统相比，无需昂贵的设置程序；客户端只需将加密的数据库上传到服务器即可。提供机密性是因为服务器仅处理加密的查询和记录。而搜索功能是由加密方案的完全同态启用的。为此，研究人员越来越关注这个问题。由于阿卡维亚等人。（CCS 2018）提出了一个对 FHE 加密数据进行安全搜索的框架，并给出了一个名为 SPiRiT 的工作实现，已经提出了几个更有效的实现。在本文中，我们确定了该框架的主要瓶颈，并展示了如何显着提高基于 FHE 的安全搜索的性能。特别是， 1. 要检索 $\ell$ 匹配项，现有框架需要按顺序重复协议 $\ell$ 次。在我们的新框架中，在单个协议执行中并行检索所有匹配项。2. Wren 等人的最新工作。(CCS 2020) 需要 $O(n)$ 乘法来计算第一个匹配索引。我们的解决方案不需要同态乘法，而是只使用加法和标量乘法来编码所有匹配的索引。3. 我们的实现和实验表明，为了获取 16 条匹配记录，我们的系统在获取查询结果方面比现有技术提高了 1800 倍，从而使完整搜索功能的速度提高了 26 倍。