Searchable Encryption (SE) enables users to query outsourced encrypted data while preserving data confidentiality. However, most efficient schemes still leak the search pattern and access pattern, which may allow an honest-but-curious cloud server to infer query contents, user interests, or returned records from repeated searches and observed results. Existing pattern-hiding solutions mainly target keyword queries and do not naturally support Boolean range queries over encrypted spatial data. This paper presents BRASP, a searchable encryption scheme for Boolean range queries over encrypted spatial data. BRASP combines Hilbert-curve-based prefix encoding with encrypted prefix--ID and keyword--ID inverted indexes to support efficient spatial range filtering and conjunctive keyword matching. To hide the search pattern and access pattern under a dual-server setting, BRASP integrates index shuffling for encrypted keyword and prefix entries with ID-field redistribution across two non-colluding cloud servers. BRASP also supports dynamic updates and achieves forward security. We formalize the security of BRASP through confidentiality, shuffle indistinguishability, query unforgeability, and forward-security analyses, and we evaluate its performance experimentally on a real-world dataset. The results show that BRASP effectively protects query privacy while incurring relatively low computation and communication overhead. To facilitate reproducibility and further research, the source code of BRASP is publicly available at https://github.com/Egbert-Lannister/BRASP

翻译：可搜索加密（SE）使用户能够在保护数据机密性的同时查询外包加密数据。然而，大多数高效方案仍会泄露搜索模式和访问模式，这可能使诚实但好奇的云服务器通过重复搜索和观察结果推断查询内容、用户兴趣或返回记录。现有的模式隐藏方案主要针对关键词查询，无法自然支持加密空间数据上的布尔范围查询。本文提出BRASP——一种适用于加密空间数据布尔范围查询的可搜索加密方案。BRASP将基于希尔伯特曲线的前缀编码与加密前缀-标识符及关键词-标识符倒排索引相结合，以支持高效的空间范围过滤与合取关键词匹配。为在双服务器设置下隐藏搜索模式和访问模式，BRASP将加密关键词和前缀条目的索引洗牌与跨两个非共谋云服务器的标识符字段重新分配相集成。BRASP还支持动态更新并具备前向安全性。通过机密性、洗牌不可区分性、查询不可伪造性和前向安全性分析形式化定义了BRASP的安全性，并在真实数据集上通过实验评估其性能。结果表明，BRASP在有效保护查询隐私的同时，仅引入较低的计算与通信开销。为促进可复现性与进一步研究，BRASP源代码已公开于https://github.com/Egbert-Lannister/BRASP。