Traditional approaches to vector similarity search over encrypted data rely on fully homomorphic encryption (FHE) to enable computation without decryption. However, the substantial computational overhead of FHE makes it impractical for large-scale real-time applications. This work explores a more efficient alternative: using additively homomorphic encryption (AHE) for privacy-preserving similarity search. We consider scenarios where either the query vector or the database vectors remain encrypted, a setting that frequently arises in applications such as confidential recommender systems and secure federated learning. While AHE only supports addition and scalar multiplication, we show that it is sufficient to compute inner product similarity--one of the most widely used similarity measures in vector retrieval. Compared to FHE-based solutions, our approach significantly reduces computational overhead by avoiding ciphertext-ciphertext multiplications and bootstrapping, while still preserving correctness and privacy. We present an efficient algorithm for encrypted similarity search under AHE and analyze its error growth and security implications. Our method provides a scalable and practical solution for privacy-preserving vector search in real-world machine learning applications.

翻译：传统加密数据向量相似性搜索方法依赖全同态加密技术，以实不解密计算。然而，全同态加密的巨大计算开销使其难以适用于大规模实时应用。本研究探索了一种更高效的替代方案：使用加法同态加密实现隐私保护相似性搜索。我们考虑查询向量或数据库向量保持加密状态的场景，这种设置在机密推荐系统与安全联邦学习等应用中频繁出现。虽然加法同态加密仅支持加法与标量乘法运算，但我们证明其足以计算向量检索中最广泛使用的相似性度量——内积相似度。相较于基于全同态加密的解决方案，我们的方法通过避免密文-密文乘法与自举操作，显著降低了计算开销，同时仍保持正确性与隐私性。我们提出了一种在加法同态加密下实现加密相似性搜索的高效算法，并分析了其误差增长与安全影响。本方法为现实机器学习应用中的隐私保护向量搜索提供了可扩展的实用解决方案。