A Note on Efficient Privacy-Preserving Similarity Search for Encrypted Vectors
Dongfang Zhao
TL;DR
This paper addresses privacy-preserving vector similarity search when data is encrypted, arguing that fully homomorphic encryption (FHE) is impractical for real-time use. It demonstrates that additively homomorphic encryption (AHE) suffices to compute inner-product similarity between a plaintext query and encrypted vectors, avoiding expensive ciphertext-ciphertext multiplications and bootstrapping. The authors present a concrete algorithm to compute Enc(\sum_i x_i y_i) under AHE, analyze noise growth and security under IND-CPA, and derive a computational complexity of $O(d \log^2 N)$, highlighting substantial efficiency gains. The approach is particularly applicable to scenarios where only one side is encrypted, such as secure federated learning and confidential recommender systems, enabling scalable privacy-preserving vector search for real-world ML tasks.
Abstract
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.