A Note on Efficient Privacy-Preserving Similarity Search for Encrypted Vectors

TL;DR

This paper proposes an efficient privacy-preserving vector similarity search method using additively homomorphic encryption, reducing computational overhead while maintaining accuracy and privacy in encrypted data retrieval.

Contribution

It introduces a novel approach leveraging AHE for inner product similarity, offering a practical alternative to FHE for large-scale encrypted vector search.

Findings

Significantly reduces computational overhead compared to FHE-based methods.

Supports inner product similarity computation with additively homomorphic encryption.

Provides scalable and practical solutions for real-world privacy-preserving vector search.

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.