Encrypted Vector Similarity Computations Using Partially Homomorphic Encryption: Applications and Performance Analysis
It addresses privacy-preserving similarity search for applications such as facial recognition and recommendation engines, but is incremental as it adapts existing PHE methods to a specific task.
This paper tackled the problem of encrypted vector similarity search by using partially homomorphic encryption (PHE) as a more practical alternative to fully homomorphic encryption (FHE), achieving faster computation, smaller ciphertexts and keys, and suitability for memory-constrained environments in applications like facial recognition.
This paper explores the use of partially homomorphic encryption (PHE) for encrypted vector similarity search, with a focus on facial recognition and broader applications like reverse image search, recommendation engines, and large language models (LLMs). While fully homomorphic encryption (FHE) exists, we demonstrate that encrypted cosine similarity can be computed using PHE, offering a more practical alternative. Since PHE does not directly support cosine similarity, we propose a method that normalizes vectors in advance, enabling dot product calculations as a proxy. We also apply min-max normalization to handle negative dimension values. Experiments on the Labeled Faces in the Wild (LFW) dataset use DeepFace's FaceNet128d, FaceNet512d, and VGG-Face (4096d) models in a two-tower setup. Pre-encrypted embeddings are stored in one tower, while an edge device captures images, computes embeddings, and performs encrypted-plaintext dot products via additively homomorphic encryption. We implement this with LightPHE, evaluating Paillier, Damgard-Jurik, and Okamoto-Uchiyama schemes, excluding others due to performance or decryption complexity. Tests at 80-bit and 112-bit security (NIST-secure until 2030) compare PHE against FHE (via TenSEAL), analyzing encryption, decryption, operation time, cosine similarity loss, key/ciphertext sizes. Results show PHE is less computationally intensive, faster, and produces smaller ciphertexts/keys, making it well-suited for memory-constrained environments and real-world privacy-preserving encrypted similarity search.