# Encrypted Vector Similarity Computations Using Partially Homomorphic Encryption: Applications and Performance Analysis

arXiv: https://arxiv.org/abs/2503.05850 · HTML: https://mlsanity.com/paper/2503.05850/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 4 of 4)

- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [TenSEAL: A Library for Encrypted Tensor Operations Using Homomorphic Encryption](https://mlsanity.com/paper/2104.03152/) (2021)
- [LightPHE: Integrating Partially Homomorphic Encryption into Python with Extensive Cloud Environment Evaluations](https://mlsanity.com/paper/2408.05219/) (2024)
- [CipherFace: A Fully Homomorphic Encryption-Driven Framework for Secure Cloud-Based Facial Recognition](https://mlsanity.com/paper/2502.18514/) (2025)

## Built on by (most cited first, 1 of 1)

- [Policy-Driven AI in Dataspaces: Taxonomy, Explainability, and Pathways for Compliant Innovation](https://mlsanity.com/paper/2507.20014/) (2025)

## Abstract (arXiv)

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.