This research demonstrates a practical approach to encrypted vector similarity computations using Partially Homomorphic Encryption (PHE) instead of more complex Fully Homomorphic Encryption.

• Enables privacy-preserving similarity search for facial recognition, recommendation engines, and LLMs
• Proposes novel method to calculate cosine similarity using PHE despite mathematical limitations
• Compares performance of different encryption schemes (Paillier, Damgard-Jurik, Okamoto-Uchiyama)
• Offers a practical security solution that balances privacy protection with computational efficiency

This advancement matters because it allows AI systems to compare vectors (like embeddings) while keeping the data encrypted end-to-end, addressing critical privacy concerns without sacrificing functionality.

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