Modern music retrieval runs on vector embeddings, and once these embeddings are shared for search or matching they can be copied, probed, or used to train generative models. Fully homomorphic encryption can compute on them but is impractical at scale because of ciphertext--ciphertext multiplication and bootstrapping. We observe that when only one operand is encrypted, the query or the database, similarity search reduces to ciphertext addition and ciphertext--plaintext multiplication, which additive homomorphic encryption supports cheaply (through Paillier, or CKKS restricted to additive operations). Building on this observation, we (i) implement two music-specific inference attacks and quantify the privacy--utility tradeoff of provable mitigations, (ii) introduce structure-aware additive primitives with learned per-block weighting at no extra cryptographic cost, and (iii) show across four audio datasets that additive search preserves nearest-neighbor rankings exactly while avoiding the ciphertext--ciphertext multiplication and bootstrapping of full-depth FHE and scaling far better in embedding dimension than a true-additive Paillier baseline.

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