HERS: Homomorphically Encrypted Representation Search

We present a method to search for a probe (or query) image representation against a large gallery in the encrypted domain. We require that the probe and gallery images be represented in terms of a fixed-length representation, which is typical for representations obtained from learned networks. Our encryption scheme is agnostic to how the fixed-length representation is obtained and can therefore be applied to any fixed-length representation in any application domain. Our method, dubbed HERS (Homomorphically Encrypted Representation Search), operates by (i) compressing the representation towards its estimated intrinsic dimensionality with minimal loss of accuracy (ii) encrypting the compressed representation using the proposed fully homomorphic encryption scheme, and (iii) efficiently searching against a gallery of encrypted representations directly in the encrypted domain, without decrypting them. Numerical results on large galleries of face, fingerprint, and object datasets such as ImageNet show that, for the first time, accurate and fast image search within the encrypted domain is feasible at scale (500 seconds; $275\times$ speed up over state-of-the-art for encrypted search against a gallery of 100 million).