Executing Cosine Similarity and Euclidean Distance Directly Over Encrypted Vectors

Core engineering and protocols for Homomorphic Vector Matching.

The Catastrophic Vulnerability of Centralized Biometric Databases

Unlike passwords or cryptographic keys, human biometrics (faces, irises, fingerprints) cannot be changed if compromised. Centralized databases containing millions of raw biometric templates represent catastrophic single points of failure. FHEID resolves this fundamental dilemma through Fully Homomorphic Encryption: biometrics are encrypted at the edge device and remain permanently encrypted in the cloud.

Executing Vector Arithmetic in the Encrypted Domain

FHEID uses the Cheon-Kim-Kim-Song (CKKS) homomorphic scheme. By packing the 512 normalized feature components into a single polynomial, the cloud server evaluates the cosine similarity: SIM(u, v) = u . v. The cloud processes this vector dot product using homomorphic multiplications and cyclic rotations, outputting an encrypted scalar score without ever accessing the cleartext vector.