Secure distortion computation among untrusting parties using homomorphic encryption

Alice and Bob possess sequences xⁿ and yⁿ respectively and would like to compute d(xⁿ, yⁿ) where d(· , ·) is a distortion measure. However, Alice and Bob do not trust each other and do not wish to reveal their data to each other. This paper describes and analyzes a protocol that uses homomorphic encryption for secure calculation of some special distortion functions without revealing xⁿ and yⁿ. The resulting distortion result is also in encrypted form. Two variants of the protocol are presented, one for the Hamming distance between binary vectors, and the other for squared error distortion between integer vectors. An application of the protocol for private biometric authentication is described in which Bob interacts with a remote encrypted fingerprint database (Alice) to achieve access control without revealing his own identity.