Privacy Preserving Distance Computation using Somewhat-trusted Third Parties

A critically important component of most signal processing procedures is that of computing the distance between signals. In multi-party processing applications where these signals belong to different parties, this introduces privacy challenges. The signals may themselves be private, and the parties to the computation may not be willing to expose them. Solutions proposed to the problem in the literature generally invoke homomorphic encryption schemes, secure multi-party computation, or other cryptographic methods which introduce significant computational complexity into the proceedings, often to the point of making more complex computations requiring repeated computations unfeasible. Other solutions invoke third parties, making unrealistic assumptions about their trustworthiness. In this paper we propose an alternate approach, also based on third party computation, but without assuming as much trust in the third party. Individual participants to the computation "secure" their data through a proposed secure hashing scheme with shared keys, prior to sharing it with the third party. The hashing ensures that the third party cannot recover any information about the individual signals or their statistics, either from analysis of individual computations or their long-term aggregate patterns. We provide theoretical proof of these properties and empirical demonstration of the feasibility of the computation.