  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.
