Secure Fast Covariance Intersection Using Partially Homomorphic and Order Revealing Encryption Schemes

Fast covariance intersection is a widespread technique for state estimate fusion in sensor networks when cross-correlations are not known and fast computations are desired. The common requirement of sending estimates from one party to another during fusion forfeits local privacy. Current secure fusion algorithms rely on encryption schemes that do not provide sufficient flexibility. As a result, excess communication between estimate producers is required, which is often undesirable. We propose a novel method of homomorphically computing the fast covariance intersection algorithm on estimates encrypted with a combination of encryption schemes. Using order revealing encryption, we show how an approximate solution to the fast covariance intersection weights can be computed and combined with partially homomorphic encryptions of estimates, to calculate an encryption of the fused result. The described approach allows secure fusion of any number of private estimates, making third-party cloud processing a viable option when working with sensitive state estimates or when performing estimation over untrusted networks.