On the Asymptotic Capacity of Information Theoretical Privacy-preserving Epidemiological Data Collection

We formulate a new secure distributed computation problem, where a simulation center can require any linear combination of $K$ users' data through a caching layer consisting of $N$ servers. The users, servers, and data collector do not trust each other. For users, any data is required to be protected from up to $E$ servers; for servers, any more information than the desired linear combination cannot be leaked to the data collector; and for the data collector, any single server knows nothing about the coefficients of the linear combination. Our goal is to find the optimal download cost, which is defined as the size of message uploaded to the simulation center by the servers, to the size of desired linear combination. We proposed a scheme with the optimal download cost when $E < N-1$. We also prove that when $E\geq N-1$, the scheme is not feasible.