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

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