  Private Computation (PC), recently introduced by Sun and Jafar, is a
generalization of Private Information Retrieval (PIR) in which a user wishes to
privately compute an arbitrary function of data stored across several servers.
We construct a PC scheme which accounts for server collusion, coded data, and
non-linear functions. For data replicated over several possibly colluding
servers, our scheme computes arbitrary functions of the data with rate equal to
the asymptotic capacity of PIR for this setup. For systematically encoded data
stored over colluding servers, we privately compute arbitrary functions of the
columns of the data matrix and calculate the rate explicitly for polynomial
functions. The scheme is a generalization of previously studied star-product
PIR schemes.
