Efficient polynomial delegation under standard assumptions

In this paper we present a new scheme for verifiable delegation of polynomials in a cloud computing scenario. The security of our scheme is based on a standard assumption, the subgroup membership one. Furthermore, the scheme is highly efficient since the number of operations is independent of the degree of the polynomial. We also propose a second scheme that allows to hide the polynomial to be delegated and that improves the efficiency of the scheme by Benabbas et al. in [BGV11]. Moreover, we give a third polynomial delegation scheme which is the first that allows the client to hide the input point.