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We study the problem of computing on large datasets that are stored on an untrusted server. We follow the approach of amortized verifiable computation introduced by Gennaro, Gentry, and Parno in CRYPTO 2010. We present the first practical verifiable computation scheme for high degree polynomial functions. Such functions can be used, for example, to make predictions based on polynomials fitted to a large number of sample points in an experiment. In addition to the many non-cryptographic applications of delegating high degree polynomials, we use our verifiable computation scheme to obtain new solutions for verifiable keyword search, and proofs of retrievability. Our constructions are based on the DDH assumption and its variants, and achieve adaptive security, which was left as an open problem by Gennaro et al.(albeit for general functionalities).

Our second result is a primitive which we call …