POLYNOMIAL EVALUATION DELEGATION

Shares for one or more data values in a dataset can be computed using evaluation point values and sharing polynomials. Lagrangian coefficients can also be computed for the evaluation point values. The shares and the Lagrangian coefficients may be used to evaluate the polynomials on the data values. The technique can also include encrypting the Lagrangian coefficients according to an encryption scheme that provides for addition operations between encrypted values. An operation on representations of coefficients of the evaluation polynomial, representations of the shares, and the encrypted representations of the Lagrangian coefficients can be delegated to a remote computing environment. The operation can be performed at the remote computing environment, such as by performing a map-reduce operation. Results of the delegated operation can be received from the remote computing environment and processed to produce representation(s) of evaluation(s) of the polynomial on the data value(s).