Polynomial function secret sharing provides for computation of reconstruction share results for a polynomial function on an input. An allocatable share of the polynomial function is received at a computing system of the share result computation systems. The allocatable share is generated from the polynomial function. Each of the allocatable shares is distributed to a unique share result computation system of the share result computation systems. Each allocatable share includes a share element for each coefficient in the polynomial function, wherein the share elements for a coefficient across the share result computation systems summing to the coefficient. A reconstruction share result is generated at the computing system by computing a dot product of the input and the allocatable share received by the computing system. A combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function on the input.