Function secret sharing (FSS) ⇒ DPF

Fully-black-box reduction · standard model · BGI15 · security loss: none: the DPF hiding game is the FSS hiding game restricted to point functions

Statement

A DPF is two-party function secret sharing for the class of point functions: a two-party FSS scheme for a class $\mathcal{F}$ containing every point function $f_{\alpha ,\beta }$ ($f_{\alpha ,\beta }(\alpha )=\beta$ and $f_{\alpha ,\beta }(x)=0$ for $x\ne \alpha$) is, restricted to those functions, a DPF — BGI15.

Sketch

Run the FSS key generation on $f_{\alpha ,\beta }$. Correctness (the shares sum to $f_{\alpha ,\beta }(x)$) and hiding are the FSS properties restricted to point functions.