*09:17*[Pub][ePrint] Adaptively Secure Puncturable Pseudorandom Functions in the Standard Model, by Susan Hohenberger and Venkata Koppula and Brent Waters

We study the adaptive security of constrained PRFs in the standard model. We initiate our exploration with puncturable PRFs. A puncturable PRF family is a special class of constrained PRFs, where the constrained key is associated with an element $x\'$ in the input domain. The key allows evaluation at all points $x\\neq x\'$.

We show how to build puncturable PRFs with adaptive security proofs in the standard model that involve only polynomial loss to the underlying assumptions. Prior work had either super-polynomial loss or applied the random oracle heuristic. Our construction uses indistinguishability obfuscation and DDH-hard algebraic groups of composite order.