Lifting Standard Model Reductions to Common Setup Assumptions

In this paper we show that standard model black-box reductions naturally lift to various setup assumptions, such as the random oracle (ROM) or ideal cipher model. Concretely, we prove that a black-box reduction from a security notion P to security notion Q in the standard model can be turned into a non-programmable black-box reduction from PO to QO in a model with a setup assumption O, where PO and QO are the natural extensions of P and Q to a model with a setup assumption O. Our results rely on a generalization of the recent framework by Hofheinz and Nguyen (PKC 2019) to support primitives which make use of a trusted setup. Our framework encompasses standard idealized settings like the random oracle and the ideal cipher model. At the core of our main result lie novel properties of negligible functions that can be of independent interest.