Fine-Grained Non-interactive Key Exchange, Revisited

We revisit the construction of multiparty non-interactive key-exchange protocols with fine-grained security, which was recently studied in (Afshar et al., Eurocrypt 2023). Their work introduced a 4-party non-interactive key exchange with quadratic hardness, and proved it secure in Shoup’s generic group model. This positive result was complemented with a proof that n-party non-interactive key exchange with superquadratic security cannot exist in Maurer’s generic group model, for any \(n\ge 3\) . Because Shoup’s model is stronger than Maurer’s model, this leaves a gap between the positive and the negative result, and their work left as an open question the goal of closing this gap, and of obtaining fine-grained non-interactive key exchange without relying on idealized models. In this work, we make significant progress on both questions. We obtain two main results: