Déjà Q All Over Again: Tighter and Broader Reductions of q-Type Assumptions
- Cite this paper as:
- Chase M., Maller M., Meiklejohn S. (2016) Déjà Q All Over Again: Tighter and Broader Reductions of q-Type Assumptions. In: Cheon J., Takagi T. (eds) Advances in Cryptology – ASIACRYPT 2016. ASIACRYPT 2016. Lecture Notes in Computer Science, vol 10032. Springer, Berlin, Heidelberg
In this paper, we demonstrate that various cryptographic constructions—including ones for broadcast, attribute-based, and hierarchical identity-based encryption—can rely for security on only the static subgroup hiding assumption when instantiated in composite-order bilinear groups, as opposed to the dynamic q-type assumptions on which their security previously was based. This specific goal is accomplished by more generally extending the recent Déjà Q framework (Chase and Meiklejohn, Eurocrypt 2014) in two main directions. First, by teasing out common properties of existing reductions, we expand the q-type assumptions that can be covered by the framework; i.e., we demonstrate broader classes of assumptions that can be reduced to subgroup hiding. Second, while the original framework applied only to asymmetric composite-order bilinear groups, we provide a reduction to subgroup hiding that works in symmetric (as well as asymmetric) composite-order groups. As a bonus, our new reduction achieves a tightness of \(\log (q)\) rather than q.