Déjà Q All Over Again: Tighter and Broader Reductions of q-Type Assumptions

Conference paper

DOI: 10.1007/978-3-662-53890-6_22

Part of the Lecture Notes in Computer Science book series (LNCS, volume 10032)
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.

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.Microsoft Research RedmondRedmondUSA
  2. 2.University College LondonLondonUK

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