Cryptology ePrint Archive: Report 2016/840

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

Melissa Chase and Mary Maller and Sarah Meiklejohn

Abstract: 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 Deja 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.

Category / Keywords: foundations / assumptions, reductions

Original Publication (with minor differences): IACR-ASIACRYPT-2016

Date: received 30 Aug 2016

Contact author: s meiklejohn at ucl ac uk

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Version: 20160906:122540 (All versions of this report)

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