Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting

In this paper, we explore a general methodology for converting composite order pairing-based cryptosystems into the prime order setting. We employ the dual pairing vector spaceapproach initiated by Okamoto and Takashima and formulate versatile tools in this frame-work that can be used to translate composite order schemes for which the prior techniquesof Freeman were insufficient. Our techniques are typically applicable for composite orderschemes relying on the canceling property and proven secure from variants of the subgroupdecision assumption, and will result in prime order schemes that are proven secure fromthe decisional linear assumption. As an instructive example, we obtain a translation of theLewko-Waters composite order IBE scheme. This provides a close analog of the Boneh-Boyen IBE scheme that is proven fully secure from the decisional linear assumption. Wealso provide a translation of the Lewko-Waters unbounded HIBE scheme.