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 space approach initiated by Okamoto and Takashima and formulate versatile tools in this framework that can be used to translate composite order schemes for which the prior techniques of Freeman were insufficient. Our techniques are typically applicable for composite order schemes relying on the canceling property and proven secure from variants of the subgroup decision assumption, and will result in prime order schemes that are proven secure from the decisional linear assumption. As an instructive example, we obtain a translation of the Lewko-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. In the full version of this paper, we also provide a translation of the Lewko-Waters unbounded