International Association
for Cryptologic Research

Composite-order bilinear groups provide many structural features that have proved useful for both constructing cryptographic primitives and as a technique in security reductions. Despite these convenient features, however, composite-order bilinear groups are less desirable than prime-order bilinear groups for reasons of efficiency. A recent line of work has therefore focused on translating these structural features from the composite-order to the prime-order setting; much of this work focused on two such features, projecting and canceling, in isolation, but a recent result due to Seo and Cheon showed that both features can be obtained simultaneously in the prime-order setting.

In this paper, we reinterpret the construction of Seo and Cheon in the context of dual pairing vector spaces, a tool previously used to simulate other desirable features of composite-order groups in the prime-order setting. In this way, we are able to obtain a unified framework that simulates all of the known composite-order features in the prime-order setting. We demonstrate the strength of this framework by showing that the addition of even a weak form of projecting on top of the pre-existing uses of dual pairing vector spaces can be leveraged to \"boost\" a fully IND-CPA secure identity-based encryption scheme to one that is fully IND-CCA1 secure.