IACR News item: 03 September 2012
Alex Escala, Javier Herranz, Benoit Libert, Carla Rafols
ePrint ReportThe notion of security for IB-TDFs put forward by Bellare \\textit{et al.} easily extends to the hierarchical scenario, but an (H)IB-TDF secure in this sense is not known to generically imply other related primitives with security against adaptive-id adversaries, not even IND-ID-CPA secure encryption. Our first contribution is to define a new security property for (H)IB-TDFs. We show that functions satisfying this property imply secure cryptographic primitives in the adaptive identity-based setting: these include encryption schemes with semantic security under chosen-plaintext attacks, deterministic encryption schemes, and (non-adaptive) hedged encryption schemes that maintain some security when messages are encrypted using randomness of poor quality. We emphasize that some of these primitives were unrealized in the (H)IB setting previous to this work.
As a second contribution, we describe the first pairing-based HIB-TDF realization. This is also the first example of hierarchical trapdoor function based on traditional number theoretic assumptions: so far, constructions were only known under lattice assumptions. Our HIB-TDF construction is based on techniques that differ from those of Bellare {\\it et al.} in that it uses a
hierarchical predicate encryption scheme as a key ingredient. The resulting HIB-TDF is proved to satisfy the new security definition, against either selective or, for hierarchies of constant depth, adaptive adversaries. In either case, we only need the underlying predicate encryption system to be selectively secure.
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