Re: [P1363:] HIBE Scheme
Dear list,
I do not agree that the Boneh-Boyen HIBE framework [BBG-HIBE]
outperforms the Gentry-Silverberg [GS-HIBE] by every criterion.
First, [GS-HIBE] is more efficient than [BBG-HIBE] at least for
encryption. [GS-HIBE] is more efficient than [BBG-HIBE] also for
decryption if t< 3, where t is the depth of hierarchy.
Second, the security assumption of [GS-HIBE] differs from that of
[BBG-HIBE]. That is, [GS-HIBE] is secure in the Random Oracle model
assuming the BDH assumption, where [BBG-HIBE] is secure in the generic
model assuming the l-BDH assumption. I cannot say which outperforms the
other.
[GS-HIBE] Hierarchical ID-Based Cryptography, C.Gentry, A.Silverberg,
ASIACRYPT2002
Security: random oracle model, BDH assumption
Efficiency for encryption: (t-1) EC-Scalar Mults
Efficiency for decryption: t Pairings
[BBG-HIBE] Hierachical Identity Based Encryption with Constant Size
Ciphertext, D.Boneh, X.Boyen, E.Goh, EUROCRYPT2005
Security: generic model, l-BDH assumption
Efficiency for encryption: 1 Pairing + t EC-Scalar Mults
Efficiency for decryption: 2 Pairings + (2t+4) EC-Scalar Mults
> On May 20, 2009, at 10:49 PM, kobayashi.tetsutaro wrote:
>
> > B) Scheme
> > P1363.3 D1 should have a scheme for HIBE primitives. For example, we
> > propose as follows.
> >
> > 8.5 The GS-HIBE Scheme
> > GS-HIBE uses the P-GS-HIBE family of primitives to construct an HIBE
> > scheme
> > that has a security reduction to the Bilinear Diffie-Hellman (BDH)
> > problem.
> > This HIBE scheme is based on the work of GS02 and YKZHMI06.
>
>
> As I understand things, the Boneh-Boyen HIBE framework outperforms
> Gentry-Silverberg by every criterion. Why do you prefer GS to BB?
> Unless there are legacy uses of GS we want to capture, I'd strongly
> prefer sticking to one or both of BB HIBE and Boyen's Eurocrypt '07
> HIBE for BB2/SK. (This assuming we decide HIBE is something we want
> to consider in the first go-round of .3.)
>
> -hs.
>
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--
Kobayashi Tetsutaro <kobayashi.tetsutaro@xxxxxxxxxxxxx>
TEL: 0422-59-3462 FAX: 0422-59-4015
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