The Exact Security of an Identity Based Signature and its Applications.
Benoît Libert, Jean-Jacques Quisquater · 2004
This paper first positively answers the previously open question of whether it was possible to obtain an optimal security reduction for an identity based signature (IBS) under a reasonable computational assumption. We revisit the Sakai-Ogishi-Kasahara IBS that was recently proven secure by Bellare, Namprempre and Neven through a general framework applying to a large family of schemes. We show that their modified SOK-IBS scheme can be viewed as a one-level instantiation of Gentry and Silverberg's alternative hierarchical IBS the exact security of which was never considered before. We also show that this signature is as secure as the one-more Diffie-Hellman problem. As an application, we propose a modification of Boyen's "Swiss Army Knife" identity based signature encryption (IBSE) that presents better security reductions and satisfies the same strong security requirements with a similar efficiency.