On Constructing Pairing-Free Identity-Based Encryptions

Abstract

In this paper, we focus on constructing IBE from hardness assumptions without pairings. Especially, we propose two IBE schemes that are provably secure under new number theoretic assumptions over the group ZN2∗, in the Random Oracle (RO) model. We essentially take advantage of the underlying algebraic structure to overcome the difficulties in devising an IBE scheme. More precisely, our contributions are two-fold and can be summarised as follows: (i) We give two concrete pairing-free constructions of IBE based on a variant of DDH assumption and Paillier’s DCR assumption respectively over the group ZN2∗. These schemes are quite efficient and easily to be proven IND- ID- CPA in the random oracle model. (ii) We also provide a generic construction of selectively secure IBE from DDH group with a DL -solvable subgroup in the standard model by employing puncturable PRFs and indistinguishability obfuscation.