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2018 | OriginalPaper | Chapter

On Constructing Pairing-Free Identity-Based Encryptions

Authors : Xin Wang, Bei Liang, Shimin Li, Rui Xue

Published in: Information Security

Publisher: Springer International Publishing

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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 \(\mathbb {Z}_{N^2}^*\), 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 \(\mathsf {DCR}\) assumption respectively over the group \(\mathbb {Z}_{N^2}^*\). These schemes are quite efficient and easily to be proven \(\mathsf {IND}\text {-}\mathsf {ID}\text {-}\mathsf {CPA}\) in the random oracle model. (ii) We also provide a generic construction of selectively secure IBE from DDH group with a \(\mathsf {DL}\)-solvable subgroup in the standard model by employing puncturable PRFs and indistinguishability obfuscation.

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Of course, this cannot be realized in a prime order group due to the hardness of discrete logarithm problem, instead we can choose a composite order group with unknown order.

Note that since \(\ell \) is a polynomial of the security parameter \(\kappa \), but N is exponentially large, a brute force may not be possible to retrieve \(a_i\in \mathbb {Z}_{\lfloor N/\ell \rfloor }\) from \(g^{a_i}\). For instance, practically \(\ell =80\), \(N=2^{1024}\).

Observe that g generates the 2N-th power residue subgroup of \(\mathbb {Z}_{N^2}^*\), namely \(\mathbb {G}_{N}\) w.h.p: the probability that g is not a generator is \(\frac{p'+q'-1}{p'q'}\le \frac{1}{p'}+\frac{1}{q'}\).

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Title: On Constructing Pairing-Free Identity-Based Encryptions
Authors: Xin Wang
Bei Liang
Shimin Li
Rui Xue
Publisher: Springer International Publishing
Book: Information Security
Print ISBN: 978-3-319-99135-1

Electronic ISBN: 978-3-319-99136-8

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-99136-8_17

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