Abstract
The main approaches currently used to construct identity-based encryption (IBE) schemes are based on bilinear mappings, quadratic residues and lattices. Among them, the most attractive approach is the one based on quadratic residues, due to the fact that the underlying security assumption is a well-understood hard problem. The first such IBE scheme was constructed by Cocks, and some of its deficiencies were addressed in subsequent works. In this paper, we focus on two constructions that address the anonymity problem inherent in Cocks’ scheme, and we tackle some of their incomplete theoretical claims. More precisely, we rigorously study Clear et al.’s and Zhao et al.’s schemes and give accurate probabilities of successful decryption and identity detection in the non-anonymized version of the schemes. Furthermore, in the case of Zhao et al.’s scheme, we give a proper description of the underlying security assumptions.
Highlights
From a desire to avoiding several issues inherent to public-key cryptography, Shamir came up in 1984 with an interesting and novel concept: identity-based encryption [1]
An identity-based encryption (IBE) scheme consists of four probabilistic polynomial-time (PPT) algorithms: Setup, KeyGen, Enc and Dec
We further present a slightly improved version of Clear et al.’s IBE scheme
Summary
From a desire to avoiding several issues (e.g., management of trust, public-key recovery) inherent to public-key cryptography, Shamir came up in 1984 with an interesting and novel concept: identity-based encryption [1]. The test has been thoroughly analyzed in [5,6] Despite this impediment, several schemes that achieve anonymity have been proposed in the literature [5,7,8,9,10,11]. This structure was later studied and simplified by Joye [8] As a consequence, he managed to improve both the speed and ciphertext expansion of Clear et al.’s IBE scheme. By taking a different approach, Zhao et al [10] managed to further speed up encryption Their scheme have twice the ciphertext expansion compared to Joye’s scheme. In. Sections 4 and 5, we apply our results to obtain precise characterizations of Clear et al.’s and Zhao et al.’s IBE schemes.
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