Cryptology ePrint Archive: Report 2021/677

Generalized Galbraith's Test: Characterization and Applications to Anonymous IBE Schemes

Paul Cotan and George Teseleanu

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 will focus on two constructions that address the anonymity problem inherent in Cocks' scheme and we will tackle some of their incomplete theoretical claims. More precisely, we rigorously study Clear et. al and Zhao et. al's schemes and give accurate probabilities of successful decryption and identity detection in the non-anonymized version of the schemes. Also, in the case of Zhao \emph{et. al}'s scheme, we give a proper description of the underlying security assumptions.

Category / Keywords: public-key cryptography / Galbraith's test, anonymity, identity-based encryption, probability distribution, statistical distance

Original Publication (with minor differences): MDPI Mathematics

Date: received 24 May 2021

Contact author: george teseleanu at yahoo com, paulcotan at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20210525:071053 (All versions of this report)

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