Collusion Attacks to Tanaka's Corrected ID-Based Non-interactive Key Sharing Scheme

Ik Rae JEONG  Jeong Ok KWON  Dong Hoon LEE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.3   pp.932-934
Publication Date: 2009/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.932
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
non-interactive key sharing,  identity-based cryptosystem,  collusion attacks,  

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In 2006, Tanaka has proposed an efficient variant of Maurer-Yacobi's identity-based non-interactive key sharing scheme. In Tanaka's scheme, the computational complexity to generate each user's secret information is much smaller than that of Maurer-Yacobi's scheme. Tanaka's original key sharing scheme does not provide completeness, and so Tanaka has corrected the original scheme to provide completeness. In this paper, we show that Tanaka's corrected key sharing scheme is not secure against collusion attacks. That is, two users can collaborate to factorize a system modulus with their secret information and thus break the key sharing scheme.