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On the Security of Combinatorial Design Based Group Key Management Scheme



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Journal of Information Systems Security
Volume 15, Number 2 (2019)
Pages 101116
ISSN 1551-0123 (Print)
ISSN 1551-0808 (Online)
Shravani M. Patil — National Institute of Technology Goa, India
B. R. Purushothama — National Institute of Technology Goa, India
Information Institute Publishing, Washington DC, USA




The combinatorial design based group key management scheme is proposed by Eltoweissy et al. with an objective to reduce the number of keys to be stored by the users and number of rekey messages required to handle the group member join and leave events. The scheme requires lesser number of keys and rekey message compared to the logical key hierarchy based group key management scheme. However, we show that the scheme by Eltoweissy et al. cannot be used in practice since any two leaving group users can collude to get the group key of the group. Surprisingly it is true for any user leave event. We show that if the scheme has to be collusion resistant, the number of keys and the rekey messages required will never be optimal and it will be worse than the logical key hierarchy based scheme. In particular, we show that the number of rekey messages grow towards being linear in the number of group users. So, the scheme would start reflecting the cost similar to that of a star network.




Group Key Management, Combinatorial Optimization, Collusion, Exclusion Basis System




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