We solve the problem of resisting the collusion
attack in the one-way hash chain based self-healing key distributions introduced by Dutta et al., coupling it with the prearranged life cycle based approach of Tian et al. that uses the same self-healing mechanism introduced in Dutta et al. Highly efficient schemes are developed compared to the existing works with the trade-off in pre-arranged life cycles on users by the group manager and a slight increase in the storage overhead. For scalability of business it is often necessary to design more innovation and flexible business strategies in certain business models that allow contractual subscription or rental, such as subscription of mobile connection or TV channel for a
pre-defined period. The subscribers are not allowed to revoke before their contract periods (life cycles) are over. Our schemes fit into such business environment. The proposed schemes are proven to be computationally secure and resist collusion between new joined users and revoked users together with forward and backward secrecy. The security proof is in an appropriate security model. Moreover, our schemes do not forbid revoked users from rejoining in later sessions unlike the existing self-
healing key distribution schemes
