On Self-healing Key Distribution Schemes.

Self-healing key distribution schemes allow group managers to broadcast session keys to large and dynamic groups of users over unreliable channels. Roughly speaking, even if during a certain session some broadcast messages are lost due to network faults, the self-healing property of the scheme enables each group member to recover the key from the broadcast messages he/she has received before and after that session. Such schemes are quite suitable in supporting secure communication in wireless networks and mobile wireless ad-hoc networks. Recent papers have focused on self-healing key distribution, and have provided definitions, stated in terms of the entropy function, and some constructions. The contribution of this paper is the following: • We analyse current definitions of self-healing key distribution and, for two of them, we show that no protocol can achieve the definition. • We show that a lower bound on the size of the broadcast message, previously derived, does not hold. • We propose a new definition of self-healing key distribution, and we show that it can be achieved by concrete schemes. • We give some lower bounds on the resources required for implementing such schemes i.e., user memory storage and communication complexity. We prove that the bounds are tight. Along the same lines of previous works on the sub ject, we use concepts and techniques from Information Theory in our analysis of existing models, in proving/confuting statements, and in stating our new definition.