Secure Re-Keying in Group Key Management Using Combinatorial Designs

Wireless Sensor Networks (WSNs) are emerging as a vital technology in future network utilization due to their broad application range and cost-effectiveness. The Exclusion Basis System (EBS) is a combinatorial technique of group key management that offers long-term and flexible security mechanism in WSNs while allowing the efficient eviction of compromised nodes and secure updates to the key system through its re-keying strategy. Combinatorial design theory is an innovative technique to developing and analysing cryptographic algorithms for secure communication in WSNs. This article generalised the study of N. Karst and S. B. Wicker to [Formula: see text]-design with [Formula: see text], triangular Partially Balanced Incomplete Block Designs (PBIBD) with [Formula: see text]=1 and [Formula: see text]=0, transversal design (TD[Formula: see text]), and [Formula: see text]-net. We observed that [Formula: see text]-design ([Formula: see text]) with [Formula: see text] provides less re-keying value than N. Karst and S. B. Wicker result [34]. Furthermore, when [Formula: see text], TD[Formula: see text] and triangular PBIBD yield the same re-keying values, whereas when [Formula: see text], TD[Formula: see text] provides a lower re-keying value than triangular PBIBD, except at [Formula: see text], where they are equal. Additionally, when [Formula: see text] and [Formula: see text] triangular PBIBD shows lower re-keying values than TD[Formula: see text] if [Formula: see text] otherwise equal and when [Formula: see text], the re-keying value of triangular PBIBD is consistently lower than TD[Formula: see text]. Finally, when [Formula: see text], TD[Formula: see text] and [Formula: see text]-net provide the same re-keying value.