This document discusses rekeying load in group key distributions that use cover-free families. It provides bounds on the number of messages needed to rekey a distribution after one or two users have been ejected simultaneously. For certain distributions based on symmetric combinatorial designs, the bounds shown are tight. In general, determining the minimal number of messages needed for rekeying a system based on a cover-free family is an NP-hard problem.

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On the Rekeying Load in Group Key Distributions Using Cover-
Free Families
Abstract
Key distributions based on cover-free families have been recently proposed for
secure rekeying in group communication systems after multiple simultaneous user
ejections. Existing literature has not quantified how difficult this rekeying operation
might be. This study provides upper bounds on the number messages necessary to rekey a
key distribution based on symmetric combinatorial designs after one or two simultaneous
user ejections. Connections are made to results from finite geometry to show that these
bounds are tight for certain key distributions. It is shown that in general determining the
minimal number of messages necessary to rekey a group communication system based on
a cover-free family is NP-hard.
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