  In a resource-constrained IoT network, end nodes like WSN, RFID, and embedded
systems are used which have memory, processing, and energy limitations. One of
the key distribution solutions in these types of networks is to use the key
pre-distribution scheme, which accomplishes the key distribution operation
offline before the resource-constrained devices deployment in the environment.
Also, in order to reduce the shared key discovery computing and communication
overhead, the use of combinatorial design in key pre-distribution has been
proposed as a solution in recent years. In this study, a ${\mu}$-PBIBD
combinatorial design is introduced and constructed and the mapping of such
design as a key pre-distribution scheme in the resource-constrained IoT network
is explained. Through using such key pre-distribution scheme, more keys are
obtained for communication between two devices in the IoT network. This means
that there will be a maximum of q + 2 keys between the two devices in the
network, where q is the prime power, that is, instead of having a common key
for a direct secure connection, the two devices can have q + 2 common keys in
their key chain. Accordingly, we would increase the resilience of the key
pre-distribution scheme compared to the SBIBD, TD, Trade-KP, UKP *, RD * and
2-D ${\mu}$-PBIBD designs.
  Keywords: resource-constrained IoT network; combinatorial design;
${\mu}$-PBIBD; resilience.
