In 2014, Chen et al. proposed a one-way hash self-healing group key distribution scheme for resource-constrained wireless networks in the journal of Sensors (14(14):24358-24380, doi: 10.3390/ s141224358). They asserted that their Scheme 2 achieves mt-revocation capability, mt-wise forward secrecy, any-wise backward secrecy and has mt-wise collusion attack resistance capability. Unfortunately, this paper pointed out that their scheme does not satisfy the forward security, mt-revocation capability and mt-wise collusion attack resistance capability.

In resource-constrained wireless networks, resources such as storage space and communication bandwidth are limited. To guarantee secure communication in resource-constrained wireless networks, group keys should be distributed to users. The self-healing group key distribution (SGKD) scheme is a promising cryptographic tool, which can be used to distribute and update the group key for the secure group communication over unreliable wireless networks. Among all known SGKD schemes, exponential arithmetic based SGKD (E-SGKD) schemes reduce the storage overhead to constant, thus is suitable for the the resource-constrained wireless networks. In this paper, we provide a new mechanism to achieve E-SGKD schemes with backward secrecy. We first propose a basic E-SGKD scheme based on a known polynomial-based SGKD, where it has optimal storage overhead while having no backward secrecy. To obtain the backward secrecy and reduce the communication overhead, we introduce a novel approach for message broadcasting and self-healing. Compared with other E-SGKD schemes, our new E-SGKD scheme has the optimal storage overhead, high communication efficiency and satisfactory security. The simulation results in Zigbee-based networks show that the proposed scheme is suitable for the resource-restrained wireless networks. Finally, we show the application of our proposed scheme.