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Recently, the Industrial Internet of Things (IIoT) has become increasingly important for applications in the industry. IIoT has essentially become a prime security focus for implementing secure communication. Among the available cryptographic tools, identity-based signcryption provide a sound solution to fulfill the security requirement of IIoT. On the other hand a generalized proxy signcryption can work adaptively as proxy signature and proxy signcryption using a single algorithm. In order to accomplish effective and on-time communication whenever the manager of the company went out for a usual business trip or an IIoT device which has lack of resources, then it must need to delegate her/his signcryption rights to their subordinates (proxy agents/device). For this purpose, to make the delegation procedure more efficient and reliable, we proposed a lightweight identity-based generalized proxy signcryption (IBGPS …