This document proposes a secure auditing storage scheme with efficient key updates for a cognitive industrial internet of things (IIoT) environment. It discusses how cognitive computing and IIoT can advance manufacturing capabilities. The existing auditing schemes only consider data integrity and elements without key exposure resistance, so the proposed scheme uses techniques like homomorphic verifiable authenticators and proxy recryption to allow third-party auditors to efficiently update keys and authenticators in the cloud without recovering old keys or data. It aims to support data and sub-block auditing to address owners' concerns about data security in the cloud.