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Attribute-based encryption (ABE) and attribute-based keyword search (ABKS) facilitate fine-grained access and search control for cloud-assisted Industrial Internet of Things (IIoT). However, existing schemes suffer from the following drawbacks:(1) their computational overhead in data outsourcing and retrieval is exceptionally high;(2) they obtain wrong search results if one or more of the queried keywords are wrongly selected;(3) in most existing ABKS, the untrustworthiness of the cloud server is not taken into account, and the correctness of the search results is not verified;(4) existing verifiable ABKS schemes do not support search results verification without the main data, and verifiers have to first download the search results and then check their correctness. In this paper, we design a verifiable online/offline multi-keyword search (VMKS) scheme providing high-level solutions to the aforementioned problems. We …