<p>Cloud-assisted edge computing offers a more flexible, efficient, and secure computing paradigm for various industries and application areas, thereby enhancing digital transformation and intelligent development. As is known, private data is encrypted when stored on a cloud, and searchable encryption is an efficient method for achieving keyword search on ciphertext. With the rapid growth of ciphertext size on the clouds, the vast amount of data imposes higher requirements on the search performance. Research works have proposed Searchable Public-key Ciphertexts with Hidden Structures (SPCHS), which achieve a high number of complex ciphertexts within sublinear search time. However, this type of scheme is considered only for a single data owner; moreover, due to the specificity of SPCHS, it is impossible to extend the existing access control scheme directly to SPCHS. To address the aforementioned issues, we propose a Fast Keyword Search Scheme (FKSS) with access control for cloud-assisted edge computing in multi-owner environments. Specifically, we designed a fast keyword search algorithm in which each data owner constructs a ciphertext with hidden relations, enabling the reduction of ciphertext matches by publishing the hidden relations to achieve sublinear search complexity in the search process. Formal security proof demonstrates that the proposed FKSS is secure, while the performance evaluation and analysis demonstrated its feasibility and efficiency.</p>