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Cloud-assisted Internet of Things (IoT) is a popular system model to merge the advantages of both the cloud and IoT. In this model, IoT collects the real-world data, and the cloud maximizes the value of these data by sharing and analyzing them. Due to the sensitivity of the collected data, maintaining the security of these data is one of the main requirements in practice. Searchable public-key encryption is a fundamental tool to achieve secure delegated keyword search over ciphertexts in the cloud. To accelerate the search performance, Xu et al. propose a new concept of searchable public-key ciphertexts with hidden structures (SPCHSs), and it constructs a SPCHS instance to achieve search complexity that is sublinear with the total number of ciphertexts rather than the linear complexity as in the traditional works. However, this paper cannot achieve the parallel keyword search due to its inherent limitations. Clearly, the aforementioned instance is impractical. To address this problem, we propose a new instance of SPCHS to achieve fast and parallel keyword search over public-key ciphertexts. In contrast to the work by Xu et al., a new type of hidden relationship among searchable ciphertexts is constructed by the new instance, where every searchable ciphertext has a hidden relationship with a common and public parameter. Upon receiving a keyword search trapdoor, one can disclose all corresponding relationships in parallel and then find all matching ciphertexts. Hence, the new relationship allows a keyword search task to be performed in parallel. In addition, due to the limited capability of IoT, the new instance achieves a more efficient encryption algorithm to save time and communication cost.

Fast and Parallel Keyword Search Over Public-Key Ciphertexts for Cloud-Assisted IoT