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Public Key Encryption with Equality Test. Construction of Public key Encryption with Equality Test With Provable Security. With the continuous development of the Internet of Things (IoT), a growing number of users choose to store the data collected from their smart devices on a cloud server for saving costs. However, the security and privacy issues that accompany the cloud-assisted IoT are also becoming increasingly apparent. Considering the untrusted nature of cloud server, the data collected by the smart sensor should be encrypted before being transmitted to the cloud. Nevertheless, the above mechanism raises another serious problem. For users of another public key cryptosystem, it is impractical to download all the data stored in the cloud to find the data they need. Therefore, in this book, we chose the equality test to solve the problem of performing the search functionality on the ciphertext stored in the cloud server without disclosing any information related to these ciphertexts.