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In this work, we first design a function encryption scheme by using key encapsulation. We combine public key encryption with symmetric encryption to implement the idea of key encapsulation. In the key encapsulation, we use a key to turn a message (plaintext) into a ciphertext by symmetric encryption, and then we use public key encryption to turn this key into another ciphertext. In the design of function encryption scheme, we use the public key encryption system, symmetric encryption system,doi:10.1155/2019/8567534 fatcat:ra5nwpp7snhhjir24avb3xbkfi