Abstract: Public key encryption with equality test can determine whether the plaintexts of ciphertexts encrypted with different public keys in the cloud server are identical. Most of the public key encryption schemes with equality test based on traditional PKI system are implemented by bilinear pairs, whose computation is cumbersome and inefficient. At the same time, with the increase in the number of users, the generation, application, issuance and revocation of a large number of certificates become more and more onerous, which brings challenges to the maintenance and sustainable work of the system. To address this problem, this paper proposes a pairing-free identity-based public key encryption with equality test. The scheme determines a straight line through the two points constructed from the plaintext information, and uses the straight line to implement the encryption, decryption, authorization and equality test processes, which gets rid of the restriction of bilinear pairs and improves the computational efficiency. Meanwhile, the scheme is constructed based on the identity cryptosystem, which solves the complex certificate management problem in the traditional PKI system. Under the CDH and DDH assumptions in the random oracle model, the proposed scheme is capable to achieve the security of OW-ID-CCA and IND-ID-CCA. 

Key words: identity-based, public key encryption, straight line, equality test