Pairing-free equality test over short ciphertexts

The concept of public key encryption with equality test was introduced at CT-RSA 2010. It has been used in many fields, especially in cloud storage. However, the previous schemes do not provide an effective authorization mechanism. To fill this gap, Ma et al. presented a public key encryption with equality test supporting flexible authorization based on the bilinear pairings. Recently, Lin et al. presented a pairing-free scheme that employs quadratic curve to perform the equality tests, which can achieve a trade-off between computational cost and storage space. In this article, we show that the equality test can be better performed by using a straight line, rather than a quadratic curve. Moreover, we simplify the encryption algorithm, as well as reduce the ciphertext storage space.