© 2013 IEEE. Sensitive data would be encrypted before uploading to the cloud due to the privacy issue. However, how to compare the encrypted data efficiently becomes a problem. Public Key Encryption with Equality Test (PKEET) provides an efficient way to check whether two ciphertexts (of possibly different users) contain the same message without decryption. As an enhanced variant, Attribute-based Encryption with Equality Test (ABEET) provides a flexible mechanism of authorization on the equality test. Most of the existing ABEET schemes are only proved to be secure in the random oracle model. Their security, however, would not be guaranteed if random oracles are replaced with real-life hash functions. In this work, we propose a construction of CP-ABEET scheme and prove its security based on some reasonable assumptions in the standard model. We then show how to modify the scheme to outsource complex computations in decryption and equality test to a third-party server in order to support thin clients.