Abstract: Identity-based encryption with equality test (IBEET) is proposed to check whether the underlying messages of ciphertexts, even those encrypted with different public keys, are the same or not without decryption. Since people prefer to encrypt before outsourcing their data for privacy protection nowadays, the research of IBEET on cloud computing applications naturally attracts attention. However, we claim that the existing IBEET schemes suffer from the illegal trapdoor sharing problem caused by the inherited key escrow problem of the Identity-Based Encryption (IBE) mechanism. In traditional IBEET, the private key generator (PKG) with the master secret key generates trapdoors for all authorized cloud servers. Considering the reality in practice, the PKG is usually not fully trusted. In this case, the Private-Key Generator (PKG) may generate, share, or even sell any trapdoor without any risk of being caught, or not being held accountable, which may lead to serious consequences such as the illegal sharing of a gene bank’s trapdoors. In this paper, to relieve the illegal trapdoor sharing problem in IBEET, we present a new notion, called IBEET Supporting Accountable Authorization (IBEET-AA). In IBEET-AA, if there is a disputed trapdoor, the generator will be distinguished among the PKG and suspected testers by an additional tracing algorithm. For the additional tracing function, except for the traditional indistinguishability (IND) and one-way (OW) security models in IBEET, we define three more security models to protect the tracing security against dishonest authorizers, PKG, and testers, respectively. Based on Gentry’s IBE scheme, we instantiate IBEET-AA and give a specific construction along with a formalized security proof with random oracles.