We present an encryption scheme for authorized equality test on ciphertexts (SEET), which allows the data owner to authorize a tester to compare her ciphertexts without decrypting their values. The security of SEET is formally proved against three types of adversary, two of them for ciphertext confidentiality in the phases before and after authorization respectively, and the third for token privacy. To the best of our knowledge, our SEET construction is the first encryption scheme supporting equality test on ciphertexts that is proven secure against the three types of adversary in the standard model. Our SEET construction outperforms existing schemes in terms of ciphertext size and encryption/decryption/testing costs. To show its application in set operations, we extend it into schemes for controlled set distance computation, such that a curious server is able to deduce the similarity/dissimilarity score between two encrypted user sets without knowing their elements.