What term is used to describe encryption that can allow computations to be conducted on ciphertext, with the results matching what would have happened if the same computations were performed on the original plain text?

Homomorphic encryption can perform computations on the ciphertext without access to the private key that the ciphertext was encrypted with. When the computations are completed, the results are the same as if those computations had been performed against the original plain text. Identity-preserving and replicable encryption were made up for this question.