Controlling verification of key-value stores

Deferred verification of the integrity of data operations over a set of data that is hosted at an untrusted module (UM) is controlled. The controlling includes generating a request for a data operation on the set of data. The request includes an authentication portion. The request is sent to the UM. A response to the request is received from the UM. The response includes cryptographic verification information attesting the integrity of the data operation with respect to prior data operations on the set of data. The response includes results from deferred verification at a trusted module (TM).