Interrupting export of memory regions

An apparatus for processing data comprises memory access circuitry to enforce ownership rights of a plurality of memory regions within a first memory. The memory access circuitry is responsive to a first export command received from a first export command source to perform a first export operation to encrypt the given owned data to form given encrypted data and to store the given encrypted data in a second memory. The memory access circuitry is responsive to a second export command for the given memory region received from a second export command source while the first export operation is being performed to determine whether said second export command source has higher priority than the first export command source and, when the second export command source has a higher priority, to interrupt the first export operation and to perform a second export operation specified by the second export command.