Making cryptographic claims about stored data using an anchoring system

A data storage system creates a data signature for a data element that is to be stored by hashing the data element. The data storage system also creates a sequence signature for the data element and stores the sequence signature in a signature database. The sequence signature is created using the data signature of the data element and the previous sequence signature stored in the signature database. The data storage system transmits a copy of the sequence signature to an anchor system. The anchor system stores the copy as an export anchor and creates an import anchor based on the export anchor and information associated with the present time. The anchor system stores the import anchor and transmits a copy to the data storage system. An audit system uses the export anchor and import anchor to determine whether data stored by the data storage system has been modified.