A facility is provided for storing in a backup memory only those blocks of a file, or disk partition, which differ from corresponding blocks forming an earlier version of the file. Specifically, a file is divided into a number of blocks and a "signature" is generated for each such block. A block is then stored in the backup memory only if its associated signature differs from a signature generated for an earlier version of the block. In addition, if two blocks of the current version of the file have identical signatures and are to be stored in the backup memory, then only one of the two blocks is stored in the memory and a simple message indicating that the other block is equal to the one block is stored in the memory for the other block. Further, the application of such signatures is advantageously applied to the opposite case of restoring a file using copies of previous versions of the file that are stored in the backup memory.