You can only compress to a certain level. For example, you can't compress a sufficiently random bitstream because there are no patterns. See also information th

You can only compress to a certain level. For example, you can't compress a sufficiently random bitstream because there are no patterns. See also information theory. I wrote a game for programmers about 5 years ago that used a toy proof-of-storage system. It gave as many 1GB blobs to players as requested, picked random chunks and stored checksums of those. The player doesn't know which chunks have been picked. Some hours later you could start the challenge that you still have the file and the system challenged you to send the checksum of the chunks it picked. If you could answer this, you obviously still have the file and got points. This allowed the system to force a player to store 1GB of data while the verification only needed some bytes of storage.