As described above, yes.

However, if you don’t want to have to keep the file, you can pre-compute combinations of nonce, byte-range, and hash. Store these sets in a much smaller file, and then use the next one from the list to challenge the provider.

So for example, say you want the provider to be able to prove storage once a week for a decade. You’ll need ~600 tuples of nonce/byte-range/hash. Each of these records would take roughly 128 bytes to store. 128 x 600 = ~77Kb.

Thus for a decade of weekly storage proofs, you need to store less than a tenth of a megabyte per file.

Note that this storage requirement is completely independent of the file size. So it may be advantageous to combine related files together into an archive (zip) so that you need only pay the tuple storage cost once.

Each tuple should be used only once. So if you’re planning to have multiple suppliers, you’ll want to multiply by that number when precalculating.