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Given hash(x) and y, can I verify z = hash(x + y)?

Say I only know hash(x) and y.

I receive z that is supposed to be hash(x + y)? Is there any way I can verify that without knowing x?

I'm interested in any mechanism that could make such check possible rather than particular hash and + operations.

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To clear up a bit:

  • y is public, it's a timestamp
  • there is A who knows x - it's a file
  • A tells B hash(x) (or any other needed piece of information about x, but not the x itself - it's too big)
  • A sends x to C
  • C needs to send confirmation to B "I have x at the moment, as a proof here's hash(x, y)
  • B needs to verify that what it received is indeed a hash of a file and a timestamp (but it doesn't have the full file, only a piece of information about it)

The real verification I want to make in B is that C actually has full file x at the time y.