How to ensure that a "received value" is not altered?
From my point of view, multi-hashing will slow down things, but it won't add the security you are looking for in this case.


  Is cryptography able to solve this problem?


Yes. What you need is a message authentication code (MAC), which is a short piece of information used to authenticate a message and to provide integrity and authenticity assurances on the message. Integrity assurances detect accidental and intentional message changes, while authenticity assurances affirm the message's origin. 

For your further research endeavours, "MAC" and "HMAC" are the relevant keywords.

Nota Bene: In bis comment, @fgrieu hints at practically using a HMAC with SHA256... which indeed seems to be the most logic choice (because it's pretty minimal while currently offering expected security).