Any algorithm that mangles/hashes a string but can be matched against?

Any algorithm that mangles/hashes a string but can be matched against?

Usage case: client needs to send a huge string over HTTP. The server replies whether the string contains some substring. However, huge string is huge. This system is as a result really inefficient. Moreover, huge string contains some sensitive info, so this is really insecure.
Is there some pseudo-hashing mechanism that somehow summarizes a big string into some number, which all substrings of this big string would hash to the same number, but non-substrings will with high probability not hash to this big string?