Does a cipher exist with the following properties?
Could you be looking for a password hashing KDF function with a secret parameter (a.k.a. pepper)?

With the correct password, the verification succeeds in a flash; without it, you can neither find the password, nor the keys derived from it. 

Also, since it's not data/message encryption, the input and output are "short".

Of course, what appears to meet the description could still fail to provide the functionality that you want, so you have to rethink from the start to determine what security service(s) you want. 

E.g.


confidentiality, 
integrity protection, 
authenticity guarantee, 
non-repudiation, 
recipient exclusion, 
proof-of-work.