McEliece Public Key Encryption
A decision problem is to decide if something is true or not (typically phrased in terms of membership of a language). In complexity theory, decision problems are useful for understanding, and most problems can be reduced to a decision problem of some form.

However, in everyday life we are usually not trying to solve decision problems. The algorithms in a public key cryptosystem aren't trying to solve decision problems, so you cannot use the language of decision problems. It just doesn't make sense, as you have discovered.

The notion of polynomial time still makes sense, though.