Suppose you encrypt a list of names of Americans with a 512-bit secret-key algorithm. Currently no supercomputer can break it, but someday a supercomputer might exist that could iterate through all possible keys and find a key that decrypts the list to what sound like American-sounding names, and when you find that, you know you've probably got the right key.
Is there a term for secret-key encryption where many possible keys will decrypt the ciphertext to realistic-looking plaintext, so the encryption can never be brute-forced, because even if you find a key that decrypts to one of the realistic plaintexts, you won't know if you got the right one? (And thus, presumably, the encryption could be done with a shorter encryption key, since it can't be brute-forced anyway.)
A one-time pad would have this property, of course, but presumably so could other systems.
Say, instead of storing a list of American names, you come up with an index of every American first name and every American last name. Then when storing the firstname-lastname pairs, you store them as pairs of numbers. Then any key that decrypts the ciphertext to a list of numbers will thereby decrypt to a list of names. (Except, you'd need to do more work than that, because some names are more common than others, so the attacker could try to find a key which decrypts to a list where the names follow the expected distribution. But that's the idea.)
So does this have a name? Many-plaintext encryption or something?