Assume that we want to encrypt a file with gnupg using AES-256 as the encryption algorithm. (Hence, symmetric encryption.)
In this mode, gnupg requires a passphrase from the user. I understand that gnupg then derives from this passphrase a 256-bit key, which it uses for encryption.
This question is about choosing a passphrase that is at least as difficult to crack as the rest of the encryption scheme.
Now, passphrases are typically strings of printable characters, but if we used a random 256-bit string as the "passphrase", then such a "passphrase" would be at least as secure as the rest of this encryption scheme.
In contrast, a passphrase consisting of a single ASCII character (8 bits) would probably not be deemed secure, since it would be too easy to guess through a brute-force search.
The comparison between the strentgth of the passphrase and the strength of a random 256-bit key is not straightforward, however, for at least two reasons.
First, in order to derive the key from the passphrase, gnupg uses "passphrase stretching", which increases the computational cost of performing a brute-force search for the passphrase.
Second, passphrases are made of printable ASCII characters, so a 32-character (== 256-bit) passphrase, even if it were a random string of printable ASCII characters, would still have less entropy than a random 256-bit key, despite having the same number of bits.
So my question is, if we take into account both gnupg's passphrase stretching as well as the fact that passphrases consist of printable ASCII characters, what would be the length of the shortest random passphrase that would be equally hard to guess as a random 256-bit string without passphrase stretching?