Nit: I think you mean hashing, not encryption. Though, my bank uses a dual-password setup where the first password is required in its entirety and a few letter

Nit: I think you mean hashing, not encryption. Though, my bank uses a dual-password setup where the first password is required in its entirety and a few letters of the second password are required. I suspect this is stored by using a (hopefully memory-hard) salted key derivation function/password hash function (such as Argon2 or scrypt) to derive an encryption key from the first password, which is then used to decrypt the second password. At least, that's the way I'd design the system to minimize consequences of database compromise. Users are often not creative and often use related passwords. You'd want all of the stored information about the second password to provide clues to the first password only if the attacker had already cracked the first password. Hashing all of the permutations really blows up storage space and DB I/O.