If I'm encrypting very short/small data - like an int or a long (32 or 64 bits), does it make any sense to authenticate the ciphertext, when using an "online" mode of operation (like EAX)?
Essentially, guessing the plain text would (assuming no weaknesses in either the encryption or the authentication) be easier than forging the authentication tag if the plain text is shorter than the block size of the cipher - or equally hard if truncating the tag to the same length as the data when using EAX.
Are there any scenarios in which tags longer than the data would be useful? (Or are there any actual research results on this?)
Does any of this change if the key with which the individual ints are encrypted changes?