Alice knows that she will want to send a single 128-bit message to Bob at
some point in the future. To prepare, Alice and Bob first select a 128-bit
key k ∈ {0, 1} 128 uniformly at random. When the time comes to send a message
x ∈ {0, 1} 128 to Bob, Alice considers two ways of doing so. She can
use the key as a one time pad, sending Bob k ⊕ x. Alternatively, she can us
AES to encrypt x. Recall that AES is a 128-bit block cipher which can
use a 128-bit key, so in this case she would encrypt x as a single block
and send Bob AESk (x). Assume Eve will see either k ⊕ x or AESk (x),
that Eve knows an initial portion of x (a standard header), and that she
wishes to recover the remaining portion of x.
If Eve is an all powerful adversary and has time to try out every
possible key k ∈ {0, 1} 128, which scheme would be more secure?
(a) The one time pad would be more secure. Even if Eve tried all possible
keys, she would not be able to recover the unknown portion of x. If
AES was used, Eve could eventually learn the unknown portion of x.
(b) AES would be more secure. Even if Eve tried all possible keys, she
would not be able to recover the unknown portion of x. If the one time
pad was used, Eve could eventually learn the unknown portion of x.
(c) They would be equally secure. Either way, Eve could eventually learn
the unknown portion of x.
(d) They would be equally secure. Either way, Eve would not be able to
learn the unknown portion of x.