On a practice question for my intro cryptography exam, it asks the following:
Assuming that keys are chosen with equal likelihood, the shift cipher provides:
A) computational security
B) perfect secrecy
C) semantic security
D) none of the above
I chose "none of the above", though I wasn't too sure. But I was certain it was not "perfect secrecy". However, when I review the exam solution key, it says "perfect secrecy" is, in fact, the answer.
Given that the message space of a shift cipher is huge, and the key space's cardinality is only 26, how can it possibly provide perfect secrecy under any circumstances?