Can a shift cipher attain perfect secrecy? 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 &quot;none of the above&quot;, though I wasn't too sure. But I was certain it was not &quot;perfect secrecy&quot;. However, when I review the exam solution key, it says &quot;perfect secrecy&quot; 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?
The Caesar cipher (aka Shift cipher) has, as you said, a key space of size 26. To achieve perfect secrecy, it thus can have at most 26 plaintexts and ciphertexts. With a message space of one character (and every key only used once), it would fit the definition of perfect secrecy.

For the usual use with messages longer than one character, or multiple messages with the same key, none of the given options fit (other than the "None" option).