Is Caesar cipher perfectly secret? The only time a shift cipher considers to be perfectly secure is when used on a single letter of plaintext and no more. Having that in mind, we can say it is certainly not perfectly secure.
Caesar cipher is perfectly secret only in the special case with the assumption that 26 keys are used in equal probability. Suppose that we have a plaintext of 50 characters long if each key for each character is chosen equiprobably then you end with
26^50 possible keys.
That is my answer, is it correct?
Yes, because instead of a Caesar cipher you now have a One-time pad.
In particular, it meets the requirements of a key that is random and as long as the message. So as long as the key is kept secret and never used for another message, you have OTP security.