flaw in perfect secrecy of shift cipher?

Why do we say shift cipher is perfectly secure when it is easy to break it (source)? Let's say I have a plaintext. "Australia is a big country"; I encrypt it using a shift of 2; That ciphertext can be broken using brute force search over 26 numbers.

• Could you please provide a link to a claim where it says that a shift cipher is perfectly secure? I think you're mistaking the simple caesar cipher with the secure one-time pad. Jan 28, 2019 at 15:47
• It appears that you are confused about the message-space of the "ShiftCipher" discussed in the source. It is stated quite clearly that the message is an element of $\mathbb{Z}_{26}$. "Australia is a big country" is in no way an element of $\mathbb{Z}_{26}$. Jan 28, 2019 at 16:28
• No, $\mathbb{Z}_{26}$ are the integers $\{0,\dots,25\}$. Those can be thought of as an encoding of the 26 letters in the English alphabet if you like. But a message can consist of only a single letter. Jan 28, 2019 at 16:43