# Perfect Indistinguishability in shift cipher

I have the following question:

Which of the following attackers can be used to demonstrate that the shift cipher for 3-character messages does not satisfy perfect indistinguishability?

Output m0 = 'aaa' and m1 = 'bbb'. Given challenge ciphertext C, output 0 if the first character of C is 'a'.

Output m0 = 'abc' and m1 = 'bcd'. Given challenge ciphertext C, output 1 if the three characters of C are all different.

Output m0 = 'aaa' and m1 = 'abc'. Given challenge ciphertext C, output 1 if the three characters of C are all different.

Output m0 = 'aaa' and m1 = 'abc'. Given challenge ciphertext C, output 0 if the first character of C is 'a'.

I assumed it was "Output m0 = 'aaa' and m1 = 'bbb'. Given challenge ciphertext C, output 0 if the first character of C is 'a'." since the shift cipher would be predictable (this is what I think) if the messages had the same characters in a row.

Can anyone explain why it should be : Output m0 = 'aaa' and m1 = 'abc'. Given challenge ciphertext C, output 1 if the three characters of C are all different.

I'm assuming that, that attacker produce $$m_0$$ and $$m_1$$ and given one of their ciphertext as a challenge.
1. given $$c$$, the attacker cannot distinguish whether it is encryption of $$m_1$$ or $$m_2$$. Since, he doesn't know the key. He can guess only 1/2 probability. For this attacker, it has perfect indistinguishability.
2. given $$c$$, the attacker can distinguish that the plaintext has all characters different. Because the shift cipher's property, $$c = E_k(m_1) \text{ and } c=E_k(m_1) \Leftrightarrow m_1 = m_2$$ and he output $$m_0$$ and $$m_1$$ with all different characters.
3. given $$c$$, the attacker can distinguish that the plaintext has all characters different. Because the shift cipher's property and and he was output $$m_0$$ as $$aaa$$ and $$m_1$$ as all different characters.
4. given $$c$$, the attacker can distinguish that because the attacker output $$m_0$$ and $$m_1$$, on advance he knows that first letter is always an $$a$$