Vigenère cipher

I am attending a cryptography course on Coursera. I am stuck at one question which I cannot answer right, even after a few tries.

Which of the following are true about Vigenère cipher? (Check all that apply)

1. A Vigenère cipher with key of length 100 can be broken (in a reasonable amount of time) using exhaustive search of the key space.
2. The Vigenère cipher can always be broken, regardless of the length of the key and regardless of the length of plaintext being encrypted
3. The Vigenère cipher is computationally infeasible to break if the key has length 100, even if 1000s of characters of plaintext are encrypted.
4. The Vigenère cipher is perfectly secret if the length of the key is equal to the length of the messages in the message space.

I am not sure about answer nr. 1--whether it can be broken in a reasonable amount of time. Non-computationally? For sure not.

I think the second answer is also wrong, as by definition. If the key and message are the same length, it is perfectly secret. (well the key has to be randomly chosen...)

Third answer is also wrong since the key repeats.

The fourth one is true as I mentioned for the second one.

I am not sure what possibilities I have tried, but I cannot pass this one.

• First is false. Even if your alphabet has only two members, you'd have to check $2^{100}$ keys which is considered infeasible for now. Commented Jan 29, 2017 at 16:06

Let's consider claim 1 first. If the ciphertext alphabet has, say, 26 letters, then a Vigenère cipher with a 100-character key length has $26^{100}$ possible keys. You may wish to do your own back-of-the envelope calculation of how long it would take to exhaustively search that keyspace, assuming e.g. that you have access to a billion computers that can each test a billion keys per second. Or just let Google do it for you.