Please forgive my ignorance here as I'm far from a math major and I've never looked into cryptography before so if this seems stupid - it probably is. There is a question in a quiz I'm attempting that is just doing my head in. If you are wondering - I'm not doing this course for credit or receiving any certification for passing it, just for my own interest.
I've attempted this question multiple times now and I'm still getting it wrong and I don't understand why. Here is the question:
Consider the Vigenere cipher over the lowercase English alphabet, where the key has length 6. For which of the following message spaces will this scheme be perfectly secret? (Check all that apply.)
- The set of all 7-character strings of lowercase English letters.
- The set of all strings of lowercase English letters containing at most 6 characters.
- The set of all 6-character strings of lowercase English letters.
- The set of all 5-character strings of lowercase English letters.
I know I'm getting punished by the combinations that are available due to the 'check all that apply' criteria, but I'm now at the point of blind guessing - which just isn't learning.
I'm particularly annoyed with this because further down in the same quiz the following is considered to be a correct answer for an aspect of another question:
'The Vigenere cipher is perfectly secret if the length of the key is equal to the length of the messages in the message space.'
To me then, it seems that the answer would be: 2 and 3 and 4 - Wrong
Perhaps this is wrong because 'the key' is only as long as one individual member of 'the strings' in the message space, not the length of 'all the messages in the message' space combined? (i.e. which would effectively be turning it into a One Time Pad where the key is the same length as the total message space?)
How should I go about breaking down this question to arrive at the answer with some sort of mathematical reasoning, rather than taking blind shots at it (which is where I'm at now)?
Description of the Vigenere Cipher
Now when we introduced the Vigenère cipher, we presented it in the following way. We said that the key was a string of letters. From the English alphabet and the plaintext will also consist of letters from the English alphabet. To encrypt a given plaintext with a key, what you do is simply shift every character in the plaintext by the amount dictated by the next character of the key. You can view this simple as addition modular 26, because there are 26 letters in the English alphabet. And if the key is shorter then the plaintext you simply wrap around in the key as needed, and decryption just reverses the process.