I'm trying to solve a question about one time pads but I'm not sure if my assumptions are correct.

I am to assume that I have a one time pad with perfect secrecy. This one time pad is used to encrypt a message of 7 bits in length (message space size is 2^7). This encryption yields a ciphertext of "0110011". What is the probability that the encrypted message was "1001001".

My understanding of one time pads is that if we assume the pad has perfect secrecy, then we can no nothing about the message given the ciphertext and thus we cannot determine the probability. Am I right in my assumption?

• Well, no, not exactly. We can determine the probability: It's the same for every ciphertext.
– Nova
Commented Jan 31, 2015 at 2:59
• Hmm. Then my only other guess would be that the probability would have to be 1/2^7. Commented Jan 31, 2015 at 3:20
• Yes, correct. That's the basic principle of the one time pad. You can't say which one of the encrypted messages is right, because the key is fully random and every message is equally likely.
– Nova
Commented Jan 31, 2015 at 3:37

The piece of information that you have not been given is the probability distribution that the plaintext was originally chosen from. Perhaps all 128 possible plaintexts were chosen with equal probability (that is, with probability $1/128$). Perhaps the plaintext 1001001 was chosen with probability 0.25, and the plaintext 0110110 was chosen with probability 0.75, and all other plaintexts had zero probability. The point is that you do not know.