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I am using this cipher-text

c   = 04 10 12 00 01 08 67 0A 19 65 0F 03 0A 00

with two possible keys

k_1 = 45 44 46 41 42 43 47 4B 4D 45 4B 42 5D 4E

and

k_2 = 45 44 46 41 42 43 47 4B 4D 45 41 4C 45 4E 

If I decrypt the cipher-text with k_1 I am getting 'ATTACK AT DAWN' and with k_2 'ATTACK AT NOON'. Which of the plaintexts is more likely to be the original plaintext and why?

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  • $\begingroup$ This is ill-formatted homework! You cannot get OTP keys! Anyway, What do you think about it? $\endgroup$ – kelalaka Nov 16 '19 at 23:04
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    $\begingroup$ What I have learned is that the OTP is 'perfectly secure'. In my opinion I don't think there is a way to assume that one plaintext is more likely to be the original. $\endgroup$ – NimeQ Nov 16 '19 at 23:10
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    $\begingroup$ Yes, As long as there is no additional information about the message, All keys are valid for OTP. Therefore, your two messages are valid. $\endgroup$ – kelalaka Nov 16 '19 at 23:12
  • $\begingroup$ 'perfectly secure' Which is exactly what @kelalaka has said. That's why we use OTPs. And if you run the numbers, the message might say 'CONGLOBULATING'. $\endgroup$ – Paul Uszak Nov 16 '19 at 23:24
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Which of the plaintexts is more likely to be the original plaintext and why?

A very literal and devious answer to the question (at least as you have posed it) is that 'ATTACK AT DAWN' is more likely to be the original plaintext because it can be independently established that attacks at dawn are more common than attacks at noon. 😑

Which means there's a subtle flaw in the question: what cryptanalysis is supposed to accomplish is to use the ciphertext as evidence that favors some candidate plaintexts over others. The point isn't really which plaintext is more likely, it's whether an analysis of the ciphertext can rationally demand that you change your mind about their relative likelihood. Like, you go into it thinking that 'ATTACK AT DAWN' is twice as likely as 'ATTACK AT NOON', but analysis of the ciphertext compels you to conclude some other proportion.

The point of all this is the often-missed nuance that the famous perfect secrecy of one-time pads is not that the attacker cannot figure out what candidate plaintext is more likely, but rather that analyzing the ciphertext is of no use in achieving that end.

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It seems odd for one character to be lower case, but they could both be valid. I would likely guess it to be the one with all upper case characters, especially if the enemy is known to traditionally use all upper case characters for their plaintexts. Perhaps they made a typo or were trying to trick me somehow though. Either is equally probable without such indications being used. Mathematically either is equally valid and probable, but I would, if forced to pick, guess the enemy to attack at dawn.

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  • $\begingroup$ please don't answer homework questions. $\endgroup$ – kelalaka Nov 17 '19 at 12:50
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    $\begingroup$ That answer is invalid, because the lowercase k is a typo (perhaps intentional; in that case, it briefly fouled us). My bets are NOON, because ] :-) $\endgroup$ – fgrieu Dec 17 '19 at 10:21

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