I want to know the answer for the question above, given that we encrypt a message that ends with a "0" and the encryption key is concatenated with a "0" to, in that case that case the cyphertext would also end with a zero, knowing that the attacker would know that the last bit of the key and the message is the same, would that cause a problem in case we're using a OTP to encrypt our messages?
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$\begingroup$ What is "a OPT ciphertext"? $\endgroup$– user991Sep 24, 2016 at 22:00
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$\begingroup$ I'm sorry I meant OTP for one time pad i just corrected it ! $\endgroup$– devSep 24, 2016 at 22:02
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$\begingroup$ Didn't we just have another question about this same exercise? $\endgroup$– Ilmari KaronenSep 24, 2016 at 22:40
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$\begingroup$ I don't think so sorry $\endgroup$– devSep 24, 2016 at 22:51
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$\begingroup$ Ah, here it is. IMO, that question was kind of poorly asked, though, so I'm not voting to close yours as a duplicate of it. $\endgroup$– Ilmari KaronenSep 24, 2016 at 23:02
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1 Answer
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No, this wouldn't cause problems.
The reason for this is the way how perfect secrecy is defined.
The definition says that a scheme is perfectly secret if an attacker doesn't learn anything new about the message when giving a cipher text, also see my other answer for a more "mathy" formulation.
So an attacker knows a certain bit is fixed, thus he can't ever learn anything new about it from the cipher text. And he also can't learn anything new about the rest of the message because only the corresponding key bit is fixed and the rest of the key stream is still uniformly and independently random and is thus still an OTP.
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$\begingroup$ Thanks for your answer you made things very clear for me thanks again! $\endgroup$– devSep 25, 2016 at 20:07