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I am a beginner to cryptography, and have started reading Katz and Lindell's book titled "Introduction to Modern Cryptography". I'm unable to understand what the probability distribution over the message space $\mathcal{M}$ represents in the definition of perfect secrecy of encryption schemes (Definition 2.3 in the above textbook). Does it represent the a priori knowledge that the adversary has about the message being encrypted? Or does it actually represent the probability distribution with which the message is being selected for encryption? It would be very helpful if someone can provide me an intuitive and a rigorous interpretation of the message space distribution $\mathcal{M}$.

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  • $\begingroup$ "Does it represent the a priori knowledge that the adversary has about the message being encrypted?" - that's the idea. $\endgroup$ – SEJPM May 17 '17 at 10:59
  • $\begingroup$ Thank you for your response. I'm not totally convinced with why the message space distribution represent the a priori knowledge that the adversary has.....sounds a little vague to me....how does the adversary fix on this distribution? $\endgroup$ – Itachi May 17 '17 at 11:59
  • $\begingroup$ For example if the adversary knows (only) that the last bit of the message is $0$, then the message distribution is no longer uniform over $\{0,1\}^n$. Rather, $P(M=x)$ equals $2^{-(n-1)}$ if the last bit of $x$ is $0$, and $0$ otherwise. $\endgroup$ – fkraiem May 17 '17 at 22:15

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