Shannon's secrecy can be defined as:

$$P_M (M=m) = P_{SK,M}(M=m|E(SK,m)=c)$$

What does $P_M$ means? (same question for $P_{SK,M}$)

I know that is the probability space M, M being the messages; I do not really understand why that has to be specified - or in general I don't understand what this means.

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    $\begingroup$ Whatever source you are reading should properly explain its notation. If it doesn't, find another one. $\endgroup$ – fkraiem Feb 10 '16 at 5:57

This is standard notation in information theory but it is redundant as given here, usually it is used as below.

For example $P_M(m)$ would be used instead of $P_M(M=m)$ both of which refer to the random variable $M$ and the probability that it equals $m$.

$P_{M,X}(M=m,X=x)=P_{M,X}(m,x)$ would refer to a joint distribution in the same way.

| improve this answer | |
  • $\begingroup$ @graphtheory92 does this answer your question? $\endgroup$ – kodlu Jun 10 '16 at 0:20

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