The application of Shannon theory in Cryptography _ Cryptography

The basis of probability theory

Suppose X and y are random variables defined on a finite set of x and Y respectively. Joint probability P (xi,yi) p (x_i,y_i) is the probability of X=xi,y=yi x=x_i and y=y_i. Conditional probability P (xi|yi) p (x_i \vert y_i) is the probability of Y=yi y=y_i when X=xi x=x_i. If there are P (x,y) =p (x) p (Y) p (x, y) = P (x) p (y) in any x∈x,y∈y x \in x, y \in y, then the random variable x and y are statistically independent. Bayes theorem:

P (x| Y) =p (X) P (y| X) P (Y) p (x| Y) = \frac{p (X) P (y| X)}{p (Y)}

In a cryptography system, you can define the following:
P (p|c) =p (p) p (c|p) p (c) =p (p) ∑{k:p=dk (c)}p (k) ∑{k:c∈c (k)}p (k) p