I'm new to cryptography. I want to ask about OTP-perfect secrecy diagram like figure below:
On the overlapping region (middle), notated by R(X;Y;Z). R can be calculated by I(X;Y) - I(X;Y|Z). That region is symmetric in X, Y, Z and can be negative. For example when X and Y are independent bits, and Z = X xor Y, then I(X;Y) = I(X;Z) = I(Y;Z) = 0, but I(X;Y|Z) > 0.
What is the "meaning/philosophy" of that region? I mean when the region is negative, when the region is positive, and how to describe that?
I have been trying to find the answer but no result.