Table 2. BAN logic notations.

A∣ ≡ X	A believes a statement X
$A\stackrel{K}{\leftrightarrow }B$	Share a key K between A and B
#X	X is fresh
A⊲X	A sees X
A ⇒ X	A controls X
A∣ ∼ X	A said X
(X)K	The formula X is hashed by K
< X, Y > K	X and Y are encrypted with the key K
(X, Y)	The formula X or Y is one part of the formula (X, Y)