Table 2 Notations of BAN logic

P believes X

P believes the message X and acts as if it is true

P sees X

P receives the message X

P said X

P previously sent the message X

P controls X

P has authority on X

#(X)

X is fresh

\(P \overset {K}{\leftrightarrow } Q\)

K is a secret key shared between P and Q

\(\overset {K}{\rightarrow } P\)

K is the P’s public key

\(P \overset {K}{\leftrightarrow } Q\)

K is a shared secret between P and Q.

{X}_K

X is encrypted with K

〈X〉_K

X is combined with a secret K