Table 3 Rules of BAN logic

MM: Message Meaning Rule

\(\frac {P\ {\text {believes}}\ P \overset {K}{\leftrightarrow } Q,\ P\ {\text {sees}}\ \{X\}_{K}}{P\ {\text {believes}}\ Q\ {\text {said}}\ X}\)

\(\frac {P\ {\text {believes}}\ P \overset {K}{\Leftrightarrow } Q,\ P\ {\text {sees}}\ \langle X \rangle _{K}}{P\ {\text {believes}}\ Q\ {\text {said}}\ X}\)

\(\frac {P\ {\text {believes}} \overset {K}{\rightarrow } Q,\ P\ {\text {sees}}\ \{X\}_{Q^{-1}}}{P\ {\text {believes}}\ Q\ {\text {said}}\ X}\)

NV: Nonce Verification Rule

\(\frac {P\ {\text {believes}}\ \#(X),\ P\ {\text {believes}}\ Q\ {\text {said}}\ X}{P\ {\text {believes}}\ Q\ {\text {said}}\ X}\)

JR: Jurisdiction Rule

\(\frac {P\ {\text {believes}}\ Q\ {\text {controls}}\ X,\ P\ {\text {believes}}\ Q\ {\text {believes}}\ X}{P\ {\text {believes}}\ X}\)

FR: Freshness Rule

\(\frac {P\ {\text {believes}}\ \#(X)}{P\ {\text {believes}}\ \#(X,Y)}\)

DR: Decomposition Rule

\(\frac {P\ {\text {sees}}\ (X,Y)}{P\ {\text {sees}}\ X}\)

BC: Belief Conjunction Rule

\(\frac {P\ {\text {believes}}\ X,\ P\ {\text {believes}}\ Y}{P\ {\text {believes}}\ (X,Y)} \frac {P\ {\text {believes}}\ Q,\ P\ {\text {believes}}\ (X,Y)}{P\ {\text {believes}}\ Q\ {\text {believes}}\ X}\)

\(\frac {P\ {\text {believes}}\ Q\ {\text {said}}\ (X,Y)}{P\ {\text {believes}}\ Q\ {\text {said}} X}\)

DH: Diffie-Hellman Rule

\(\frac {P\ {\text {believes}}\ Q\ {\text {said}} \overset {g^{Y}}{\rightarrow }Q,\ P\ {\text {believes}}\ \overset {g^{X}}{\rightarrow }P}{P\ {\text {believes}}\ P\ \overset {g^{XY}}{\leftrightarrow } Q}\)

\(\frac {P\ {\text {believes}}\ Q\ {\text {said}} \overset {g^{Y}}{\rightarrow }Q,\ P\ {\text {believes}}\ \overset {g^{X}}{\rightarrow }P}{P\ {\text {believes}}\ P\ \overset {g^{XY}}{\leftrightarrow } Q}\)