1. Modelling and Analysing of Security Protocol: Lecture 12 Probabilistic Modelling Checking of Anonymous Systems Tom Chothia CWI

2. Today Model Checking for finite systems Specifying properties in CTL Dinning Philosophers BREAK Probabilistic finite systems Specifying probabilistic properties in PCTL Dinning Cryptographers

3. PCTL

4. Probabilistic Model Checking

5. Dinning Cryptographers

6. Dining Cryptographers Nodes form a ring Each adjacent pair picks a random number Each node broadcasts the sum (xor) of the adjacent numbers The user who wants to send a message also adds the message The total sum (xor) is: r 1 +r 2 +r 2 +r 3 +r 3 + r 4 +r 4 +r 5 +r 5 +r 1 +m = m r1r1 r4r4 r5r5 r3r3 r2r2 r 1 +r 2 r 5 +r 1 r 4 +r 5 r 3 +r 4 r 2 +r 3 +m

7. Results of the Model Checking

9. Result of P(Tails)=0.25

11. Result of P(Tails)=0.21132

12. Today Model Checking for finite systems Specifying properties in CTL Dinning Philosophers example BREAK Probabilistic finite systems Specifying probabilistic properties in PCTL Dinning Cryptographers