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Modelling and Analysing of
Security Protocol: Lecture 12
Probabilistic Modelling Checking
of Anonymous Systems
Tom Chothia
CWI
Today
• Model Checking for finite systems
• Specifying properties in CTL
• Dinning Philosophers
BREAK
• Probabilistic finite systems
• Specifying probabilistic properties in PCTL
• Dinning Cryptographers
PCTL
Probabilistic Model Checking
Dinning Cryptographers
Dining Cryptographers
• Nodes form a ring
• Each adjacent pair picks a random number
• Each node broadcasts the sum (xor) of the
adjacent numbers
r5+r1
• The user who wants to send a
message also adds the message r
r5
1
• The total sum (xor) is:
r1+r2
r4+r5
r1+r2+r2+r3+r3+
r2
r4
r4+r4+r5+r5+r1+m = m
r
r2+r3
3
r3+r4+m
Results of the Model Checking
0,25
0,2
0,15
user1
user2
user3
0,1
0,05
user3
user2
user1
0
DAA
ADA
AAD
DDD
Results of the Model Checking
0,25
0,2
0,15
0,1
0,05
0
user1
user2
user3
user1
DDD
AAD
ADA
DAA
user3
DAA
ADA
AAD
DDD
user1
0,25
0,25
0,25
0,25
user2
0,25
0,25
0,25
0,25
user3
0,25
0,25
0,25
0,25
Result of P(Tails)=0.25
0,5
0,4
0,3
user1
user2
user3
0,2
0,1
user3
user2
user1
0
DAA
ADA
AAD
DDD
Result of P(Tails)=0.25
user1
user2
user3
user3
user1
user1
user2
user3
DDD
AAD
ADA
DAA
0,5
0,4
0,3
0,2
0,1
0
DAA
ADA
AAD
DDD
0,4375
0,1875
0,1875
0,1875
0,4375
0,1875
0,1875
0,1875
0,4375
0,1875
0,1875
0,1875
Result of P(Tails)=0.21132
user1
user2
user3
user3
user1
user1
user2
user3
DDD
AAD
ADA
DAA
0,6
0,5
0,4
0,3
0,2
0,1
0
DAA
ADA
AAD
DDD
0,50001
0,16663
0,16663
0,16663
0,50001
0,16663
0,16663
0,16663
0,50001
0,16663
0,16663
0,16663
Today
• Model Checking for finite systems
• Specifying properties in CTL
• Dinning Philosophers example
BREAK
• Probabilistic finite systems
• Specifying probabilistic properties in PCTL
• Dinning Cryptographers