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tempest/examples/pdtmc/crowds/crowds_15-5.pm

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// CROWDS [Reiter,Rubin]
// Vitaly Shmatikov, 2002
// Modified by Ernst Moritz Hahn (emh@cs.uni-sb.de)
// note:
// Change everything marked CWDSIZ when changing the size of the crowd
// Change everything marked CWDMAX when increasing max size of the crowd
dtmc
// Model parameters
const double PF; // forwarding probability
const double badC; // probability that member is untrustworthy
// Probability of forwarding
// const double PF = 0.8;
// const double notPF = 0.2; // must be 1-PF
// Probability that a crowd member is bad
// const double badC = 0.1;
// const double badC = 0.091;
// const double badC = 0.167;
// const double goodC = 0.909; // must be 1-badC
// const double goodC = 0.833; // must be 1-badC
const int CrowdSize = 15; // CWDSIZ: actual number of good crowd members
const int TotalRuns = 5; // Total number of protocol runs to analyze
const int MaxGood=20; // CWDMAX: maximum number of good crowd members
// Process definitions
module crowds
// Auxiliary variables
launch: bool init true; // Start modeling?
newInstance: bool init false; // Initialize a new protocol instance?
runCount: [0..TotalRuns] init TotalRuns; // Counts protocol instances
start: bool init false; // Start the protocol?
run: bool init false; // Run the protocol?
lastSeen: [0..MaxGood] init 0; // Last crowd member to touch msg
good: bool init false; // Crowd member is good?
bad: bool init false; // ... bad?
recordLast: bool init false; // Record last seen crowd member?
badObserve: bool init false; // Bad members observes who sent msg?
deliver: bool init false; // Deliver message to destination?
done: bool init false; // Protocol instance finished?
// Counters for attackers' observations
// CWDMAX: 1 counter per each good crowd member
observe0: [0..TotalRuns];
observe1: [0..TotalRuns];
observe2: [0..TotalRuns];
observe3: [0..TotalRuns];
observe4: [0..TotalRuns];
observe5: [0..TotalRuns];
observe6: [0..TotalRuns];
observe7: [0..TotalRuns];
observe8: [0..TotalRuns];
observe9: [0..TotalRuns];
observe10: [0..TotalRuns];
observe11: [0..TotalRuns];
observe12: [0..TotalRuns];
observe13: [0..TotalRuns];
observe14: [0..TotalRuns];
observe15: [0..TotalRuns];
observe16: [0..TotalRuns];
observe17: [0..TotalRuns];
observe18: [0..TotalRuns];
observe19: [0..TotalRuns];
[] launch -> (newInstance'=true) & (runCount'=TotalRuns) & (launch'=false);
// Set up a newInstance protocol instance
[] newInstance & runCount>0 -> (runCount'=runCount-1) & (newInstance'=false) & (start'=true);
// SENDER
// Start the protocol
[] start -> (lastSeen'=0) & (run'=true) & (deliver'=false) & (start'=false);
// CROWD MEMBERS
// Good or bad crowd member?
[] !good & !bad & !deliver & run ->
1-badC : (good'=true) & (recordLast'=true) & (run'=false) +
badC : (bad'=true) & (badObserve'=true) & (run'=false);
// GOOD MEMBERS
// Forward with probability PF, else deliver
[] good & !deliver & run -> PF : (good'=false) + 1-PF : (deliver'=true);
// Record the last crowd member who touched the msg;
// all good members may appear with equal probability
// Note: This is backward. In the real protocol, each honest
// forwarder randomly chooses the next forwarder.
// Here, the identity of an honest forwarder is randomly
// chosen *after* it has forwarded the message.
[] recordLast & CrowdSize=2 ->
1/2 : (lastSeen'=0) & (recordLast'=false) & (run'=true) +
1/2 : (lastSeen'=1) & (recordLast'=false) & (run'=true);
[] recordLast & CrowdSize=3 ->
1/3 : (lastSeen'=0) & (recordLast'=false) & (run'=true) +
1/3 : (lastSeen'=1) & (recordLast'=false) & (run'=true) +
1/3 : (lastSeen'=2) & (recordLast'=false) & (run'=true);
[] recordLast & CrowdSize=4 ->
1/4 : (lastSeen'=0) & (recordLast'=false) & (run'=true) +
1/4 : (lastSeen'=1) & (recordLast'=false) & (run'=true) +
1/4 : (lastSeen'=2) & (recordLast'=false) & (run'=true) +
1/4 : (lastSeen'=3) & (recordLast'=false) & (run'=true);
[] recordLast & CrowdSize=5 ->
1/5 : (lastSeen'=0) & (recordLast'=false) & (run'=true) +
1/5 : (lastSeen'=1) & (recordLast'=false) & (run'=true) +
1/5 : (lastSeen'=2) & (recordLast'=false) & (run'=true) +
1/5 : (lastSeen'=3) & (recordLast'=false) & (run'=true) +
1/5 : (lastSeen'=4) & (recordLast'=false) & (run'=true);
[] recordLast & CrowdSize=10 ->
1/10 : (lastSeen'=0) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=1) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=2) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=3) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=4) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=5) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=6) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=7) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=8) & (recordLast'=false) & (run'=true) +
1/10 : (lastSeen'=9) & (recordLast'=false) & (run'=true);
[] recordLast & CrowdSize=15 ->
1/15 : (lastSeen'=0) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=1) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=2) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=3) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=4) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=5) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=6) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=7) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=8) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=9) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=10) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=11) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=12) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=13) & (recordLast'=false) & (run'=true) +
1/15 : (lastSeen'=14) & (recordLast'=false) & (run'=true);
[] recordLast & CrowdSize=20 ->
1/20 : (lastSeen'=0) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=1) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=2) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=3) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=4) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=5) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=6) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=7) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=8) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=9) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=10) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=11) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=12) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=13) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=14) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=15) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=16) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=17) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=18) & (recordLast'=false) & (run'=true) +
1/20 : (lastSeen'=19) & (recordLast'=false) & (run'=true);
// BAD MEMBERS
// Remember from whom the message was received and deliver
// CWDMAX: 1 rule per each good crowd member
[] lastSeen=0 & badObserve & observe0 <TotalRuns -> (observe0' =observe0 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=1 & badObserve & observe1 <TotalRuns -> (observe1' =observe1 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=2 & badObserve & observe2 <TotalRuns -> (observe2' =observe2 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=3 & badObserve & observe3 <TotalRuns -> (observe3' =observe3 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=4 & badObserve & observe4 <TotalRuns -> (observe4' =observe4 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=5 & badObserve & observe5 <TotalRuns -> (observe5' =observe5 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=6 & badObserve & observe6 <TotalRuns -> (observe6' =observe6 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=7 & badObserve & observe7 <TotalRuns -> (observe7' =observe7 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=8 & badObserve & observe8 <TotalRuns -> (observe8' =observe8 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=9 & badObserve & observe9 <TotalRuns -> (observe9' =observe9 +1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=10 & badObserve & observe10<TotalRuns -> (observe10'=observe10+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=11 & badObserve & observe11<TotalRuns -> (observe11'=observe11+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=12 & badObserve & observe12<TotalRuns -> (observe12'=observe12+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=13 & badObserve & observe13<TotalRuns -> (observe13'=observe13+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=14 & badObserve & observe14<TotalRuns -> (observe14'=observe14+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=15 & badObserve & observe15<TotalRuns -> (observe15'=observe15+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=16 & badObserve & observe16<TotalRuns -> (observe16'=observe16+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=17 & badObserve & observe17<TotalRuns -> (observe17'=observe17+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=18 & badObserve & observe18<TotalRuns -> (observe18'=observe18+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
[] lastSeen=19 & badObserve & observe19<TotalRuns -> (observe19'=observe19+1) & (deliver'=true) & (run'=true) & (badObserve'=false);
// RECIPIENT
// Delivery to destination
[] deliver & run -> (done'=true) & (deliver'=false) & (run'=false) & (good'=false) & (bad'=false);
// Start a newInstance instance
[] done -> (newInstance'=true) & (done'=false) & (run'=false) & (lastSeen'=MaxGood);
endmodule
label "observe0Greater1" = observe0 > 1;
label "observeIGreater1" = observe1 > 1 | observe2 > 1 | observe3 > 1 | observe4 > 1 | observe5 > 1 | observe6 > 1 | observe7 > 1 | observe8 > 1 | observe9 > 1 | observe10 > 1 | observe11 > 1 | observe12 > 1 | observe13 > 1 | observe14 > 1;
label "observeOnlyTrueSender" = observe0 > 1 & observe1 <= 1 & observe2 <= 1 & observe3 <= 1 & observe4 <= 1 & observe5 <= 1 & observe6 <= 1 & observe7 <= 1 & observe8 <= 1 & observe9 <= 1 & observe10 <= 1 & observe11 <= 1 & observe12 <= 1 & observe13 <= 1 & observe14 <= 1;