model.prism (0.01 MB) property.props (0.01 MB) model.jani (0.28 MB)
Taken from QVBS (January 2026). The given benchmark (including parameter instantiation and property) has been considered in QComp 2019 and QComp 2020. Original Prism model and property files have been adapted for compatibility and simplicity: - Constants: All open constants are now explicitly set within model.prism (no need to set them via command line) - Properties: The properties only refer to labels and rewards as defined in the model.prism file. No variables or constants are used in the property. - Formulas: some PRISM formula declarations have been renamed so that their identify does not crash with a label.
// randomized protocol for signing contracts Even, Goldreich and Lempel dtmc // we now let B to makes his/her choices based on what he/she knows // to do this I have added non-determinism to the previous version // and changed the modules so that only "B's view" is visible // then reveal the values when B thinks he has an advantage // to model the non-deterministic behaviour of corrupt party (party B) // we have a set of possible initial states corresponding to what messages // he/she tries to over hear when sending - we could do this with nondeterminism // but it will just make the model less structured and B has to make the choices // at the start anyway since B's view at this point should tell him nothing // (we use the new construct init...endinit to specify the set of initial states) // note that certain variables that belong to a party appear in the other party's module // as this leads to a more structured model - without this PRISM runs out of memory // note we have included the case when B stops if he/she thinks that the protocol has reached // a state where he/she has an advantage // currently, this model only works for N up to 20 const int N=10; // number of pairs of secrets the party sends const int L=8; // number of bits in each secret module counter b : [1..L]; // counter for current bit to be send (used in phases 2 and 3) n : [0..max(N-1,1)]; // counter as parties send N messages in a row phase : [1..5]; // phase of the protocol party : [1..2]; // which party moves // 1 first phase of the protocol (sending messages of the form OT(.,.,.,.) // 2 and 3 - second phase of the protocol (sending secretes 1..n and n+1..2n respectively) // 4 finished the protocol // FIRST PHASE [receiveB] phase=1 & party=1 -> (party'=2); // first A sends a message then B does [receiveA] phase=1 & party=2 & n(party'=1) & (n'=n+1); // after B sends a message we move onto the next message [receiveA] phase=1 & party=2 & n=N-1 -> (party'=1) & (phase'=2) & (n'=0); // B has sent his final message - move to next phase // SECOND AND THIRD PHASES // when A sends [receiveB] ((phase)>=(2)&(phase)<=(3))& party=1 & n=0-> (party'=2); // A transmits bth bit of secrets 1..N or N=1..2N [receiveA] ((phase)>=(2)&(phase)<=(3))& party=2 & n (n'=n+1); // A transmits bth bit of secrets 1..N or N=1..2N [receiveA] ((phase)>=(2)&(phase)<=(3))& party=2 & n=N-1 -> (party'=1) & (n'=1); // finished for party A now move to party B // when A sends [receiveB] ((phase)>=(2)&(phase)<=(3))& party=1 & n 0 -> (n'=n+1); // B transmits bth bit of secrets 1..N or N=1..2N [receiveB] ((phase)>=(2)&(phase)<=(3))& party=1 & n=N-1 & b (party'=1) & (n'=0) & (b'=b+1); // finished for party B move to next bit [receiveB] phase=2 & party=1 & n=N-1 & b=L -> (phase'=3) & (party'=1) & (n'=0) & (b'=1); // finished for party B move to next phase [receiveB] phase=3 & party=1 & n=N-1 & b=L -> (phase'=4); // finished protocol (reveal values) // FINISHED [] phase=4 -> (phase'=4); // loop endmodule // party A module partyA // bi the number of bits of B's ith secret A knows // (keep pairs of secrets together to give a more structured model) b0 : [0..L]; b20 : [0..L]; b1 : [0..L]; b21 : [0..L]; b2 : [0..L]; b22 : [0..L]; b3 : [0..L]; b23 : [0..L]; b4 : [0..L]; b24 : [0..L]; b5 : [0..L]; b25 : [0..L]; b6 : [0..L]; b26 : [0..L]; b7 : [0..L]; b27 : [0..L]; b8 : [0..L]; b28 : [0..L]; b9 : [0..L]; b29 : [0..L]; b10 : [0..L]; b30 : [0..L]; b11 : [0..L]; b31 : [0..L]; b12 : [0..L]; b32 : [0..L]; b13 : [0..L]; b33 : [0..L]; b14 : [0..L]; b34 : [0..L]; b15 : [0..L]; b35 : [0..L]; b16 : [0..L]; b36 : [0..L]; b17 : [0..L]; b37 : [0..L]; b18 : [0..L]; b38 : [0..L]; b19 : [0..L]; b39 : [0..L]; // first step (get either secret i or (N-1)+i with equal probability) [receiveA] phase=1 & n=0 -> 0.5 : (b0'=L) + 0.5 : (b20'=L); [receiveA] phase=1 & n=1 -> 0.5 : (b1'=L) + 0.5 : (b21'=L); [receiveA] phase=1 & n=2 -> 0.5 : (b2'=L) + 0.5 : (b22'=L); [receiveA] phase=1 & n=3 -> 0.5 : (b3'=L) + 0.5 : (b23'=L); [receiveA] phase=1 & n=4 -> 0.5 : (b4'=L) + 0.5 : (b24'=L); [receiveA] phase=1 & n=5 -> 0.5 : (b5'=L) + 0.5 : (b25'=L); [receiveA] phase=1 & n=6 -> 0.5 : (b6'=L) + 0.5 : (b26'=L); [receiveA] phase=1 & n=7 -> 0.5 : (b7'=L) + 0.5 : (b27'=L); [receiveA] phase=1 & n=8 -> 0.5 : (b8'=L) + 0.5 : (b28'=L); [receiveA] phase=1 & n=9 -> 0.5 : (b9'=L) + 0.5 : (b29'=L); [receiveA] phase=1 & n=10 -> 0.5 : (b10'=L) + 0.5 : (b30'=L); [receiveA] phase=1 & n=11 -> 0.5 : (b11'=L) + 0.5 : (b31'=L); [receiveA] phase=1 & n=12 -> 0.5 : (b12'=L) + 0.5 : (b32'=L); [receiveA] phase=1 & n=13 -> 0.5 : (b13'=L) + 0.5 : (b33'=L); [receiveA] phase=1 & n=14 -> 0.5 : (b14'=L) + 0.5 : (b34'=L); [receiveA] phase=1 & n=15 -> 0.5 : (b15'=L) + 0.5 : (b35'=L); [receiveA] phase=1 & n=16 -> 0.5 : (b16'=L) + 0.5 : (b36'=L); [receiveA] phase=1 & n=17 -> 0.5 : (b17'=L) + 0.5 : (b37'=L); [receiveA] phase=1 & n=18 -> 0.5 : (b18'=L) + 0.5 : (b38'=L); [receiveA] phase=1 & n=19 -> 0.5 : (b19'=L) + 0.5 : (b39'=L); // second step (secrets 0,...,N-1) [receiveA] phase=2 & n=0 -> (b0'=min(b0+1,L)); [receiveA] phase=2 & n=1 -> (b1'=min(b1+1,L)); [receiveA] phase=2 & n=2 -> (b2'=min(b2+1,L)); [receiveA] phase=2 & n=3 -> (b3'=min(b3+1,L)); [receiveA] phase=2 & n=4 -> (b4'=min(b4+1,L)); [receiveA] phase=2 & n=5 -> (b5'=min(b5+1,L)); [receiveA] phase=2 & n=6 -> (b6'=min(b6+1,L)); [receiveA] phase=2 & n=7 -> (b7'=min(b7+1,L)); [receiveA] phase=2 & n=8 -> (b8'=min(b8+1,L)); [receiveA] phase=2 & n=9 -> (b9'=min(b9+1,L)); [receiveA] phase=2 & n=10 -> (b10'=min(b10+1,L)); [receiveA] phase=2 & n=11 -> (b11'=min(b11+1,L)); [receiveA] phase=2 & n=12 -> (b12'=min(b12+1,L)); [receiveA] phase=2 & n=13 -> (b13'=min(b13+1,L)); [receiveA] phase=2 & n=14 -> (b14'=min(b14+1,L)); [receiveA] phase=2 & n=15 -> (b15'=min(b15+1,L)); [receiveA] phase=2 & n=16 -> (b16'=min(b16+1,L)); [receiveA] phase=2 & n=17 -> (b17'=min(b17+1,L)); [receiveA] phase=2 & n=18 -> (b18'=min(b18+1,L)); [receiveA] phase=2 & n=19 -> (b19'=min(b19+1,L)); // second step (secrets N,...,2N-1) [receiveA] phase=3 & n=0 -> (b20'=min(b20+1,L)); [receiveA] phase=3 & n=1 -> (b21'=min(b21+1,L)); [receiveA] phase=3 & n=2 -> (b22'=min(b22+1,L)); [receiveA] phase=3 & n=3 -> (b23'=min(b23+1,L)); [receiveA] phase=3 & n=4 -> (b24'=min(b24+1,L)); [receiveA] phase=3 & n=5 -> (b25'=min(b25+1,L)); [receiveA] phase=3 & n=6 -> (b26'=min(b26+1,L)); [receiveA] phase=3 & n=7 -> (b27'=min(b27+1,L)); [receiveA] phase=3 & n=8 -> (b28'=min(b28+1,L)); [receiveA] phase=3 & n=9 -> (b29'=min(b29+1,L)); [receiveA] phase=3 & n=10 -> (b30'=min(b30+1,L)); [receiveA] phase=3 & n=11 -> (b31'=min(b31+1,L)); [receiveA] phase=3 & n=12 -> (b32'=min(b32+1,L)); [receiveA] phase=3 & n=13 -> (b33'=min(b33+1,L)); [receiveA] phase=3 & n=14 -> (b34'=min(b34+1,L)); [receiveA] phase=3 & n=15 -> (b35'=min(b35+1,L)); [receiveA] phase=3 & n=16 -> (b36'=min(b36+1,L)); [receiveA] phase=3 & n=17 -> (b37'=min(b37+1,L)); [receiveA] phase=3 & n=18 -> (b38'=min(b38+1,L)); [receiveA] phase=3 & n=19 -> (b39'=min(b39+1,L)); endmodule // construct module for party B through renaming module partyB=partyA[b0 =a0 ,b1 =a1 ,b2 =a2 ,b3 =a3 ,b4 =a4 ,b5 =a5 ,b6 =a6 ,b7 =a7 ,b8 =a8 ,b9 =a9, b10=a10,b11=a11,b12=a12,b13=a13,b14=a14,b15=a15,b16=a16,b17=a17,b18=a18,b19=a19, b20=a20,b21=a21,b22=a22,b23=a23,b24=a24,b25=a25,b26=a26,b27=a27,b28=a28,b29=a29, b30=a30,b31=a31,b32=a32,b33=a33,b34=a34,b35=a35,b36=a36,b37=a37,b38=a38,b39=a39, receiveA=receiveB] endmodule // formulae formula kB = ( (a0=L & a20=L) | (a1=L & a21=L) | (a2=L & a22=L) | (a3=L & a23=L) | (a4=L & a24=L) | (a5=L & a25=L) | (a6=L & a26=L) | (a7=L & a27=L) | (a8=L & a28=L) | (a9=L & a29=L) | (a10=L & a30=L) | (a11=L & a31=L) | (a12=L & a32=L) | (a13=L & a33=L) | (a14=L & a34=L) | (a15=L & a35=L) | (a16=L & a36=L) | (a17=L & a37=L) | (a18=L & a38=L) | (a19=L & a39=L)); formula kA = ( (b0=L & b20=L) | (b1=L & b21=L) | (b2=L & b22=L) | (b3=L & b23=L) | (b4=L & b24=L) | (b5=L & b25=L) | (b6=L & b26=L) | (b7=L & b27=L) | (b8=L & b28=L) | (b9=L & b29=L) | (b10=L & b30=L) | (b11=L & b31=L) | (b12=L & b32=L) | (b13=L & b33=L) | (b14=L & b34=L) | (b15=L & b35=L) | (b16=L & b36=L) | (b17=L & b37=L) | (b18=L & b38=L) | (b19=L & b39=L)); // labels label "knowB" = kB; label "knowA" = kA;
"unfairA": P=? [ F !"knowA" & "knowB" ];
{
"actions": [
{
"name": "receiveA"
},
{
"name": "receiveB"
}
],
"automata": [
{
"edges": [
{
"destinations": [
{
"assignments": [
{
"comment": "phase <- 4",
"ref": "phase",
"value": 4
}
],
"location": "l"
}
],
"guard": {
"comment": "(phase = 4)",
"exp": {
"left": "phase",
"op": "=",
"right": 4
}
},
"location": "l"
},
{
"action": "receiveA",
"destinations": [
{
"assignments": [
{
"comment": "n <- (n + 1)",
"ref": "n",
"value": {
"left": "n",
"op": "+",
"right": 1
}
},
{
"comment": "party <- 1",
"ref": "party",
"value": 1
}
],
"location": "l"
}
],
"guard": {
"comment": "(((phase = 1) & (party = 2)) & (n < (10 - 1)))",
"exp": {
"left": {
"left": {
"left": "phase",
"op": "=",
"right": 1
},
"op": "∧",
"right": {
"left": "party",
"op": "=",
"right": 2
}
},
"op": "∧",
"right": {
"left": "n",
"op": "<",
"right": 9
}
}
},
"location": "l"
},
{
"action": "receiveA",
"destinations": [
{
"assignments": [
{
"comment": "n <- 0",
"ref": "n",
"value": 0
},
{
"comment": "phase <- 2",
"ref": "phase",
"value": 2
},
{
"comment": "party <- 1",
"ref": "party",
"value": 1
}
],
"location": "l"
}
],
"guard": {
"comment": "(((phase = 1) & (party = 2)) & (n = (10 - 1)))",
"exp": {
"left": {
"left": {
"left": "phase",
"op": "=",
"right": 1
},
"op": "∧",
"right": {
"left": "party",
"op": "=",
"right": 2
}
},
"op": "∧",
"right": {
"left": "n",
"op": "=",
"right": 9
}
}
},
"location": "l"
},
{
"action": "receiveA",
"destinations": [
{
"assignments": [
{
"comment": "n <- (n + 1)",
"ref": "n",
"value": {
"left": "n",
"op": "+",
"right": 1
}
}
],
"location": "l"
}
],
"guard": {
"comment": "((((phase >= 2) & (phase <= 3)) & (party = 2)) & (n < (10 - 1)))",
"exp": {
"left": {
"left": {
"left": "n",
"op": "<",
"right": 9
},
"op": "∧",
"right": {
"left": "phase",
"op": "≤",
"right": 3
}
},
"op": "∧",
"right": {
"left": {
"left": "party",
"op": "=",
"right": 2
},
"op": "∧",
"right": {
"left": "phase",
"op": "≥",
"right": 2
}
}
}
},
"location": "l"
},
{
"action": "receiveA",
"destinations": [
{
"assignments": [
{
"comment": "n <- 1",
"ref": "n",
"value": 1
},
{
"comment": "party <- 1",
"ref": "party",
"value": 1
}
],
"location": "l"
}
],
"guard": {
"comment": "((((phase >= 2) & (phase <= 3)) & (party = 2)) & (n = (10 - 1)))",
"exp": {
"left": {
"left": {
"left": "n",
"op": "=",
"right": 9
},
"op": "∧",
"right": {
"left": "phase",
"op": "≤",
"right": 3
}
},
"op": "∧",
"right": {
"left": {
"left": "party",
"op": "=",
"right": 2
},
"op": "∧",
"right": {
"left": "phase",
"op": "≥",
"right": 2
}
}
}
},
"location": "l"
},
{
"action": "receiveB",
"destinations": [
{
"assignments": [
{
"comment": "party <- 2",
"ref": "party",
"value": 2
}
],
"location": "l"
}
],
"guard": {
"comment": "((phase = 1) & (party = 1))",
"exp": {
"left": {
"left": "phase",
"op": "=",
"right": 1
},
"op": "∧",
"right": {
"left": "party",
"op": "=",
"right": 1
}
}
},
"location": "l"
},
{
"action": "receiveB",
"destinations": [
{
"assignments": [
{
"comment": "party <- 2",
"ref": "party",
"value": 2
}
],
"location": "l"
}
],
"guard": {
"comment": "((((phase >= 2) & (phase <= 3)) & (party = 1)) & (n = 0))",
"exp": {
"left": {
"left": {
"left": "n",
"op": "=",
"right": 0
},
"op": "∧",
"right": {
"left": "phase",
"op": "≤",
"right": 3
}
},
"op": "∧",
"right": {
"left": {
"left": "party",
"op": "=",
"right": 1
},
"op": "∧",
"right": {
"left": "phase",
"op": "≥",
"right": 2
}
}
}
},
"location": "l"
},
{
"action": "receiveB",
"destinations": [
{
"assignments": [
{
"comment": "n <- (n + 1)",
"ref": "n",
"value": {
"left": "n",
"op": "+",
"right": 1
}
}
],
"location": "l"
}
],
"guard": {
"comment": "(((((phase >= 2) & (phase <= 3)) & (party = 1)) & (n < (10 - 1))) & (n > 0))",
"exp": {
"left": {
"left": {
"left": {
"left": "n",
"op": ">",
"right": 0
},
"op": "∧",
"right": {
"left": "phase",
"op": "≤",
"right": 3
}
},
"op": "∧",
"right": {
"left": "party",
"op": "=",
"right": 1
}
},
"op": "∧",
"right": {
"left": {
"left": "n",
"op": "<",
"right": 9
},
"op": "∧",
"right": {
"left": "phase",
"op": "≥",
"right": 2
}
}
}
},
"location": "l"
},
{
"action": "receiveB",
"destinations": [
{
"assignments": [
{
"comment": "b <- (b + 1)",
"ref": "b",
"value": {
"left": "b",
"op": "+",
"right": 1
}
},
{
"comment": "n <- 0",
"ref": "n",
"value": 0
},
{
"comment": "party <- 1",
"ref": "party",
"value": 1
}
],
"location": "l"
}
],
"guard": {
"comment": "(((((phase >= 2) & (phase <= 3)) & (party = 1)) & (n = (10 - 1))) & (b < 8))",
"exp": {
"left": {
"left": {
"left": {
"left": "b",
"op": "<",
"right": 8
},
"op": "∧",
"right": {
"left": "phase",
"op": "≤",
"right": 3
}
},
"op": "∧",
"right": {
"left": "party",
"op": "=",
"right": 1
}
},
"op": "∧",
"right": {
"left": {
"left": "n",
"op": "=",
"right": 9
},
"op": "∧",
"right": {
"left": "phase",
"op": "≥",
"right": 2
}
}
}
},
"location": "l"
},
{
"action": "receiveB",
"destinations": [
{
"assignments": [
{
"comment": "b <- 1",
"ref": "b",
"value": 1
},
{
"comment": "n <- 0",
"ref": "n",
"value": 0
},
{
"comment": "phase <- 3",
"ref": "phase",
"value": 3
},
{
"comment": "party <- 1",
"ref": "party",
"value": 1
}
],
"location": "l"
}
],
"guard": {
"comment": "((((phase = 2) & (party = 1)) & (n = (10 - 1))) & (b = 8))",
"exp": {
"left": {
"left": {
"left": "b",
"op": "=",
"right": 8
},
"op": "∧",
"right": {
"left": "party",
"op": "=",
"right": 1
}
},
"op": "∧",
"right": {
"left": {
"left": "n",
"op": "=",
"right": 9
},
"op": "∧",
"right": {
"left": "phase",
"op": "=",
"right": 2
}
}
}
},
"location": "l"
},
{
"action": "receiveB",
"destinations": [
{
"assignments": [
{
"comment": "phase <- 4",
"ref": "phase",
"value": 4
}
],
"location": "l"
}
],
"guard": {
"comment": "((((phase = 3) & (party = 1)) & (n = (10 - 1))) & (b = 8))",
"exp": {
"left": {
"left": {
"left": "b",
"op": "=",
"right": 8
},
"op": "∧",
"right": {
"left": "party",
"op": "=",
"right": 1
}
},
"op": "∧",
"right": {
"left": {
"left": "n",
"op": "=",
"right": 9
},
"op": "∧",
"right": {
"left": "phase",
"op": "=",
"right": 3
}
}
}
},
"location": "l"
}
],
"initial-locations": [
"l"
],
"locations": [
{
"name": "l",
"transient-values": [
{
"comment": "knowB <- kB(a0, a20, a1, a21, a2, a22, a3, a23, a4, a24, a5, a25, a6, a26, a7, a27, a8, a28, a9, a29, a10, a30, a11, a31, a12, a32, a13, a33, a14, a34, a15, a35, a16, a36, a17, a37, a18, a38, a19, a39)",
"ref": "knowB",
"value": {
"args": [
"a0",
"a20",
"a1",
"a21",
"a2",
"a22",
"a3",
"a23",
"a4",
"a24",
"a5",
"a25",
"a6",
"a26",
"a7",
"a27",
"a8",
"a28",
"a9",
"a29",
"a10",
"a30",
"a11",
"a31",
"a12",
"a32",
"a13",
"a33",
"a14",
"a34",
"a15",
"a35",
"a16",
"a36",
"a17",
"a37",
"a18",
"a38",
"a19",
"a39"
],
"function": "kB",
"op": "call"
}
},
{
"comment": "knowA <- kA(b0, b20, b1, b21, b2, b22, b3, b23, b4, b24, b5, b25, b6, b26, b7, b27, b8, b28, b9, b29, b10, b30, b11, b31, b12, b32, b13, b33, b14, b34, b15, b35, b16, b36, b17, b37, b18, b38, b19, b39)",
"ref": "knowA",
"value": {
"args": [
"b0",
"b20",
"b1",
"b21",
"b2",
"b22",
"b3",
"b23",
"b4",
"b24",
"b5",
"b25",
"b6",
"b26",
"b7",
"b27",
"b8",
"b28",
"b9",
"b29",
"b10",
"b30",
"b11",
"b31",
"b12",
"b32",
"b13",
"b33",
"b14",
"b34",
"b15",
"b35",
"b16",
"b36",
"b17",
"b37",
"b18",
"b38",
"b19",
"b39"
],
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}
}
]
}
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}
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