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proof900_fkm31.mod
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--
-- c-fkm32 true
--
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
--
eq (m3 = me3(intruder,p10,q10,c30)) = false .
--
eq s' = fkm31(s,p10,q10,c30) .
red istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq (rand(hash(c30)) = rand(expo(m22))) = false .
eq rand(expo(hash(c30))) = rand(expo(m22)) .
eq rand(hash(c30)) = rand(expo(c30)) .
--
eq s' = fkm31(s,p10,q10,c30) .
red inv740(s,m21,m3) implies istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq (rand(hash(c30)) = rand(expo(m22))) = false .
eq rand(expo(hash(c30))) = rand(expo(m22)) .
eq (rand(hash(c30)) = rand(expo(c30))) = false .
--
eq s' = fkm31(s,p10,q10,c30) .
red istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq (rand(hash(c30)) = rand(expo(m22))) = false .
eq (rand(expo(hash(c30))) = rand(expo(m22))) = false .
--
eq s' = fkm31(s,p10,q10,c30) .
red istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq hash(c30) \in hashes(s) = true .
--
eq rand(hash(c30)) = rand(expo(m22)) .
eq rand(point(expo(hash(c30)))) = rand(point(expo(m22))) .
eq (rand(expo(hash(c30))) = rand(expo(c30))) = false .
eq (rand(expo(m22)) = rand(expo(c30))) = false .
--
eq s' = fkm31(s,p10,q10,c30) .
red istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq hash(c30) \in hashes(s) = true .
--
eq rand(hash(c30)) = rand(expo(m22)) .
eq rand(point(expo(hash(c30)))) = rand(point(expo(m22))) .
eq (rand(expo(hash(c30))) = rand(expo(c30))) = false .
eq rand(expo(m22)) = rand(expo(c30)) .
--
eq s' = fkm31(s,p10,q10,c30) .
red istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq hash(c30) \in hashes(s) = true .
--
eq rand(hash(c30)) = rand(expo(m22)) .
eq rand(point(expo(hash(c30)))) = rand(point(expo(m22))) .
eq rand(expo(hash(c30))) = rand(expo(c30)) .
--
eq creator(m22) = intruder .
eq rand(expo(m22)) \in randsi(s) = true .
--
eq s' = fkm31(s,p10,q10,c30) .
red inv730(s,m21,expo(m22)) and
inv180(s,m22) and
inv600(s,m21,expo(hash(c30))) and
inv350(s,c30)
implies istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq hash(c30) \in hashes(s) = true .
--
eq rand(hash(c30)) = rand(expo(m22)) .
eq rand(point(expo(hash(c30)))) = rand(point(expo(m22))) .
eq rand(expo(hash(c30))) = rand(expo(c30)) .
--
eq creator(m22) = intruder .
eq rand(expo(m22)) \in randsi(s) = false .
--
eq s' = fkm31(s,p10,q10,c30) .
red inv320(s,m21,rand(expo(c30))) and inv120(s,hash(c30)) implies istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq hash(c30) \in hashes(s) = true .
--
eq rand(hash(c30)) = rand(expo(m22)) .
eq rand(point(expo(hash(c30)))) = rand(point(expo(m22))) .
eq rand(expo(hash(c30))) = rand(expo(c30)) .
--
eq (creator(m22) = intruder) = false .
--
eq s' = fkm31(s,p10,q10,c30) .
red inv320(s,m22,rand(expo(m22))) and
inv320(s,m21,rand(expo(c30))) and
inv110(s,m22) and
inv120(s,hash(c30))
implies istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
eq hash(c30) \in hashes(s) = false .
--
eq rand(hash(c30)) = rand(expo(m22)) .
eq rand(point(expo(hash(c30)))) = rand(point(expo(m22))) .
eq rand(expo(hash(c30))) = rand(expo(c30)) .
--
eq s' = fkm31(s,p10,q10,c30) .
red istep900(m1,m21,m22,m3,p,q) .
close
-- c-fkm32 true
open ISTEP
ops p10 q10 : -> Principal .
op c30 : -> Cipher3 .
--
eq m1 \in network(s) = true .
eq m21 \in network(s) = true .
eq m22 \in network(s) = true .
eq sender(m3) = q .
eq receiver(m3) = p .
eq creator(m21) = p .
eq sender(m21) = p .
eq receiver(m21) = q .
eq sender(m22) = q .
eq knowspi(p) = true .
eq receiver(m22) = p .
eq (p = intruder) = false .
eq (q = p) = false .
eq expo(m21) = expo(cipher3(m3)) .
eq (creator(m21) = creator(m3)) = false .
eq dpar(cipher1(m1)) = dpar(point(expo(m21))) .
eq rand(cipher1(m1)) = rand(point(expo(m21))) .
eq dpar(cipher1(m1)) = dpar(cipher3(m3)) .
eq (hash(cipher3(m3)) = hash(rand(expo(m21)),expo(m22))) = false .
--
eq c-fkm31(s,p10,q10,c30) = true .
-- by c-fkm31 we have:
eq c30 \in cipher3s(s) = true .
--
-- eq (m3 = me3(intruder,p10,q10,c30)) = true .
eq creator(m3) = intruder .
eq sender(m3) = p10 .
eq receiver(m3) = q10 .
eq cipher3(m3) = c30 .
--
--
eq rand(hash(c30)) = rand(expo(m22)) .
eq (rand(point(expo(hash(c30)))) = rand(point(expo(m22)))) = false .
--
eq s' = fkm31(s,p10,q10,c30) .
red istep900(m1,m21,m22,m3,p,q) .
close