#base: inv230(init,p,q,r) #inductive: istep230(p,q,r) #successor: s' #action: sdm1(s,p10,q10,r10) #constants: p10 : -> Principal q10 : -> Principal r10 : -> Random nw10 : -> Network #effective: r10 \in ur(s) = false #action: sdm2(s,p10,r10,m10) #constants: p10 : -> Principal r10 : -> Random m10 : -> Message nw10 : -> Network nw20 : -> Network #effective: nw(s) = m10 , nw10 m1?(m10) = true receiver(m10) = p10 key(cipher1(m10)) = p10 principal(cipher1(m10)) = sender(m10) r10 \in ur(s) = false #action: sdm3(s,p10,r10,m10,m20) #constants: p10 : -> Principal r10 : -> Random m10 : -> Message m20 : -> Message nw10 : -> Network #effective: nw(s) = m10 , m20 , nw10 m1?(m10) = true m2?(m20) = true creator(m10) = p10 sender(m10) = p10 receiver(m10) = sender(m20) key(cipher1(m10)) = sender(m20) nonce(cipher1(m10)) = n(p10,sender(m20),r10) principal(cipher1(m10)) = p10 receiver(m20) = p10 key(cipher2(m20)) = p10 nonce1(cipher2(m20)) = n(p10,sender(m20),r10) principal(cipher2(m20)) = sender(m20) #lemma: inv130(s,nonce2(cipher2(m20))) and \ inv170(s,p10,q,creator(m20),r10,n(q,p,r)) and \ inv260(s,q,p10,n(p10,q,r10),n(q,p,r)) #case: (enc3(sender(m20),nonce2(cipher2(m20))) = enc3(q,n(q,p,r))) = false ## (enc3(sender(m20),nonce2(cipher2(m20))) = enc3(q,n(q,p,r))) = true sender(m20) = q & nonce2(cipher2(m20)) = n(q,p,r) #case: (q = intruder) = true (q = intruder) = false #case: (p = intruder) = true (p = intruder) = false #case: (p10 = intruder) = true (p10 = intruder) = false #case: m2(q,q,p10,enc2(p10,n(p10,q,r10),n(q,p,r),q)) \in m10,m20,nw10 = true m2(q,q,p10,enc2(p10,n(p10,q,r10),n(q,p,r),q)) \in m10,m20,nw10 = false #case: (p10 = p) = true (p10 = p) = false #action: fkm11(s,p10,q10,e10) #constants: p10 : -> Principal q10 : -> Principal e10 : -> Cipher1 #effective: e10 \in cenc1(nw(s)) = true #action: fkm12(s,p10,q10,n10) #constants: p10 : -> Principal q10 : -> Principal n10 : -> Nonce #effective: n10 \in cnonce(nw(s)) = true #action: fkm21(s,p10,q10,e20) #constants: p10 : -> Principal q10 : -> Principal e20 : -> Cipher2 #effective: e20 \in cenc2(nw(s)) = true #action: fkm22(s,p10,q10,n10,n20) #constants: p10 : -> Principal q10 : -> Principal n10 : -> Nonce n20 : -> Nonce #effective: n10 \in cnonce(nw(s)) = true n20 \in cnonce(nw(s)) = true #action: fkm31(s,p10,q10,e30) #constants: p10 : -> Principal q10 : -> Principal e30 : -> Cipher3 #effective: e30 \in cenc3(nw(s)) = true #case: enc3(q,n(q,p,r)) = e30 (enc3(q,n(q,p,r)) = e30) = false #case: m3(p,p,q,e30) = m3(intruder,p10,q10,e30) (m3(p,p,q,e30) = m3(intruder,p10,q10,e30)) = false #action: fkm32(s,p10,q10,n10) #constants: p10 : -> Principal q10 : -> Principal n10 : -> Nonce #effective: n10 \in cnonce(nw(s)) = true #lemma: inv130(s,n(q,p,r)) #case: (enc3(q,n(q,p,r)) = enc3(q10,n10)) = false ## (enc3(q,n(q,p,r)) = enc3(q10,n10)) = true q10 = q & n10 = n(q,p,r) & n(q,p,r) \in cnonce(nw(s)) = true #case: (p = intruder) = true (p = intruder) = false #case: (q = intruder) = true (q = intruder) = false