#base: inv190(init,p,q,r,n) #inductive: istep190(p,q,r,n) #successor: s' #action: sdm1(s,p10,q10,r10) #constants: p10 : -> Principal q10 : -> Principal r10 : -> Random nw10 : -> Network #effective: r10 \in ur(s) = false #case: r = r10 (r = r10) = 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 #lemma: inv200(s,p,q,r) and inv210(s,p,q,r) #case: (p = intruder) = true (p = intruder) = false #case: (r = r10) = true (r = r10) = false #case: (enc2(p,n(p,q,r),n,q) \ = enc2(sender(m10),nonce(cipher1(m10)),n(p10,sender(m10),r10),p10)) = false ## (enc2(p,n(p,q,r),n,q) \ ## = enc2(sender(m10),nonce(cipher1(m10)),n(p10,sender(m10),r10),p10)) = true sender(m10) = p & nonce(cipher1(m10)) = n(p,q,r) & n = n(p10,sender(m10),r10) & p10 = q #case: r \in ur(s) = true r \in ur(s) = false #case: (q = intruder) = true (q = intruder) = 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) #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 #case: enc2(p,n(p,q,r),n,q) = e20 (enc2(p,n(p,q,r),n,q) = e20) = false #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 #lemma: inv210(s,p,q,r) #case: (p = intruder) = true (p = intruder) = false #case: r \in ur(s) = true r \in ur(s) = false #case: n(p,q,r) = n10 (n(p,q,r) = n10) = false #case: n(p,q,r) = n20 (n(p,q,r) = n20) = false #action: fkm31(s,p10,q10,e30) #constants: p10 : -> Principal q10 : -> Principal e30 : -> Cipher3 #effective: e30 \in cenc3(nw(s)) = true #action: fkm32(s,p10,q10,n10) #constants: p10 : -> Principal q10 : -> Principal n10 : -> Nonce #effective: n10 \in cnonce(nw(s)) = true