author  nipkow 
Fri, 24 Nov 2000 16:49:27 +0100  
changeset 10519  ade64af4c57c 
parent 8054  2ce57ef2a4aa 
permissions  rwrr 
2318  1 
(* Title: HOL/Auth/NS_Public_Bad 
2 
ID: $Id$ 

3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

4 
Copyright 1996 University of Cambridge 

5 

6 
Inductive relation "ns_public" for the NeedhamSchroeder PublicKey protocol. 

7 
Flawed version, vulnerable to Lowe's attack. 

8 

9 
From page 260 of 

10 
Burrows, Abadi and Needham. A Logic of Authentication. 

11 
Proc. Royal Soc. 426 (1989) 

12 
*) 

13 

4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

14 
AddEs spies_partsEs; 
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

15 
AddDs [impOfSubs analz_subset_parts]; 
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

16 
AddDs [impOfSubs Fake_parts_insert]; 
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

17 

3683  18 
AddIffs [Spy_in_bad]; 
2318  19 

8054
2ce57ef2a4aa
used image_eq_UN to speed up slow proofs of base cases
paulson
parents:
5434
diff
changeset

20 
Addsimps [image_eq_UN]; (*accelerates proofs involving nested images*) 
2ce57ef2a4aa
used image_eq_UN to speed up slow proofs of base cases
paulson
parents:
5434
diff
changeset

21 

2318  22 
(*A "possibility property": there are traces that reach the end*) 
5434
9b4bed3f394c
Got rid of not_Says_to_self and most uses of ~= in definitions and theorems
paulson
parents:
5421
diff
changeset

23 
Goal 
9b4bed3f394c
Got rid of not_Says_to_self and most uses of ~= in definitions and theorems
paulson
parents:
5421
diff
changeset

24 
"EX NB. EX evs: ns_public. Says A B (Crypt (pubK B) (Nonce NB)) : set evs"; 
2318  25 
by (REPEAT (resolve_tac [exI,bexI] 1)); 
26 
by (rtac (ns_public.Nil RS ns_public.NS1 RS ns_public.NS2 RS ns_public.NS3) 2); 

2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2497
diff
changeset

27 
by possibility_tac; 
2318  28 
result(); 
29 

30 

31 
(**** Inductive proofs about ns_public ****) 

32 

3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

33 
(*Induction for regularity theorems. If induction formula has the form 
3683  34 
X ~: analz (spies evs) > ... then it shortens the proof by discarding 
35 
needless information about analz (insert X (spies evs)) *) 

3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

36 
fun parts_induct_tac i = 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

37 
etac ns_public.induct i 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

38 
THEN 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

39 
REPEAT (FIRSTGOAL analz_mono_contra_tac) 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

40 
THEN 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

41 
prove_simple_subgoals_tac i; 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

42 

ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

43 

3683  44 
(** Theorems of the form X ~: parts (spies evs) imply that NOBODY 
2318  45 
sends messages containing X! **) 
46 

3683  47 
(*Spy never sees another agent's private key! (unless it's bad at start)*) 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

48 
Goal "evs: ns_public ==> (Key (priK A) : parts (spies evs)) = (A : bad)"; 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

49 
by (parts_induct_tac 1); 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

50 
by (Blast_tac 1); 
2318  51 
qed "Spy_see_priK"; 
52 
Addsimps [Spy_see_priK]; 

53 

5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

54 
Goal "evs: ns_public ==> (Key (priK A) : analz (spies evs)) = (A : bad)"; 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

55 
by Auto_tac; 
2318  56 
qed "Spy_analz_priK"; 
57 
Addsimps [Spy_analz_priK]; 

58 

4476  59 
AddSDs [Spy_see_priK RSN (2, rev_iffD1), 
60 
Spy_analz_priK RSN (2, rev_iffD1)]; 

2318  61 

62 

3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

63 
(**** Authenticity properties obtained from NS2 ****) 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

64 

ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

65 
(*It is impossible to reuse a nonce in both NS1 and NS2, provided the nonce 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

66 
is secret. (Honest users generate fresh nonces.)*) 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

67 
Goal "[ Crypt (pubK B) {Nonce NA, Agent A} : parts (spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

68 
\ Nonce NA ~: analz (spies evs); evs : ns_public ] \ 
3683  69 
\ ==> Crypt (pubK C) {NA', Nonce NA} ~: parts (spies evs)"; 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

70 
by (etac rev_mp 1); 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

71 
by (etac rev_mp 1); 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

72 
by (parts_induct_tac 1); 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

73 
by (ALLGOALS Blast_tac); 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

74 
qed "no_nonce_NS1_NS2"; 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

75 

4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

76 
(*Adding it to the claset slows down proofs...*) 
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

77 
val nonce_NS1_NS2_E = no_nonce_NS1_NS2 RSN (2, rev_notE); 
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

78 

3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

79 

ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

80 
(*Unicity for NS1: nonce NA identifies agents A and B*) 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

81 
Goal "[ Nonce NA ~: analz (spies evs); evs : ns_public ] \ 
3709  82 
\ ==> EX A' B'. ALL A B. \ 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

83 
\ Crypt (pubK B) {Nonce NA, Agent A} : parts (spies evs) > \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

84 
\ A=A' & B=B'"; 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

85 
by (etac rev_mp 1); 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

86 
by (parts_induct_tac 1); 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

87 
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

88 
(*NS1*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

89 
by (expand_case_tac "NA = ?y" 2 THEN Blast_tac 2); 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

90 
(*Fake*) 
3709  91 
by (Clarify_tac 1); 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

92 
by (Blast_tac 1); 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

93 
val lemma = result(); 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

94 

5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

95 
Goal "[ Crypt(pubK B) {Nonce NA, Agent A} : parts(spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

96 
\ Crypt(pubK B') {Nonce NA, Agent A'} : parts(spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

97 
\ Nonce NA ~: analz (spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

98 
\ evs : ns_public ] \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

99 
\ ==> A=A' & B=B'"; 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

100 
by (prove_unique_tac lemma 1); 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

101 
qed "unique_NA"; 
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

102 

ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

103 

ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

104 
(*Tactic for proving secrecy theorems*) 
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset

105 
fun analz_induct_tac i = 
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset

106 
etac ns_public.induct i THEN 
4686  107 
ALLGOALS Asm_simp_tac; 
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset

108 

2318  109 

110 
(*Secrecy: Spy does not see the nonce sent in msg NS1 if A and B are secure*) 

5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

111 
Goal "[ Says A B (Crypt(pubK B) {Nonce NA, Agent A}) : set evs; \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

112 
\ A ~: bad; B ~: bad; evs : ns_public ] \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

113 
\ ==> Nonce NA ~: analz (spies evs)"; 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

114 
by (etac rev_mp 1); 
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset

115 
by (analz_induct_tac 1); 
2318  116 
(*NS3*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

117 
by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 4); 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

118 
(*NS2*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

119 
by (blast_tac (claset() addDs [unique_NA]) 3); 
2318  120 
(*NS1*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

121 
by (Blast_tac 2); 
2318  122 
(*Fake*) 
2497  123 
by (spy_analz_tac 1); 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

124 
qed "Spy_not_see_NA"; 
2318  125 

126 

127 
(*Authentication for A: if she receives message 2 and has used NA 

128 
to start a run, then B has sent message 2.*) 

5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

129 
Goal "[ Says A B (Crypt(pubK B) {Nonce NA, Agent A}) : set evs; \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

130 
\ Says B' A (Crypt(pubK A) {Nonce NA, Nonce NB}): set evs; \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

131 
\ A ~: bad; B ~: bad; evs : ns_public ] \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

132 
\ ==> Says B A (Crypt(pubK A) {Nonce NA, Nonce NB}): set evs"; 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

133 
by (etac rev_mp 1); 
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

134 
(*prepare induction over Crypt (pubK A) {NA,NB} : parts H*) 
3683  135 
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

136 
by (etac ns_public.induct 1); 
2318  137 
by (ALLGOALS Asm_simp_tac); 
3709  138 
by (ALLGOALS Clarify_tac); 
139 
(*NS2*) 

4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

140 
by (blast_tac (claset() addDs [Spy_not_see_NA, unique_NA]) 3); 
2318  141 
(*NS1*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

142 
by (Blast_tac 2); 
2318  143 
(*Fake*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

144 
by (blast_tac (claset() addDs [Spy_not_see_NA]) 1); 
2318  145 
qed "A_trusts_NS2"; 
146 

4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

147 

2318  148 
(*If the encrypted message appears then it originated with Alice in NS1*) 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

149 
Goal "[ Crypt (pubK B) {Nonce NA, Agent A} : parts (spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

150 
\ Nonce NA ~: analz (spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

151 
\ evs : ns_public ] \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

152 
\==> Says A B (Crypt (pubK B) {Nonce NA, Agent A}) : set evs"; 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

153 
by (etac rev_mp 1); 
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

154 
by (etac rev_mp 1); 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

155 
by (parts_induct_tac 1); 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

156 
by (Blast_tac 1); 
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset

157 
qed "B_trusts_NS1"; 
2318  158 

159 

160 

161 
(**** Authenticity properties obtained from NS2 ****) 

162 

4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

163 
(*Unicity for NS2: nonce NB identifies nonce NA and agent A 
2318  164 
[proof closely follows that for unique_NA] *) 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

165 
Goal "[ Nonce NB ~: analz (spies evs); evs : ns_public ] \ 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

166 
\ ==> EX A' NA'. ALL A NA. \ 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

167 
\ Crypt (pubK A) {Nonce NA, Nonce NB} : parts (spies evs) \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

168 
\ > A=A' & NA=NA'"; 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

169 
by (etac rev_mp 1); 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

170 
by (parts_induct_tac 1); 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

171 
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); 
2318  172 
(*NS2*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

173 
by (expand_case_tac "NB = ?y" 2 THEN Blast_tac 2); 
2318  174 
(*Fake*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

175 
by (Blast_tac 1); 
2318  176 
val lemma = result(); 
177 

5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

178 
Goal "[ Crypt(pubK A) {Nonce NA, Nonce NB} : parts(spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

179 
\ Crypt(pubK A'){Nonce NA', Nonce NB} : parts(spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

180 
\ Nonce NB ~: analz (spies evs); \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

181 
\ evs : ns_public ] \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

182 
\ ==> A=A' & NA=NA'"; 
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset

183 
by (prove_unique_tac lemma 1); 
2318  184 
qed "unique_NB"; 
185 

186 

187 
(*NB remains secret PROVIDED Alice never responds with round 3*) 

5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

188 
Goal "[ Says B A (Crypt (pubK A) {Nonce NA, Nonce NB}) : set evs; \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

189 
\ ALL C. Says A C (Crypt (pubK C) (Nonce NB)) ~: set evs; \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

190 
\ A ~: bad; B ~: bad; evs : ns_public ] \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

191 
\ ==> Nonce NB ~: analz (spies evs)"; 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

192 
by (etac rev_mp 1); 
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

193 
by (etac rev_mp 1); 
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset

194 
by (analz_induct_tac 1); 
4091  195 
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); 
3709  196 
by (ALLGOALS Clarify_tac); 
3703  197 
(*NS3: because NB determines A*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

198 
by (blast_tac (claset() addDs [unique_NB]) 4); 
3703  199 
(*NS2: by freshness and unicity of NB*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

200 
by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 3); 
3703  201 
(*NS1: by freshness*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

202 
by (Blast_tac 2); 
2318  203 
(*Fake*) 
2497  204 
by (spy_analz_tac 1); 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

205 
qed "Spy_not_see_NB"; 
2318  206 

207 

208 

209 
(*Authentication for B: if he receives message 3 and has used NB 

2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

210 
in message 2, then A has sent message 3to somebody....*) 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

211 
Goal "[ Says B A (Crypt (pubK A) {Nonce NA, Nonce NB}) : set evs; \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

212 
\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

213 
\ A ~: bad; B ~: bad; evs : ns_public ] \ 
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

214 
\ ==> EX C. Says A C (Crypt (pubK C) (Nonce NB)) : set evs"; 
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

215 
by (etac rev_mp 1); 
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset

216 
(*prepare induction over Crypt (pubK B) NB : parts H*) 
3683  217 
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); 
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset

218 
by (parts_induct_tac 1); 
4091  219 
by (ALLGOALS (asm_simp_tac (simpset() addsimps [ex_disj_distrib]))); 
3709  220 
by (ALLGOALS Clarify_tac); 
4197  221 
(*NS3: because NB determines A (this use of unique_NB is more robust) *) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

222 
by (blast_tac (claset() addDs [Spy_not_see_NB] 
4197  223 
addIs [unique_NB RS conjunct1]) 3); 
3703  224 
(*NS1: by freshness*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

225 
by (Blast_tac 2); 
2318  226 
(*Fake*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

227 
by (blast_tac (claset() addDs [Spy_not_see_NB]) 1); 
2318  228 
qed "B_trusts_NS3"; 
229 

230 

231 
(*Can we strengthen the secrecy theorem? NO*) 

5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

232 
Goal "[ A ~: bad; B ~: bad; evs : ns_public ] \ 
3465  233 
\ ==> Says B A (Crypt (pubK A) {Nonce NA, Nonce NB}) : set evs \ 
5114
c729d4c299c1
Deleted leading parameters thanks to new Goal command
paulson
parents:
5076
diff
changeset

234 
\ > Nonce NB ~: analz (spies evs)"; 
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset

235 
by (analz_induct_tac 1); 
3709  236 
by (ALLGOALS Clarify_tac); 
3703  237 
(*NS2: by freshness and unicity of NB*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

238 
by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 3); 
3703  239 
(*NS1: by freshness*) 
4556
e7a4683c0026
Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents:
4551
diff
changeset

240 
by (Blast_tac 2); 
2318  241 
(*Fake*) 
2497  242 
by (spy_analz_tac 1); 
3703  243 
(*NS3: unicity of NB identifies A and NA, but not B*) 
3683  244 
by (forw_inst_tac [("A'","A")] (Says_imp_spies RS parts.Inj RS unique_NB) 1 
245 
THEN REPEAT (eresolve_tac [asm_rl, Says_imp_spies RS parts.Inj] 1)); 

4477
b3e5857d8d99
New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents:
4476
diff
changeset

246 
by Auto_tac; 
3703  247 
by (rename_tac "C B' evs3" 1); 
2318  248 

249 
(* 

250 
THIS IS THE ATTACK! 

3703  251 
Level 8 
3683  252 
!!evs. [ A ~: bad; B ~: bad; evs : ns_public ] 
3703  253 
==> Says B A (Crypt (pubK A) {Nonce NA, Nonce NB}) : set evs > 
3683  254 
Nonce NB ~: analz (spies evs) 
3703  255 
1. !!C B' evs3. 
256 
[ A ~: bad; B ~: bad; evs3 : ns_public; 

257 
Says A C (Crypt (pubK C) {Nonce NA, Agent A}) : set evs3; 

258 
Says B' A (Crypt (pubK A) {Nonce NA, Nonce NB}) : set evs3; C : bad; 

259 
Says B A (Crypt (pubK A) {Nonce NA, Nonce NB}) : set evs3; 

260 
Nonce NB ~: analz (spies evs3) ] 

2318  261 
==> False 
262 
*) 