author | paulson |
Wed, 07 May 1997 13:01:43 +0200 | |
changeset 3121 | cbb6c0c1c58a |
parent 2637 | e9b203f854ae |
child 3432 | 04412cfe6861 |
permissions | -rw-r--r-- |
1995 | 1 |
(* Title: HOL/Auth/Yahalom |
1985
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2 |
ID: $Id$ |
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3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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4 |
Copyright 1996 University of Cambridge |
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5 |
|
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6 |
Inductive relation "otway" for the Yahalom protocol. |
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7 |
|
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8 |
From page 257 of |
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9 |
Burrows, Abadi and Needham. A Logic of Authentication. |
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10 |
Proc. Royal Soc. 426 (1989) |
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11 |
*) |
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12 |
|
1995 | 13 |
open Yahalom; |
1985
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parents:
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14 |
|
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Tidied many proofs, using AddIffs to let equivalences take
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15 |
proof_timing:=true; |
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16 |
HOL_quantifiers := false; |
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17 |
Pretty.setdepth 25; |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
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parents:
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18 |
|
3121
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19 |
(*Replacing the variable by a constant improves speed*) |
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20 |
val Says_imp_sees_Spy' = read_instantiate [("lost","lost")] Says_imp_sees_Spy; |
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21 |
|
1995 | 22 |
|
2322 | 23 |
(*A "possibility property": there are traces that reach the end*) |
1995 | 24 |
goal thy |
25 |
"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
|
2032 | 26 |
\ ==> EX X NB K. EX evs: yahalom lost. \ |
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27 |
\ Says A B {|X, Crypt K (Nonce NB)|} : set_of_list evs"; |
1995 | 28 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
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29 |
by (rtac (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS |
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30 |
yahalom.YM4) 2); |
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31 |
by possibility_tac; |
2013 | 32 |
result(); |
1995 | 33 |
|
34 |
||
1985
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35 |
(**** Inductive proofs about yahalom ****) |
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36 |
|
2110 | 37 |
(*Monotonicity*) |
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38 |
goal thy "!!evs. lost' <= lost ==> yahalom lost' <= yahalom lost"; |
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39 |
by (rtac subsetI 1); |
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40 |
by (etac yahalom.induct 1); |
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41 |
by (REPEAT_FIRST |
3121
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42 |
(blast_tac (!claset addIs (impOfSubs (sees_mono RS analz_mono RS synth_mono) |
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43 |
:: yahalom.intrs)))); |
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44 |
qed "yahalom_mono"; |
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45 |
|
1985
84cf16192e03
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parents:
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46 |
|
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47 |
(*Nobody sends themselves messages*) |
2051 | 48 |
goal thy "!!evs. evs: yahalom lost ==> ALL A X. Says A A X ~: set_of_list evs"; |
2032 | 49 |
by (etac yahalom.induct 1); |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
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50 |
by (Auto_tac()); |
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51 |
qed_spec_mp "not_Says_to_self"; |
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52 |
Addsimps [not_Says_to_self]; |
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53 |
AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
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54 |
|
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55 |
|
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56 |
(** For reasoning about the encrypted portion of messages **) |
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57 |
|
1995 | 58 |
(*Lets us treat YM4 using a similar argument as for the Fake case.*) |
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59 |
goal thy "!!evs. Says S A {|Crypt (shrK A) Y, X|} : set_of_list evs ==> \ |
2032 | 60 |
\ X : analz (sees lost Spy evs)"; |
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61 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS analz.Inj]) 1); |
2032 | 62 |
qed "YM4_analz_sees_Spy"; |
1985
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63 |
|
2110 | 64 |
bind_thm ("YM4_parts_sees_Spy", |
65 |
YM4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
|
66 |
||
2133 | 67 |
(*Relates to both YM4 and Oops*) |
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68 |
goal thy "!!evs. Says S A {|Crypt (shrK A) {|B, K, NA, NB|}, X|} \ |
1995 | 69 |
\ : set_of_list evs ==> \ |
2032 | 70 |
\ K : parts (sees lost Spy evs)"; |
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71 |
by (blast_tac (!claset addSEs partsEs |
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72 |
addSDs [Says_imp_sees_Spy' RS parts.Inj]) 1); |
2110 | 73 |
qed "YM4_Key_parts_sees_Spy"; |
74 |
||
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75 |
(*For proving the easier theorems about X ~: parts (sees lost Spy evs). |
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76 |
We instantiate the variable to "lost" since leaving it as a Var would |
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77 |
interfere with simplification.*) |
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78 |
val parts_sees_tac = |
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79 |
forw_inst_tac [("lost","lost")] YM4_parts_sees_Spy 6 THEN |
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80 |
forw_inst_tac [("lost","lost")] YM4_Key_parts_sees_Spy 7 THEN |
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81 |
prove_simple_subgoals_tac 1; |
1985
84cf16192e03
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82 |
|
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83 |
val parts_induct_tac = |
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84 |
etac yahalom.induct 1 THEN parts_sees_tac; |
1985
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parents:
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85 |
|
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86 |
|
2032 | 87 |
(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY |
2013 | 88 |
sends messages containing X! **) |
1985
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89 |
|
2133 | 90 |
(*Spy never sees another agent's shared key! (unless it's lost at start)*) |
1985
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parents:
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91 |
goal thy |
2133 | 92 |
"!!evs. evs : yahalom lost \ |
93 |
\ ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)"; |
|
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94 |
by parts_induct_tac; |
cbb6c0c1c58a
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95 |
by (Fake_parts_insert_tac 1); |
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96 |
by (Blast_tac 1); |
2133 | 97 |
qed "Spy_see_shrK"; |
98 |
Addsimps [Spy_see_shrK]; |
|
1985
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99 |
|
2133 | 100 |
goal thy |
101 |
"!!evs. evs : yahalom lost \ |
|
102 |
\ ==> (Key (shrK A) : analz (sees lost Spy evs)) = (A : lost)"; |
|
103 |
by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
|
104 |
qed "Spy_analz_shrK"; |
|
105 |
Addsimps [Spy_analz_shrK]; |
|
1985
84cf16192e03
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parents:
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106 |
|
2133 | 107 |
goal thy "!!A. [| Key (shrK A) : parts (sees lost Spy evs); \ |
108 |
\ evs : yahalom lost |] ==> A:lost"; |
|
3121
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parents:
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|
109 |
by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2133 | 110 |
qed "Spy_see_shrK_D"; |
1985
84cf16192e03
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parents:
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111 |
|
2133 | 112 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
113 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
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114 |
|
84cf16192e03
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115 |
|
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116 |
(*Nobody can have used non-existent keys!*) |
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117 |
goal thy "!!evs. evs : yahalom lost ==> \ |
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118 |
\ Key K ~: used evs --> K ~: keysFor (parts (sees lost Spy evs))"; |
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119 |
by parts_induct_tac; |
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120 |
(*YM4: Key K is not fresh!*) |
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121 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 3); |
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122 |
(*YM3*) |
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123 |
by (Blast_tac 2); |
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124 |
(*Fake*) |
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125 |
by (best_tac |
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126 |
(!claset addIs [impOfSubs analz_subset_parts] |
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127 |
addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
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128 |
impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
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|
129 |
addss (!simpset)) 1); |
2160 | 130 |
qed_spec_mp "new_keys_not_used"; |
1985
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parents:
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131 |
|
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132 |
bind_thm ("new_keys_not_analzd", |
2032 | 133 |
[analz_subset_parts RS keysFor_mono, |
134 |
new_keys_not_used] MRS contra_subsetD); |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
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|
135 |
|
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parents:
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136 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
84cf16192e03
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137 |
|
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138 |
|
2133 | 139 |
(*Describes the form of K when the Server sends this message. Useful for |
140 |
Oops as well as main secrecy property.*) |
|
2110 | 141 |
goal thy |
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|
142 |
"!!evs. [| Says Server A {|Crypt (shrK A) {|Agent B, Key K, NA, NB|}, X|} \ |
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143 |
\ : set_of_list evs; \ |
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144 |
\ evs : yahalom lost |] \ |
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|
145 |
\ ==> K ~: range shrK"; |
2133 | 146 |
by (etac rev_mp 1); |
147 |
by (etac yahalom.induct 1); |
|
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148 |
by (ALLGOALS Asm_simp_tac); |
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|
149 |
by (Blast_tac 1); |
2133 | 150 |
qed "Says_Server_message_form"; |
2110 | 151 |
|
152 |
||
153 |
(*For proofs involving analz. We again instantiate the variable to "lost".*) |
|
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154 |
val analz_sees_tac = |
2133 | 155 |
forw_inst_tac [("lost","lost")] YM4_analz_sees_Spy 6 THEN |
156 |
forw_inst_tac [("lost","lost")] Says_Server_message_form 7 THEN |
|
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|
157 |
assume_tac 7 THEN REPEAT ((etac exE ORELSE' hyp_subst_tac) 7); |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
158 |
|
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paulson
parents:
diff
changeset
|
159 |
|
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paulson
parents:
diff
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|
160 |
(**** |
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paulson
parents:
diff
changeset
|
161 |
The following is to prove theorems of the form |
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paulson
parents:
diff
changeset
|
162 |
|
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|
163 |
Key K : analz (insert (Key KAB) (sees lost Spy evs)) ==> |
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|
164 |
Key K : analz (sees lost Spy evs) |
1985
84cf16192e03
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paulson
parents:
diff
changeset
|
165 |
|
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paulson
parents:
diff
changeset
|
166 |
A more general formula must be proved inductively. |
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paulson
parents:
diff
changeset
|
167 |
****) |
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Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
168 |
|
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paulson
parents:
diff
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|
169 |
(** Session keys are not used to encrypt other session keys **) |
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paulson
parents:
diff
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|
170 |
|
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parents:
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|
171 |
goal thy |
2032 | 172 |
"!!evs. evs : yahalom lost ==> \ |
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|
173 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
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|
174 |
\ (Key K : analz (Key``KK Un (sees lost Spy evs))) = \ |
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|
175 |
\ (K : KK | Key K : analz (sees lost Spy evs))"; |
2032 | 176 |
by (etac yahalom.induct 1); |
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|
177 |
by analz_sees_tac; |
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|
178 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
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changeset
|
179 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
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|
180 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
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|
181 |
(*Base*) |
3121
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|
182 |
by (Blast_tac 1); |
2133 | 183 |
(*YM4, Fake*) |
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|
184 |
by (REPEAT (spy_analz_tac 1)); |
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|
185 |
qed_spec_mp "analz_image_freshK"; |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
186 |
|
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parents:
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changeset
|
187 |
goal thy |
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|
188 |
"!!evs. [| evs : yahalom lost; KAB ~: range shrK |] ==> \ |
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|
189 |
\ Key K : analz (insert (Key KAB) (sees lost Spy evs)) = \ |
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|
190 |
\ (K = KAB | Key K : analz (sees lost Spy evs))"; |
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|
191 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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|
192 |
qed "analz_insert_freshK"; |
1985
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paulson
parents:
diff
changeset
|
193 |
|
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paulson
parents:
diff
changeset
|
194 |
|
2110 | 195 |
(*** The Key K uniquely identifies the Server's message. **) |
196 |
||
197 |
goal thy |
|
198 |
"!!evs. evs : yahalom lost ==> \ |
|
2133 | 199 |
\ EX A' B' NA' NB' X'. ALL A B NA NB X. \ |
2110 | 200 |
\ Says Server A \ |
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changeset
|
201 |
\ {|Crypt (shrK A) {|Agent B, Key K, NA, NB|}, X|} \ |
2133 | 202 |
\ : set_of_list evs --> A=A' & B=B' & NA=NA' & NB=NB' & X=X'"; |
2110 | 203 |
by (etac yahalom.induct 1); |
204 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
|
205 |
by (Step_tac 1); |
|
2133 | 206 |
by (ex_strip_tac 2); |
3121
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Conversion to use blast_tac (with other improvements)
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parents:
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changeset
|
207 |
by (Blast_tac 2); |
2110 | 208 |
(*Remaining case: YM3*) |
209 |
by (expand_case_tac "K = ?y" 1); |
|
210 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
2516
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|
211 |
(*...we assume X is a recent message and handle this case by contradiction*) |
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|
212 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
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|
213 |
delrules [conjI] (*no split-up to 4 subgoals*)) 1); |
2110 | 214 |
val lemma = result(); |
215 |
||
216 |
goal thy |
|
217 |
"!!evs. [| Says Server A \ |
|
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|
218 |
\ {|Crypt (shrK A) {|Agent B, Key K, NA, NB|}, X|} \ |
2110 | 219 |
\ : set_of_list evs; \ |
220 |
\ Says Server A' \ |
|
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|
221 |
\ {|Crypt (shrK A') {|Agent B', Key K, NA', NB'|}, X'|} \ |
2110 | 222 |
\ : set_of_list evs; \ |
223 |
\ evs : yahalom lost |] \ |
|
224 |
\ ==> A=A' & B=B' & NA=NA' & NB=NB'"; |
|
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|
225 |
by (prove_unique_tac lemma 1); |
2110 | 226 |
qed "unique_session_keys"; |
227 |
||
228 |
||
229 |
(*If the encrypted message appears then it originated with the Server*) |
|
230 |
goal thy |
|
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|
231 |
"!!evs. [| Crypt (shrK A) {|Agent B, Key K, NA, NB|} \ |
2110 | 232 |
\ : parts (sees lost Spy evs); \ |
233 |
\ A ~: lost; evs : yahalom lost |] \ |
|
234 |
\ ==> Says Server A \ |
|
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|
235 |
\ {|Crypt (shrK A) {|Agent B, Key K, NA, NB|}, \ |
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|
236 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
2110 | 237 |
\ : set_of_list evs"; |
238 |
by (etac rev_mp 1); |
|
3121
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changeset
|
239 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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2637
diff
changeset
|
240 |
by (Fake_parts_insert_tac 1); |
2322 | 241 |
qed "A_trusts_YM3"; |
2110 | 242 |
|
243 |
||
244 |
(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 **) |
|
2013 | 245 |
|
246 |
goal thy |
|
2133 | 247 |
"!!evs. [| A ~: lost; B ~: lost; evs : yahalom lost |] \ |
2051 | 248 |
\ ==> Says Server A \ |
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|
249 |
\ {|Crypt (shrK A) {|Agent B, Key K, NA, NB|}, \ |
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|
250 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
2110 | 251 |
\ : set_of_list evs --> \ |
252 |
\ Says A Spy {|NA, NB, Key K|} ~: set_of_list evs --> \ |
|
2051 | 253 |
\ Key K ~: analz (sees lost Spy evs)"; |
2032 | 254 |
by (etac yahalom.induct 1); |
3121
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Conversion to use blast_tac (with other improvements)
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parents:
2637
diff
changeset
|
255 |
by analz_sees_tac; |
2013 | 256 |
by (ALLGOALS |
257 |
(asm_simp_tac |
|
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|
258 |
(!simpset addsimps [not_parts_not_analz, analz_insert_freshK] |
2013 | 259 |
setloop split_tac [expand_if]))); |
260 |
(*YM3*) |
|
3121
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Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
261 |
by (blast_tac (!claset delrules [impCE] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
2637
diff
changeset
|
262 |
addSEs sees_Spy_partsEs |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
263 |
addIs [impOfSubs analz_subset_parts]) 2); |
2133 | 264 |
(*OR4, Fake*) |
2377 | 265 |
by (REPEAT_FIRST spy_analz_tac); |
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Extensive tidying and simplification, largely stemming from
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changeset
|
266 |
(*Oops*) |
3121
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paulson
parents:
2637
diff
changeset
|
267 |
by (blast_tac (!claset addDs [unique_session_keys]) 1); |
2110 | 268 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
2013 | 269 |
|
270 |
||
271 |
(*Final version: Server's message in the most abstract form*) |
|
1985
84cf16192e03
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paulson
parents:
diff
changeset
|
272 |
goal thy |
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|
273 |
"!!evs. [| Says Server A \ |
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|
274 |
\ {|Crypt (shrK A) {|Agent B, Key K, NA, NB|}, \ |
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|
275 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
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|
276 |
\ : set_of_list evs; \ |
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|
277 |
\ Says A Spy {|NA, NB, Key K|} ~: set_of_list evs; \ |
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|
278 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
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paulson
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changeset
|
279 |
\ ==> Key K ~: analz (sees lost Spy evs)"; |
2013 | 280 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
281 |
by (blast_tac (!claset addSEs [lemma]) 1); |
2032 | 282 |
qed "Spy_not_see_encrypted_key"; |
2001 | 283 |
|
284 |
||
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
285 |
goal thy |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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changeset
|
286 |
"!!evs. [| C ~: {A,B,Server}; \ |
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changeset
|
287 |
\ Says Server A \ |
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changeset
|
288 |
\ {|Crypt (shrK A) {|Agent B, Key K, NA, NB|}, \ |
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|
289 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
290 |
\ : set_of_list evs; \ |
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changeset
|
291 |
\ Says A Spy {|NA, NB, Key K|} ~: set_of_list evs; \ |
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changeset
|
292 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
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parents:
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diff
changeset
|
293 |
\ ==> Key K ~: analz (sees lost C evs)"; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
294 |
by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1); |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
295 |
by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1); |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
296 |
by (FIRSTGOAL (rtac Spy_not_see_encrypted_key)); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
297 |
by (REPEAT_FIRST (blast_tac (!claset addIs [yahalom_mono RS subsetD]))); |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
298 |
qed "Agent_not_see_encrypted_key"; |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
299 |
|
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
300 |
|
2110 | 301 |
(*** Security Guarantee for B upon receiving YM4 ***) |
2013 | 302 |
|
2110 | 303 |
(*B knows, by the first part of A's message, that the Server distributed |
304 |
the key for A and B. But this part says nothing about nonces.*) |
|
2001 | 305 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
306 |
"!!evs. [| Crypt (shrK B) {|Agent A, Key K|} : parts (sees lost Spy evs); \ |
2051 | 307 |
\ B ~: lost; evs : yahalom lost |] \ |
2001 | 308 |
\ ==> EX NA NB. Says Server A \ |
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Extensive tidying and simplification, largely stemming from
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|
309 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
2516
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|
310 |
\ Nonce NA, Nonce NB|}, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
311 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
2013 | 312 |
\ : set_of_list evs"; |
2032 | 313 |
by (etac rev_mp 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
314 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
315 |
by (Fake_parts_insert_tac 1); |
2110 | 316 |
(*YM3*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
317 |
by (Blast_tac 1); |
2110 | 318 |
qed "B_trusts_YM4_shrK"; |
319 |
||
2133 | 320 |
|
321 |
(** The Nonce NB uniquely identifies B's message. **) |
|
322 |
||
323 |
goal thy |
|
2451
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Extensive tidying and simplification, largely stemming from
paulson
parents:
2377
diff
changeset
|
324 |
"!!evs. evs : yahalom lost ==> \ |
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2377
diff
changeset
|
325 |
\ EX NA' A' B'. ALL NA A B. \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
326 |
\ Crypt (shrK B) {|Agent A, Nonce NA, NB|} : parts(sees lost Spy evs) \ |
2133 | 327 |
\ --> B ~: lost --> NA = NA' & A = A' & B = B'"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
328 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
329 |
(*Fake*) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
330 |
by (REPEAT (etac (exI RSN (2,exE)) 1) (*stripping EXs makes proof faster*) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
331 |
THEN Fake_parts_insert_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
332 |
by (asm_simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
2133 | 333 |
(*YM2: creation of new Nonce. Move assertion into global context*) |
334 |
by (expand_case_tac "NB = ?y" 1); |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
335 |
by (REPEAT (resolve_tac [exI, conjI, impI, refl] 1)); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
336 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2133 | 337 |
val lemma = result(); |
338 |
||
2110 | 339 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
340 |
"!!evs.[| Crypt (shrK B) {|Agent A, Nonce NA, NB|} \ |
2133 | 341 |
\ : parts (sees lost Spy evs); \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
342 |
\ Crypt (shrK B') {|Agent A', Nonce NA', NB|} \ |
2133 | 343 |
\ : parts (sees lost Spy evs); \ |
344 |
\ evs : yahalom lost; B ~: lost; B' ~: lost |] \ |
|
345 |
\ ==> NA' = NA & A' = A & B' = B"; |
|
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2377
diff
changeset
|
346 |
by (prove_unique_tac lemma 1); |
2133 | 347 |
qed "unique_NB"; |
348 |
||
349 |
fun lost_tac s = |
|
350 |
case_tac ("(" ^ s ^ ") : lost") THEN' |
|
351 |
SELECT_GOAL |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
352 |
(REPEAT_DETERM (dtac (Says_imp_sees_Spy' RS analz.Inj) 1) THEN |
2133 | 353 |
REPEAT_DETERM (etac MPair_analz 1) THEN |
354 |
THEN_BEST_FIRST |
|
355 |
(dres_inst_tac [("A", s)] Crypt_Spy_analz_lost 1 THEN assume_tac 1) |
|
2170 | 356 |
(has_fewer_prems 1, size_of_thm) |
357 |
(Step_tac 1)); |
|
2133 | 358 |
|
359 |
||
360 |
(*Variant useful for proving secrecy of NB*) |
|
361 |
goal thy |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
362 |
"!!evs.[| Says C D {|X, Crypt (shrK B) {|Agent A, Nonce NA, NB|}|} \ |
2133 | 363 |
\ : set_of_list evs; B ~: lost; \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
364 |
\ Says C' D' {|X', Crypt (shrK B') {|Agent A', Nonce NA', NB|}|} \ |
2133 | 365 |
\ : set_of_list evs; \ |
366 |
\ NB ~: analz (sees lost Spy evs); \ |
|
367 |
\ evs : yahalom lost |] \ |
|
368 |
\ ==> NA' = NA & A' = A & B' = B"; |
|
369 |
by (lost_tac "B'" 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
370 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
371 |
addSEs [MPair_parts] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
372 |
addDs [unique_NB]) 1); |
2133 | 373 |
qed "Says_unique_NB"; |
374 |
||
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
375 |
(*Induction for theorems of the form X ~: analz (sees lost Spy evs) --> ... |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
376 |
It simplifies the proof by discarding needless information about |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
377 |
analz (insert X (sees lost Spy evs)) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
378 |
*) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
379 |
val analz_mono_parts_induct_tac = |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
380 |
etac yahalom.induct 1 |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
381 |
THEN |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
382 |
REPEAT_FIRST |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
383 |
(rtac impI THEN' |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
384 |
dtac (sees_subset_sees_Says RS analz_mono RS contra_subsetD) THEN' |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
385 |
mp_tac) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
386 |
THEN parts_sees_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
387 |
|
2133 | 388 |
goal thy |
389 |
"!!evs. [| B ~: lost; evs : yahalom lost |] \ |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
390 |
\ ==> Nonce NB ~: analz (sees lost Spy evs) --> \ |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
391 |
\ Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}: parts(sees lost Spy evs)\ |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
392 |
\ --> Crypt (shrK B') {|Agent A', Nonce NB, NB'|} ~: parts(sees lost Spy evs)"; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
393 |
by analz_mono_parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
394 |
by (Fake_parts_insert_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
395 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS analz.Inj] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
396 |
addSIs [parts_insertI] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
397 |
addSEs partsEs) 1); |
2133 | 398 |
val no_nonce_YM1_YM2 = standard (result() RS mp RSN (2, rev_mp) RS notE); |
399 |
||
400 |
||
401 |
||
402 |
(**** Towards proving secrecy of Nonce NB ****) |
|
403 |
||
404 |
(*B knows, by the second part of A's message, that the Server distributed |
|
405 |
the key quoting nonce NB. This part says nothing about agent names. |
|
406 |
Secrecy of NB is crucial.*) |
|
407 |
goal thy |
|
408 |
"!!evs. evs : yahalom lost \ |
|
409 |
\ ==> Nonce NB ~: analz (sees lost Spy evs) --> \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
410 |
\ Crypt K (Nonce NB) : parts (sees lost Spy evs) --> \ |
2133 | 411 |
\ (EX A B NA. Says Server A \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
412 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
413 |
\ Nonce NA, Nonce NB|}, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
414 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
2133 | 415 |
\ : set_of_list evs)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
416 |
by analz_mono_parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
417 |
(*YM4 & Fake*) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
418 |
by (Blast_tac 2); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
419 |
by (Fake_parts_insert_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
420 |
(*YM3*) |
2133 | 421 |
by (Step_tac 1); |
422 |
by (lost_tac "A" 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
423 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj RS parts.Fst RS |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
424 |
A_trusts_YM3]) 1); |
2133 | 425 |
val B_trusts_YM4_newK = result() RS mp RSN (2, rev_mp); |
426 |
||
427 |
||
428 |
(*This is the original version of the result above. But it is of little |
|
429 |
value because it assumes secrecy of K, which we cannot be assured of |
|
430 |
until we know that K is fresh -- which we do not know at the point this |
|
431 |
result is applied.*) |
|
432 |
goal thy |
|
433 |
"!!evs. evs : yahalom lost \ |
|
434 |
\ ==> Key K ~: analz (sees lost Spy evs) --> \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
435 |
\ Crypt K (Nonce NB) : parts (sees lost Spy evs) --> \ |
2110 | 436 |
\ (EX A B NA. Says Server A \ |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
437 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
438 |
\ Nonce NA, Nonce NB|}, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
439 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
2110 | 440 |
\ : set_of_list evs)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
441 |
by analz_mono_parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
442 |
(*YM4 & Fake*) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
443 |
by (Blast_tac 2); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
444 |
by (Fake_parts_insert_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
445 |
(*YM3*) |
2110 | 446 |
by (Step_tac 1); |
2133 | 447 |
by (lost_tac "A" 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
448 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj RS parts.Fst RS |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
449 |
A_trusts_YM3]) 1); |
2133 | 450 |
result() RS mp RSN (2, rev_mp); |
451 |
||
452 |
||
453 |
(*YM3 can only be triggered by YM2*) |
|
454 |
goal thy |
|
455 |
"!!evs. [| Says Server A \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
456 |
\ {|Crypt (shrK A) {|Agent B, k, na, nb|}, X|} : set_of_list evs; \ |
2133 | 457 |
\ evs : yahalom lost |] \ |
458 |
\ ==> EX B'. Says B' Server \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
459 |
\ {| Agent B, Crypt (shrK B) {|Agent A, na, nb|} |} \ |
2133 | 460 |
\ : set_of_list evs"; |
461 |
by (etac rev_mp 1); |
|
462 |
by (etac yahalom.induct 1); |
|
463 |
by (ALLGOALS Asm_simp_tac); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
464 |
by (ALLGOALS Blast_tac); |
2133 | 465 |
qed "Says_Server_imp_YM2"; |
466 |
||
467 |
||
468 |
(** Dedicated tactics for the nonce secrecy proofs **) |
|
469 |
||
470 |
val no_nonce_tac = SELECT_GOAL |
|
471 |
(REPEAT (resolve_tac [impI, notI] 1) THEN |
|
472 |
REPEAT (hyp_subst_tac 1) THEN |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
473 |
etac (Says_imp_sees_Spy' RS parts.Inj RS parts.Snd RS no_nonce_YM1_YM2) 1 |
2133 | 474 |
THEN |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
475 |
etac (Says_imp_sees_Spy' RS parts.Inj RS parts.Snd) 4 |
2133 | 476 |
THEN |
477 |
REPEAT_FIRST assume_tac); |
|
478 |
||
479 |
val not_analz_insert = subset_insertI RS analz_mono RS contra_subsetD; |
|
480 |
||
481 |
||
482 |
(*The only nonces that can be found with the help of session keys are |
|
483 |
those distributed as nonce NB by the Server. The form of the theorem |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
484 |
recalls analz_image_freshK, but it is much more complicated.*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
485 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
486 |
(*As with analz_image_freshK, we take some pains to express the property |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
487 |
as a logical equivalence so that the simplifier can apply it.*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
488 |
goal thy |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
489 |
"!!evs. P --> (X : analz (G Un H)) --> (X : analz H) ==> \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
490 |
\ P --> (X : analz (G Un H)) = (X : analz H)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
491 |
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
492 |
qed "Nonce_secrecy_lemma"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
493 |
|
2133 | 494 |
goal thy |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
495 |
"!!evs. evs : yahalom lost ==> \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
496 |
\ (ALL KK. KK <= Compl (range shrK) --> \ |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
497 |
\ (ALL K: KK. ALL A B na X. \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
498 |
\ Says Server A \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
499 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|} \ |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
500 |
\ ~: set_of_list evs) --> \ |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
501 |
\ (Nonce NB : analz (Key``KK Un (sees lost Spy evs))) = \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
502 |
\ (Nonce NB : analz (sees lost Spy evs)))"; |
2133 | 503 |
by (etac yahalom.induct 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
504 |
by analz_sees_tac; |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
505 |
by (REPEAT_FIRST (resolve_tac [impI RS allI])); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
506 |
by (REPEAT_FIRST (rtac Nonce_secrecy_lemma )); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
507 |
by (rtac ccontr 7); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
508 |
by (subgoal_tac "ALL A B na X. \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
509 |
\ Says Server A \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
510 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|} \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
511 |
\ ~: set_of_list evsa" 7); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
512 |
by (eres_inst_tac [("P","?PP-->?QQ")] notE 7); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
513 |
by (subgoal_tac "ALL A B na X. \ |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
514 |
\ Says Server A \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
515 |
\ {|Crypt (shrK A) {|Agent B, Key KAB, na, Nonce NB|}, X|} \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
516 |
\ ~: set_of_list evsa" 5); |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2377
diff
changeset
|
517 |
by (ALLGOALS (*22 seconds*) |
2133 | 518 |
(asm_simp_tac |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
519 |
(analz_image_freshK_ss addsimps |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
520 |
([all_conj_distrib, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
521 |
not_parts_not_analz, analz_image_freshK] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
522 |
@ pushes @ ball_simps)))); |
2133 | 523 |
(*Base*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
524 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
525 |
(*Fake*) (** LEVEL 10 **) |
2133 | 526 |
by (spy_analz_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
527 |
(*YM3*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
528 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2133 | 529 |
(*Oops*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
530 |
by (Asm_full_simp_tac 2); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
531 |
by (blast_tac (!claset addDs [unique_session_keys]) 2); |
2133 | 532 |
(*YM4*) |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
533 |
(** LEVEL 13 **) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
534 |
by (REPEAT (resolve_tac [impI, allI] 1)); |
2377 | 535 |
by (dtac (impOfSubs Fake_analz_insert) 1 THEN etac synth.Inj 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
536 |
by (stac insert_commute 1); |
2133 | 537 |
by (eres_inst_tac [("P","Nonce NB : ?HH")] rev_mp 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
538 |
by (asm_simp_tac (analz_image_freshK_ss |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
539 |
addsimps [analz_insertI, analz_image_freshK]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
540 |
by (step_tac (!claset addSDs [not_analz_insert]) 1); |
2133 | 541 |
by (lost_tac "A" 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
542 |
(** LEVEL 20 **) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
543 |
by (dtac (Says_imp_sees_Spy' RS parts.Inj RS parts.Fst RS A_trusts_YM3) 1 |
2133 | 544 |
THEN REPEAT (assume_tac 1)); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
545 |
by (thin_tac "All ?PP" 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
546 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
547 |
qed_spec_mp "Nonce_secrecy"; |
2133 | 548 |
|
549 |
||
550 |
(*Version required below: if NB can be decrypted using a session key then it |
|
551 |
was distributed with that key. The more general form above is required |
|
552 |
for the induction to carry through.*) |
|
553 |
goal thy |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
554 |
"!!evs. [| Says Server A \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
555 |
\ {|Crypt (shrK A) {|Agent B, Key KAB, na, Nonce NB'|}, X|} \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
556 |
\ : set_of_list evs; \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
557 |
\ Nonce NB : analz (insert (Key KAB) (sees lost Spy evs)); \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
558 |
\ Nonce NB ~: analz (sees lost Spy evs); \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
559 |
\ KAB ~: range shrK; evs : yahalom lost |] \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
560 |
\ ==> NB = NB'"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
561 |
by (rtac ccontr 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
562 |
by (subgoal_tac "ALL A B na X. \ |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
563 |
\ Says Server A \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
564 |
\ {|Crypt (shrK A) {|Agent B, Key KAB, na, Nonce NB|}, X|} \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
565 |
\ ~: set_of_list evs" 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
566 |
by (eres_inst_tac [("P","Nonce NB : ?HH")] rev_mp 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
567 |
by (asm_simp_tac (analz_image_freshK_ss |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
568 |
addsimps ([Nonce_secrecy] @ ball_simps)) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
569 |
by (auto_tac (!claset addDs [unique_session_keys], (!simpset))); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
570 |
qed "single_Nonce_secrecy"; |
2133 | 571 |
|
572 |
||
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
573 |
val Says_unique_NB' = read_instantiate [("lost","lost")] Says_unique_NB; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
574 |
|
2133 | 575 |
goal thy |
576 |
"!!evs. [| A ~: lost; B ~: lost; Spy: lost; evs : yahalom lost |] \ |
|
577 |
\ ==> Says B Server \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
578 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
2133 | 579 |
\ : set_of_list evs --> \ |
580 |
\ (ALL k. Says A Spy {|Nonce NA, Nonce NB, k|} ~: set_of_list evs) --> \ |
|
581 |
\ Nonce NB ~: analz (sees lost Spy evs)"; |
|
582 |
by (etac yahalom.induct 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
583 |
by analz_sees_tac; |
2133 | 584 |
by (ALLGOALS |
585 |
(asm_simp_tac |
|
2377 | 586 |
(!simpset addsimps ([not_parts_not_analz, |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
587 |
analz_insert_freshK] @ pushes) |
2133 | 588 |
setloop split_tac [expand_if]))); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
589 |
by (blast_tac (!claset addSIs [parts_insertI] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
590 |
addSEs sees_Spy_partsEs) 2); |
2377 | 591 |
(*Proof of YM2*) (** LEVEL 4 **) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
592 |
by (blast_tac (!claset addSEs partsEs |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
593 |
addDs [Says_imp_sees_Spy' RS analz.Inj, |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
594 |
impOfSubs analz_subset_parts]) 2); |
2133 | 595 |
(*Prove YM3 by showing that no NB can also be an NA*) |
596 |
by (REPEAT (Safe_step_tac 2 ORELSE no_nonce_tac 2)); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
597 |
by (blast_tac (!claset addDs [Says_unique_NB']) 2 THEN flexflex_tac); |
2377 | 598 |
(*Fake*) |
599 |
by (spy_analz_tac 1); |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
600 |
(*YM4*) (** LEVEL 8 **) |
2133 | 601 |
by (res_inst_tac [("x1","X")] (insert_commute RS ssubst) 1); |
602 |
by (simp_tac (!simpset setloop split_tac [expand_if]) 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
603 |
(* SLOW: 13s*) |
2377 | 604 |
by (SELECT_GOAL (REPEAT_FIRST (spy_analz_tac ORELSE' Safe_step_tac)) 1); |
2133 | 605 |
by (lost_tac "Aa" 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
606 |
by (dtac (Says_imp_sees_Spy' RS parts.Inj RS parts.Fst RS A_trusts_YM3) 1); |
2133 | 607 |
by (forward_tac [Says_Server_message_form] 3); |
608 |
by (forward_tac [Says_Server_imp_YM2] 4); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
609 |
by (REPEAT_FIRST (eresolve_tac [asm_rl, bexE, exE, disjE])); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
610 |
(** LEVEL 16 **) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
611 |
(* use unique_NB to identify message components *) |
2133 | 612 |
by (lost_tac "Ba" 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
613 |
by (subgoal_tac "Aa=A & Ba=B & NAa=NA" 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
614 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS parts.Inj] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
615 |
addSEs [MPair_parts] addDs [unique_NB]) 2); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
616 |
by (blast_tac (!claset addDs [Spy_not_see_encrypted_key, |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
617 |
impOfSubs Fake_analz_insert] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
618 |
addIs [impOfSubs analz_mono]) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
619 |
(** LEVEL 20 **) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
620 |
(*Oops case*) |
2133 | 621 |
by (full_simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
622 |
by (step_tac (!claset delrules [disjE, conjI]) 1); |
|
623 |
by (forward_tac [Says_Server_imp_YM2] 1 THEN assume_tac 1 THEN etac exE 1); |
|
624 |
by (expand_case_tac "NB = NBa" 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
625 |
by (blast_tac (!claset addDs [Says_unique_NB']) 1); |
2170 | 626 |
by (rtac conjI 1); |
2133 | 627 |
by (no_nonce_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
628 |
(** LEVEL 30 **) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
629 |
by (blast_tac (!claset addSDs [single_Nonce_secrecy]) 1); |
2133 | 630 |
val Spy_not_see_NB = result() RSN(2,rev_mp) RSN(2,rev_mp) |> standard; |
631 |
||
2001 | 632 |
|
2110 | 633 |
(*What can B deduce from receipt of YM4? Note how the two components of |
634 |
the message contribute to a single conclusion about the Server's message. |
|
635 |
It's annoying that the "Says A Spy" assumption must quantify over |
|
2133 | 636 |
ALL POSSIBLE keys instead of our particular K (though at least the |
637 |
nonces are forced to agree with NA and NB). *) |
|
2001 | 638 |
goal thy |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
639 |
"!!evs. [| Says B Server \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
640 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
2133 | 641 |
\ : set_of_list evs; \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
642 |
\ Says A' B {|Crypt (shrK B) {|Agent A, Key K|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
643 |
\ Crypt K (Nonce NB)|} : set_of_list evs; \ |
2133 | 644 |
\ ALL k. Says A Spy {|Nonce NA, Nonce NB, k|} ~: set_of_list evs; \ |
645 |
\ A ~: lost; B ~: lost; Spy: lost; evs : yahalom lost |] \ |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
646 |
\ ==> Says Server A \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
647 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
648 |
\ Nonce NA, Nonce NB|}, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
649 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
2001 | 650 |
\ : set_of_list evs"; |
2133 | 651 |
by (forward_tac [Spy_not_see_NB] 1 THEN REPEAT (assume_tac 1)); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
652 |
by (etac (Says_imp_sees_Spy' RS parts.Inj RS MPair_parts) 1 THEN |
2133 | 653 |
dtac B_trusts_YM4_shrK 1); |
2170 | 654 |
by (dtac B_trusts_YM4_newK 3); |
2110 | 655 |
by (REPEAT_FIRST (eresolve_tac [asm_rl, exE])); |
2133 | 656 |
by (forward_tac [Says_Server_imp_YM2] 1 THEN assume_tac 1); |
2170 | 657 |
by (dtac unique_session_keys 1 THEN REPEAT (assume_tac 1)); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
658 |
by (blast_tac (!claset addDs [Says_unique_NB']) 1); |
2322 | 659 |
qed "B_trusts_YM4"; |