author | paulson |
Fri, 18 Oct 1996 11:42:41 +0200 | |
changeset 2110 | d01151e66cd4 |
parent 2060 | 275ef0f28e1f |
child 2133 | f00a688760b9 |
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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14 |
|
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proof_timing:=true; |
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16 |
HOL_quantifiers := false; |
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17 |
|
1995 | 18 |
|
2013 | 19 |
(*Weak liveness: there are traces that reach the end*) |
1995 | 20 |
|
21 |
goal thy |
|
22 |
"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
|
2032 | 23 |
\ ==> EX X NB K. EX evs: yahalom lost. \ |
1995 | 24 |
\ Says A B {|X, Crypt (Nonce NB) K|} : set_of_list evs"; |
25 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
|
2032 | 26 |
by (rtac (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS yahalom.YM4) 2); |
1995 | 27 |
by (ALLGOALS (simp_tac (!simpset setsolver safe_solver))); |
28 |
by (ALLGOALS Fast_tac); |
|
2013 | 29 |
result(); |
1995 | 30 |
|
31 |
||
1985
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32 |
(**** Inductive proofs about yahalom ****) |
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33 |
|
2110 | 34 |
(*Monotonicity*) |
2045
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35 |
goal thy "!!evs. lost' <= lost ==> yahalom lost' <= yahalom lost"; |
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36 |
by (rtac subsetI 1); |
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37 |
by (etac yahalom.induct 1); |
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38 |
by (REPEAT_FIRST |
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39 |
(best_tac (!claset addIs (impOfSubs (sees_mono RS analz_mono RS synth_mono) |
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40 |
:: yahalom.intrs)))); |
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41 |
qed "yahalom_mono"; |
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42 |
|
1985
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43 |
|
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44 |
(*Nobody sends themselves messages*) |
2051 | 45 |
goal thy "!!evs. evs: yahalom lost ==> ALL A X. Says A A X ~: set_of_list evs"; |
2032 | 46 |
by (etac yahalom.induct 1); |
1985
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47 |
by (Auto_tac()); |
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48 |
qed_spec_mp "not_Says_to_self"; |
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49 |
Addsimps [not_Says_to_self]; |
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50 |
AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
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51 |
|
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52 |
|
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53 |
(** For reasoning about the encrypted portion of messages **) |
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54 |
|
1995 | 55 |
(*Lets us treat YM4 using a similar argument as for the Fake case.*) |
56 |
goal thy "!!evs. Says S A {|Crypt Y (shrK A), X|} : set_of_list evs ==> \ |
|
2032 | 57 |
\ X : analz (sees lost Spy evs)"; |
58 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1); |
|
59 |
qed "YM4_analz_sees_Spy"; |
|
1985
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60 |
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2110 | 61 |
bind_thm ("YM4_parts_sees_Spy", |
62 |
YM4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
|
63 |
||
64 |
(*Relates to both YM4 and Revl*) |
|
1995 | 65 |
goal thy "!!evs. Says S A {|Crypt {|B, K, NA, NB|} (shrK A), X|} \ |
66 |
\ : set_of_list evs ==> \ |
|
2032 | 67 |
\ K : parts (sees lost Spy evs)"; |
1985
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68 |
by (fast_tac (!claset addSEs partsEs |
2032 | 69 |
addSDs [Says_imp_sees_Spy RS parts.Inj]) 1); |
2110 | 70 |
qed "YM4_Key_parts_sees_Spy"; |
71 |
||
72 |
(*We instantiate the variable to "lost". Leaving it as a Var makes proofs |
|
73 |
harder: the simplifier does less.*) |
|
74 |
val parts_Fake_tac = |
|
75 |
forw_inst_tac [("lost","lost")] YM4_parts_sees_Spy 6 THEN |
|
76 |
forw_inst_tac [("lost","lost")] YM4_Key_parts_sees_Spy 7; |
|
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77 |
|
2110 | 78 |
(*For proving the easier theorems about X ~: parts (sees lost Spy evs) *) |
79 |
fun parts_induct_tac i = SELECT_GOAL |
|
80 |
(DETERM (etac yahalom.induct 1 THEN parts_Fake_tac THEN |
|
81 |
(*Fake message*) |
|
82 |
TRY (best_tac (!claset addDs [impOfSubs analz_subset_parts, |
|
83 |
impOfSubs Fake_parts_insert] |
|
84 |
addss (!simpset)) 2)) THEN |
|
85 |
(*Base case*) |
|
86 |
fast_tac (!claset addss (!simpset)) 1 THEN |
|
87 |
ALLGOALS Asm_simp_tac) i; |
|
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88 |
|
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89 |
|
2032 | 90 |
(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY |
2013 | 91 |
sends messages containing X! **) |
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92 |
|
2110 | 93 |
(*Spy never sees another agent's shared key! (unless it is leaked at start)*) |
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94 |
goal thy |
2032 | 95 |
"!!evs. [| evs : yahalom lost; A ~: lost |] \ |
96 |
\ ==> Key (shrK A) ~: parts (sees lost Spy evs)"; |
|
2110 | 97 |
by (parts_induct_tac 1); |
1985
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98 |
by (Auto_tac()); |
2032 | 99 |
qed "Spy_not_see_shrK"; |
1985
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100 |
|
2032 | 101 |
bind_thm ("Spy_not_analz_shrK", |
102 |
[analz_subset_parts, Spy_not_see_shrK] MRS contra_subsetD); |
|
1985
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103 |
|
2032 | 104 |
Addsimps [Spy_not_see_shrK, Spy_not_analz_shrK]; |
1985
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105 |
|
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106 |
(*We go to some trouble to preserve R in the 3rd and 4th subgoals |
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107 |
As usual fast_tac cannot be used because it uses the equalities too soon*) |
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108 |
val major::prems = |
2032 | 109 |
goal thy "[| Key (shrK A) : parts (sees lost Spy evs); \ |
110 |
\ evs : yahalom lost; \ |
|
111 |
\ A:lost ==> R \ |
|
1985
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112 |
\ |] ==> R"; |
2032 | 113 |
by (rtac ccontr 1); |
114 |
by (rtac ([major, Spy_not_see_shrK] MRS rev_notE) 1); |
|
1985
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115 |
by (swap_res_tac prems 2); |
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116 |
by (ALLGOALS (fast_tac (!claset addIs prems))); |
2032 | 117 |
qed "Spy_see_shrK_E"; |
1985
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118 |
|
2032 | 119 |
bind_thm ("Spy_analz_shrK_E", |
120 |
analz_subset_parts RS subsetD RS Spy_see_shrK_E); |
|
1985
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121 |
|
2032 | 122 |
AddSEs [Spy_see_shrK_E, Spy_analz_shrK_E]; |
1985
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123 |
|
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124 |
|
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125 |
(*** Future keys can't be seen or used! ***) |
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126 |
|
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127 |
(*Nobody can have SEEN keys that will be generated in the future. |
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128 |
This has to be proved anew for each protocol description, |
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129 |
but should go by similar reasoning every time. Hardest case is the |
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130 |
standard Fake rule. |
2110 | 131 |
The Union over C is essential for the induction! *) |
2032 | 132 |
goal thy "!!evs. evs : yahalom lost ==> \ |
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133 |
\ length evs <= length evs' --> \ |
2032 | 134 |
\ Key (newK evs') ~: (UN C. parts (sees lost C evs))"; |
2110 | 135 |
by (parts_induct_tac 1); |
1985
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|
136 |
by (REPEAT_FIRST (best_tac (!claset addDs [impOfSubs analz_subset_parts, |
2032 | 137 |
impOfSubs parts_insert_subset_Un, |
138 |
Suc_leD] |
|
139 |
addss (!simpset)))); |
|
1985
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140 |
val lemma = result(); |
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141 |
|
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142 |
(*Variant needed for the main theorem below*) |
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143 |
goal thy |
2032 | 144 |
"!!evs. [| evs : yahalom lost; length evs <= length evs' |] \ |
145 |
\ ==> Key (newK evs') ~: parts (sees lost C evs)"; |
|
1985
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146 |
by (fast_tac (!claset addDs [lemma]) 1); |
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147 |
qed "new_keys_not_seen"; |
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148 |
Addsimps [new_keys_not_seen]; |
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149 |
|
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150 |
(*Another variant: old messages must contain old keys!*) |
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151 |
goal thy |
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152 |
"!!evs. [| Says A B X : set_of_list evs; \ |
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153 |
\ Key (newK evt) : parts {X}; \ |
2032 | 154 |
\ evs : yahalom lost \ |
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155 |
\ |] ==> length evt < length evs"; |
2032 | 156 |
by (rtac ccontr 1); |
157 |
by (dtac leI 1); |
|
158 |
by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Spy] |
|
2013 | 159 |
addIs [impOfSubs parts_mono]) 1); |
1985
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160 |
qed "Says_imp_old_keys"; |
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161 |
|
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162 |
|
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163 |
(*Nobody can have USED keys that will be generated in the future. |
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164 |
...very like new_keys_not_seen*) |
2032 | 165 |
goal thy "!!evs. evs : yahalom lost ==> \ |
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166 |
\ length evs <= length evs' --> \ |
2032 | 167 |
\ newK evs' ~: keysFor (UN C. parts (sees lost C evs))"; |
2110 | 168 |
by (parts_induct_tac 1); |
169 |
by (dresolve_tac [YM4_Key_parts_sees_Spy] 5); |
|
170 |
||
1995 | 171 |
(*YM1, YM2 and YM3*) |
172 |
by (EVERY (map (fast_tac (!claset addDs [Suc_leD] addss (!simpset))) [4,3,2])); |
|
173 |
(*Fake and YM4: these messages send unknown (X) components*) |
|
174 |
by (stac insert_commute 2); |
|
175 |
by (Simp_tac 2); |
|
176 |
(*YM4: the only way K could have been used is if it had been seen, |
|
177 |
contradicting new_keys_not_seen*) |
|
2110 | 178 |
by (REPEAT |
1985
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179 |
(best_tac |
2026
0df5a96bf77e
Last working version prior to introduction of "lost"
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|
180 |
(!claset addDs [impOfSubs analz_subset_parts, |
2032 | 181 |
impOfSubs (analz_subset_parts RS keysFor_mono), |
182 |
impOfSubs (parts_insert_subset_Un RS keysFor_mono), |
|
183 |
Suc_leD] |
|
184 |
addEs [new_keys_not_seen RSN(2,rev_notE)] |
|
2110 | 185 |
addss (!simpset)) 1)); |
1985
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186 |
val lemma = result(); |
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187 |
|
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188 |
goal thy |
2032 | 189 |
"!!evs. [| evs : yahalom lost; length evs <= length evs' |] \ |
190 |
\ ==> newK evs' ~: keysFor (parts (sees lost C evs))"; |
|
1985
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191 |
by (fast_tac (!claset addSDs [lemma] addss (!simpset)) 1); |
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|
192 |
qed "new_keys_not_used"; |
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193 |
|
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|
194 |
bind_thm ("new_keys_not_analzd", |
2032 | 195 |
[analz_subset_parts RS keysFor_mono, |
196 |
new_keys_not_used] MRS contra_subsetD); |
|
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|
197 |
|
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|
198 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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|
199 |
|
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|
200 |
|
2110 | 201 |
(*Describes the form of Key K when the following message is sent. The use of |
202 |
"parts" strengthens the induction hyp for proving the Fake case. The |
|
203 |
assumption A ~: lost prevents its being a Faked message. (Based |
|
204 |
on NS_Shared/Says_S_message_form) *) |
|
205 |
goal thy |
|
206 |
"!!evs. evs: yahalom lost ==> \ |
|
207 |
\ Crypt {|B, Key K, NA, NB|} (shrK A) : parts (sees lost Spy evs) \ |
|
208 |
\ --> A ~: lost --> (EX evt: yahalom lost. K = newK evt)"; |
|
209 |
by (parts_induct_tac 1); |
|
210 |
by (Auto_tac()); |
|
211 |
qed_spec_mp "Reveal_message_lemma"; |
|
212 |
||
213 |
(*EITHER describes the form of Key K when the following message is sent, |
|
214 |
OR reduces it to the Fake case.*) |
|
215 |
||
216 |
goal thy |
|
217 |
"!!evs. [| Says S A {|Crypt {|B, Key K, NA, NB|} (shrK A), X|} \ |
|
218 |
\ : set_of_list evs; \ |
|
219 |
\ evs : yahalom lost |] \ |
|
220 |
\ ==> (EX evt: yahalom lost. K = newK evt) \ |
|
221 |
\ | Key K : analz (sees lost Spy evs)"; |
|
222 |
br (Reveal_message_lemma RS disjCI) 1; |
|
223 |
ba 1; |
|
224 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj] |
|
225 |
addDs [impOfSubs analz_subset_parts]) 1); |
|
226 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj] |
|
227 |
addss (!simpset)) 1); |
|
228 |
qed "Reveal_message_form"; |
|
229 |
||
230 |
||
231 |
(*For proofs involving analz. We again instantiate the variable to "lost".*) |
|
232 |
val analz_Fake_tac = |
|
233 |
dres_inst_tac [("lost","lost")] YM4_analz_sees_Spy 6 THEN |
|
234 |
forw_inst_tac [("lost","lost")] Reveal_message_form 7; |
|
1985
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|
235 |
|
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|
236 |
|
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|
237 |
(**** |
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|
238 |
The following is to prove theorems of the form |
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|
239 |
|
2032 | 240 |
Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) ==> |
241 |
Key K : analz (sees lost Spy evs) |
|
1985
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|
242 |
|
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|
243 |
A more general formula must be proved inductively. |
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|
244 |
|
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|
245 |
****) |
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|
246 |
|
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|
247 |
|
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|
248 |
(*NOT useful in this form, but it says that session keys are not used |
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paulson
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|
249 |
to encrypt messages containing other keys, in the actual protocol. |
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paulson
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|
250 |
We require that agents should behave like this subsequently also.*) |
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|
251 |
goal thy |
2032 | 252 |
"!!evs. evs : yahalom lost ==> \ |
253 |
\ (Crypt X (newK evt)) : parts (sees lost Spy evs) & \ |
|
254 |
\ Key K : parts {X} --> Key K : parts (sees lost Spy evs)"; |
|
255 |
by (etac yahalom.induct 1); |
|
2110 | 256 |
by parts_Fake_tac; |
2060 | 257 |
by (ALLGOALS Asm_simp_tac); |
1985
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|
258 |
(*Deals with Faked messages*) |
2110 | 259 |
by (best_tac (!claset addSEs partsEs |
260 |
addDs [impOfSubs parts_insert_subset_Un] |
|
261 |
addss (!simpset)) 2); |
|
1995 | 262 |
(*Base case*) |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
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|
263 |
by (Auto_tac()); |
84cf16192e03
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parents:
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|
264 |
result(); |
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parents:
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|
265 |
|
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|
266 |
|
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|
267 |
(** Session keys are not used to encrypt other session keys **) |
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|
268 |
|
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|
269 |
goal thy |
2032 | 270 |
"!!evs. evs : yahalom lost ==> \ |
271 |
\ ALL K E. (Key K : analz (Key``(newK``E) Un (sees lost Spy evs))) = \ |
|
272 |
\ (K : newK``E | Key K : analz (sees lost Spy evs))"; |
|
273 |
by (etac yahalom.induct 1); |
|
2110 | 274 |
by analz_Fake_tac; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
275 |
by (REPEAT_FIRST (resolve_tac [allI, analz_image_newK_lemma])); |
2110 | 276 |
by (REPEAT ((eresolve_tac [bexE, disjE] ORELSE' hyp_subst_tac) 8)); |
277 |
by (ALLGOALS (*Takes 26 secs*) |
|
1985
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paulson
parents:
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|
278 |
(asm_simp_tac |
84cf16192e03
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paulson
parents:
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|
279 |
(!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK] |
2032 | 280 |
@ pushes) |
1985
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|
281 |
setloop split_tac [expand_if]))); |
2110 | 282 |
(** LEVEL 5 **) |
283 |
(*Reveal case 2, YM4, Fake*) |
|
284 |
by (EVERY (map spy_analz_tac [6, 4, 2])); |
|
285 |
(*Reveal case 1, YM3, Base*) |
|
286 |
by (REPEAT (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1)); |
|
1985
84cf16192e03
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paulson
parents:
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|
287 |
qed_spec_mp "analz_image_newK"; |
84cf16192e03
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paulson
parents:
diff
changeset
|
288 |
|
84cf16192e03
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parents:
diff
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|
289 |
goal thy |
2032 | 290 |
"!!evs. evs : yahalom lost ==> \ |
291 |
\ Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) = \ |
|
292 |
\ (K = newK evt | Key K : analz (sees lost Spy evs))"; |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
293 |
by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK, |
2032 | 294 |
insert_Key_singleton]) 1); |
1985
84cf16192e03
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paulson
parents:
diff
changeset
|
295 |
by (Fast_tac 1); |
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|
296 |
qed "analz_insert_Key_newK"; |
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|
297 |
|
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|
298 |
|
2110 | 299 |
(*** The Key K uniquely identifies the Server's message. **) |
300 |
||
301 |
goal thy |
|
302 |
"!!evs. evs : yahalom lost ==> \ |
|
303 |
\ EX A' B' NA' NB'. ALL A B NA NB. \ |
|
304 |
\ Says Server A \ |
|
305 |
\ {|Crypt {|Agent B, Key K, NA, NB|} (shrK A), \ |
|
306 |
\ Crypt {|Agent A, Key K|} (shrK B)|} \ |
|
307 |
\ : set_of_list evs --> A=A' & B=B' & NA=NA' & NB=NB'"; |
|
308 |
by (etac yahalom.induct 1); |
|
309 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
|
310 |
by (Step_tac 1); |
|
311 |
(*Remaining case: YM3*) |
|
312 |
by (expand_case_tac "K = ?y" 1); |
|
313 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
|
314 |
(*...we assume X is a very new message, and handle this case by contradiction*) |
|
315 |
by (fast_tac (!claset addEs [Says_imp_old_keys RS less_irrefl] |
|
316 |
delrules [conjI] (*prevent split-up into 4 subgoals*) |
|
317 |
addss (!simpset addsimps [parts_insertI])) 1); |
|
318 |
val lemma = result(); |
|
319 |
||
320 |
goal thy |
|
321 |
"!!evs. [| Says Server A \ |
|
322 |
\ {|Crypt {|Agent B, Key K, NA, NB|} (shrK A), \ |
|
323 |
\ Crypt {|Agent A, Key K|} (shrK B)|} \ |
|
324 |
\ : set_of_list evs; \ |
|
325 |
\ Says Server A' \ |
|
326 |
\ {|Crypt {|Agent B', Key K, NA', NB'|} (shrK A'), \ |
|
327 |
\ Crypt {|Agent A', Key K|} (shrK B')|} \ |
|
328 |
\ : set_of_list evs; \ |
|
329 |
\ evs : yahalom lost |] \ |
|
330 |
\ ==> A=A' & B=B' & NA=NA' & NB=NB'"; |
|
331 |
by (dtac lemma 1); |
|
332 |
by (REPEAT (etac exE 1)); |
|
333 |
(*Duplicate the assumption*) |
|
334 |
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1); |
|
335 |
by (fast_tac (!claset addSDs [spec]) 1); |
|
336 |
qed "unique_session_keys"; |
|
337 |
||
338 |
||
339 |
(*If the encrypted message appears then it originated with the Server*) |
|
340 |
goal thy |
|
341 |
"!!evs. [| Crypt {|Agent B, Key K, NA, NB|} (shrK A) \ |
|
342 |
\ : parts (sees lost Spy evs); \ |
|
343 |
\ A ~: lost; evs : yahalom lost |] \ |
|
344 |
\ ==> Says Server A \ |
|
345 |
\ {|Crypt {|Agent B, Key K, NA, NB|} (shrK A), \ |
|
346 |
\ Crypt {|Agent A, Key K|} (shrK B)|} \ |
|
347 |
\ : set_of_list evs"; |
|
348 |
by (etac rev_mp 1); |
|
349 |
by (parts_induct_tac 1); |
|
350 |
qed "A_trust_YM3"; |
|
351 |
||
352 |
||
2013 | 353 |
(*Describes the form of K when the Server sends this message.*) |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
354 |
goal thy |
1995 | 355 |
"!!evs. [| Says Server A \ |
356 |
\ {|Crypt {|Agent B, K, NA, NB|} (shrK A), \ |
|
357 |
\ Crypt {|Agent A, K|} (shrK B)|} : set_of_list evs; \ |
|
2110 | 358 |
\ evs : yahalom lost |] \ |
2032 | 359 |
\ ==> (EX evt: yahalom lost. K = Key(newK evt))"; |
360 |
by (etac rev_mp 1); |
|
361 |
by (etac yahalom.induct 1); |
|
2013 | 362 |
by (ALLGOALS (fast_tac (!claset addss (!simpset)))); |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
363 |
qed "Says_Server_message_form"; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
364 |
|
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
365 |
|
2110 | 366 |
(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 **) |
2013 | 367 |
|
368 |
goal thy |
|
2051 | 369 |
"!!evs. [| A ~: lost; B ~: lost; \ |
370 |
\ evs : yahalom lost; evt : yahalom lost |] \ |
|
371 |
\ ==> Says Server A \ |
|
372 |
\ {|Crypt {|Agent B, Key K, NA, NB|} (shrK A), \ |
|
373 |
\ Crypt {|Agent A, Key K|} (shrK B)|} \ |
|
2110 | 374 |
\ : set_of_list evs --> \ |
375 |
\ Says A Spy {|NA, NB, Key K|} ~: set_of_list evs --> \ |
|
2051 | 376 |
\ Key K ~: analz (sees lost Spy evs)"; |
2032 | 377 |
by (etac yahalom.induct 1); |
2110 | 378 |
by analz_Fake_tac; |
379 |
by (REPEAT_FIRST (eresolve_tac [asm_rl, bexE, disjE] ORELSE' hyp_subst_tac)); |
|
2013 | 380 |
by (ALLGOALS |
381 |
(asm_simp_tac |
|
382 |
(!simpset addsimps ([analz_subset_parts RS contra_subsetD, |
|
2032 | 383 |
analz_insert_Key_newK] @ pushes) |
2013 | 384 |
setloop split_tac [expand_if]))); |
385 |
(*YM3*) |
|
386 |
by (fast_tac (!claset addIs [parts_insertI] |
|
2032 | 387 |
addEs [Says_imp_old_keys RS less_irrefl] |
388 |
addss (!simpset)) 2); |
|
2110 | 389 |
(*Reveal case 2, OR4, Fake*) |
390 |
by (REPEAT_FIRST (resolve_tac [conjI, impI] ORELSE' spy_analz_tac)); |
|
391 |
(*Reveal case 1*) (** LEVEL 6 **) |
|
392 |
by (case_tac "Aa : lost" 1); |
|
393 |
(*But this contradicts Key K ~: analz (sees lost Spy evsa) *) |
|
394 |
by (dtac (Says_imp_sees_Spy RS analz.Inj) 1); |
|
395 |
by (fast_tac (!claset addSDs [analz.Decrypt] addss (!simpset)) 1); |
|
396 |
(*So now we have Aa ~: lost *) |
|
397 |
bd (Says_imp_sees_Spy RS parts.Inj) 1; |
|
398 |
by (fast_tac (!claset delrules [disjE] |
|
399 |
addSEs [MPair_parts] |
|
400 |
addDs [A_trust_YM3, unique_session_keys] |
|
401 |
addss (!simpset)) 1); |
|
402 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
|
2013 | 403 |
|
404 |
||
405 |
(*Final version: Server's message in the most abstract form*) |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
406 |
goal thy |
2110 | 407 |
"!!evs. [| Says Server A \ |
1995 | 408 |
\ {|Crypt {|Agent B, K, NA, NB|} (shrK A), \ |
409 |
\ Crypt {|Agent A, K|} (shrK B)|} : set_of_list evs; \ |
|
2110 | 410 |
\ Says A Spy {|NA, NB, K|} ~: set_of_list evs; \ |
411 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] ==> \ |
|
2032 | 412 |
\ K ~: analz (sees lost Spy evs)"; |
2013 | 413 |
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1); |
414 |
by (fast_tac (!claset addSEs [lemma]) 1); |
|
2032 | 415 |
qed "Spy_not_see_encrypted_key"; |
2001 | 416 |
|
417 |
||
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
418 |
goal thy |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
419 |
"!!evs. [| C ~: {A,B,Server}; \ |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
420 |
\ Says Server A \ |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
421 |
\ {|Crypt {|Agent B, K, NA, NB|} (shrK A), \ |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
422 |
\ Crypt {|Agent A, K|} (shrK B)|} : set_of_list evs; \ |
2110 | 423 |
\ Says A Spy {|NA, NB, K|} ~: set_of_list evs; \ |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
424 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] ==> \ |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
425 |
\ K ~: analz (sees lost C evs)"; |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
426 |
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
|
427 |
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
|
428 |
by (FIRSTGOAL (rtac Spy_not_see_encrypted_key)); |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
429 |
by (REPEAT_FIRST (fast_tac (!claset addIs [yahalom_mono RS subsetD]))); |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
430 |
qed "Agent_not_see_encrypted_key"; |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
431 |
|
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
432 |
|
2110 | 433 |
(*** Security Guarantee for B upon receiving YM4 ***) |
2013 | 434 |
|
2110 | 435 |
(*B knows, by the first part of A's message, that the Server distributed |
436 |
the key for A and B. But this part says nothing about nonces.*) |
|
2001 | 437 |
goal thy |
2032 | 438 |
"!!evs. [| Crypt {|Agent A, Key K|} (shrK B) : parts (sees lost Spy evs); \ |
2051 | 439 |
\ B ~: lost; evs : yahalom lost |] \ |
2001 | 440 |
\ ==> EX NA NB. Says Server A \ |
2013 | 441 |
\ {|Crypt {|Agent B, Key K, \ |
442 |
\ Nonce NA, Nonce NB|} (shrK A), \ |
|
443 |
\ Crypt {|Agent A, Key K|} (shrK B)|} \ |
|
444 |
\ : set_of_list evs"; |
|
2032 | 445 |
by (etac rev_mp 1); |
2110 | 446 |
by (parts_induct_tac 1); |
447 |
(*YM3*) |
|
448 |
by (Fast_tac 1); |
|
449 |
qed "B_trusts_YM4_shrK"; |
|
450 |
||
451 |
(*B knows, by the second part of A's message, that the Server distributed |
|
452 |
the key quoting nonce NB. This part says nothing about agent names.*) |
|
453 |
goal thy |
|
454 |
"!!evs. evs : yahalom lost \ |
|
455 |
\ ==> Key K ~: analz (sees lost Spy evs) --> \ |
|
456 |
\ Crypt (Nonce NB) K : parts (sees lost Spy evs) --> \ |
|
457 |
\ (EX A B NA. Says Server A \ |
|
458 |
\ {|Crypt {|Agent B, Key K, \ |
|
459 |
\ Nonce NA, Nonce NB|} (shrK A), \ |
|
460 |
\ Crypt {|Agent A, Key K|} (shrK B)|} \ |
|
461 |
\ : set_of_list evs)"; |
|
2032 | 462 |
by (etac yahalom.induct 1); |
2110 | 463 |
by parts_Fake_tac; |
2001 | 464 |
by (fast_tac (!claset addss (!simpset)) 1); |
2110 | 465 |
by (TRYALL (rtac impI)); |
466 |
by (REPEAT_FIRST |
|
467 |
(dtac (sees_subset_sees_Says RS analz_mono RS contra_subsetD))); |
|
468 |
by (ALLGOALS Asm_simp_tac); |
|
469 |
(*Fake, YM3, YM4*) |
|
470 |
by (fast_tac (!claset addSDs [Crypt_Fake_parts_insert] |
|
471 |
addDs [impOfSubs analz_subset_parts]) 1); |
|
472 |
by (Fast_tac 1); |
|
473 |
(*YM4*) |
|
474 |
by (Step_tac 1); |
|
475 |
by (case_tac "A : lost" 1); |
|
476 |
(*But this contradicts Key K ~: analz (sees lost Spy evsa) *) |
|
477 |
by (dtac (Says_imp_sees_Spy RS analz.Inj) 1); |
|
478 |
by (fast_tac (!claset addSDs [analz.Decrypt] addss (!simpset)) 1); |
|
479 |
by (fast_tac (!claset addDs [Says_imp_sees_Spy RS parts.Inj RS parts.Fst RS |
|
480 |
A_trust_YM3]) 1); |
|
481 |
val B_trusts_YM4_newK = result() RS mp RSN (2, rev_mp); |
|
2001 | 482 |
|
2110 | 483 |
(*What can B deduce from receipt of YM4? Note how the two components of |
484 |
the message contribute to a single conclusion about the Server's message. |
|
485 |
It's annoying that the "Says A Spy" assumption must quantify over |
|
486 |
ALL POSSIBLE nonces instead of our particular NB. Perhaps a different |
|
487 |
proof of B_trusts_YM4_newK could eliminate this problem.*) |
|
2001 | 488 |
goal thy |
489 |
"!!evs. [| Says A' B {|Crypt {|Agent A, Key K|} (shrK B), \ |
|
490 |
\ Crypt (Nonce NB) K|} : set_of_list evs; \ |
|
2110 | 491 |
\ ALL N N'. Says A Spy {|N,N', Key K|} ~: set_of_list evs; \ |
492 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
|
493 |
\ ==> EX NA. Says Server A \ |
|
2001 | 494 |
\ {|Crypt {|Agent B, Key K, \ |
495 |
\ Nonce NA, Nonce NB|} (shrK A), \ |
|
496 |
\ Crypt {|Agent A, Key K|} (shrK B)|} \ |
|
497 |
\ : set_of_list evs"; |
|
2110 | 498 |
be (Says_imp_sees_Spy RS parts.Inj RS MPair_parts) 1; |
499 |
bd B_trusts_YM4_shrK 1; |
|
500 |
bd B_trusts_YM4_newK 3; |
|
501 |
by (REPEAT_FIRST (eresolve_tac [asm_rl, exE])); |
|
502 |
by (fast_tac (!claset addDs [unique_session_keys]) 2); |
|
503 |
by (fast_tac (!claset addDs [Spy_not_see_encrypted_key]) 1); |
|
504 |
qed "B_trust_YM4"; |