author | nipkow |
Thu, 26 Jun 1997 13:20:50 +0200 | |
changeset 3465 | e85c24717cad |
parent 3464 | 315694e22856 |
child 3466 | 30791e5a69c4 |
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 |
|
3432 | 6 |
Inductive relation "yahalom" for the Yahalom protocol. |
1985
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parents:
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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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parents:
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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
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parents:
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18 |
|
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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. \ |
3465 | 27 |
\ Says A B {|X, Crypt K (Nonce NB)|} : set 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 |
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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
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parents:
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46 |
|
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47 |
(*Nobody sends themselves messages*) |
3465 | 48 |
goal thy "!!evs. evs: yahalom lost ==> ALL A X. Says A A X ~: set evs"; |
2032 | 49 |
by (etac yahalom.induct 1); |
1985
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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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parents:
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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.*) |
3465 | 59 |
goal thy "!!evs. Says S A {|Crypt (shrK A) Y, X|} : set 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|} \ |
3465 | 69 |
\ : set 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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parents:
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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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parents:
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|
94 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
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|
95 |
by (Fake_parts_insert_tac 1); |
cbb6c0c1c58a
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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
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paulson
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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paulson
parents:
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|
109 |
by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2133 | 110 |
qed "Spy_see_shrK_D"; |
1985
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paulson
parents:
diff
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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 |
|
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115 |
|
3432 | 116 |
(*Nobody can have used non-existent keys! Needed to apply analz_insert_Key*) |
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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))"; |
3121
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parents:
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|
119 |
by parts_induct_tac; |
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|
120 |
(*YM4: Key K is not fresh!*) |
3121
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parents:
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|
121 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 3); |
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122 |
(*YM3*) |
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parents:
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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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paulson
parents:
diff
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|
131 |
|
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parents:
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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:
diff
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|
135 |
|
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parents:
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|
136 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
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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|} \ |
3465 | 143 |
\ : set 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); |
|
3121
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Conversion to use blast_tac (with other improvements)
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parents:
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|
148 |
by (ALLGOALS Asm_simp_tac); |
cbb6c0c1c58a
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paulson
parents:
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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
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paulson
parents:
diff
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|
158 |
|
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parents:
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|
159 |
|
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parents:
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|
160 |
(**** |
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paulson
parents:
diff
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|
161 |
The following is to prove theorems of the form |
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parents:
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162 |
|
2516
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|
163 |
Key K : analz (insert (Key KAB) (sees lost Spy evs)) ==> |
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parents:
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|
164 |
Key K : analz (sees lost Spy evs) |
1985
84cf16192e03
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paulson
parents:
diff
changeset
|
165 |
|
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
166 |
A more general formula must be proved inductively. |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
167 |
****) |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
168 |
|
84cf16192e03
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paulson
parents:
diff
changeset
|
169 |
(** Session keys are not used to encrypt other session keys **) |
84cf16192e03
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paulson
parents:
diff
changeset
|
170 |
|
84cf16192e03
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paulson
parents:
diff
changeset
|
171 |
goal thy |
2032 | 172 |
"!!evs. evs : yahalom lost ==> \ |
2516
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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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Conversion to use blast_tac (with other improvements)
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parents:
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changeset
|
177 |
by analz_sees_tac; |
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changeset
|
178 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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parents:
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diff
changeset
|
179 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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parents:
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diff
changeset
|
180 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
3450
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Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
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parents:
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|
181 |
(*Fake*) |
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Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
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changeset
|
182 |
by (spy_analz_tac 2); |
2516
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|
183 |
(*Base*) |
3121
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|
184 |
by (Blast_tac 1); |
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changeset
|
185 |
qed_spec_mp "analz_image_freshK"; |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
186 |
|
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
187 |
goal thy |
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|
188 |
"!!evs. [| evs : yahalom lost; KAB ~: range shrK |] ==> \ |
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changeset
|
189 |
\ Key K : analz (insert (Key KAB) (sees lost Spy evs)) = \ |
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changeset
|
190 |
\ (K = KAB | Key K : analz (sees lost Spy evs))"; |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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parents:
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diff
changeset
|
191 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
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|
192 |
qed "analz_insert_freshK"; |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
193 |
|
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Tidied many proofs, using AddIffs to let equivalences take
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 ==> \ |
|
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changeset
|
199 |
\ EX A' B' na' nb' X'. ALL A B na nb X. \ |
2110 | 200 |
\ Says Server A \ |
3450
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Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
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parents:
3444
diff
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|
201 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, X|} \ |
3465 | 202 |
\ : set 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
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
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*) |
3121
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changeset
|
212 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
cbb6c0c1c58a
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parents:
2637
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changeset
|
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|} \ |
3465 | 219 |
\ : set evs; \ |
2110 | 220 |
\ Says Server A' \ |
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changeset
|
221 |
\ {|Crypt (shrK A') {|Agent B', Key K, na', nb'|}, X'|} \ |
3465 | 222 |
\ : set evs; \ |
2110 | 223 |
\ evs : yahalom lost |] \ |
3450
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changeset
|
224 |
\ ==> A=A' & B=B' & na=na' & nb=nb'"; |
2451
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Extensive tidying and simplification, largely stemming from
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parents:
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changeset
|
225 |
by (prove_unique_tac lemma 1); |
2110 | 226 |
qed "unique_session_keys"; |
227 |
||
228 |
||
229 |
(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 **) |
|
2013 | 230 |
|
231 |
goal thy |
|
2133 | 232 |
"!!evs. [| A ~: lost; B ~: lost; evs : yahalom lost |] \ |
2051 | 233 |
\ ==> Says Server A \ |
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changeset
|
234 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
235 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
3465 | 236 |
\ : set evs --> \ |
237 |
\ Says A Spy {|na, nb, Key K|} ~: set evs --> \ |
|
2051 | 238 |
\ Key K ~: analz (sees lost Spy evs)"; |
2032 | 239 |
by (etac yahalom.induct 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
240 |
by analz_sees_tac; |
2013 | 241 |
by (ALLGOALS |
242 |
(asm_simp_tac |
|
3450
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Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
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|
243 |
(!simpset addsimps [analz_insert_eq, not_parts_not_analz, |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
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changeset
|
244 |
analz_insert_freshK] |
2013 | 245 |
setloop split_tac [expand_if]))); |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
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diff
changeset
|
246 |
(*Oops*) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
247 |
by (blast_tac (!claset addDs [unique_session_keys]) 3); |
2013 | 248 |
(*YM3*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
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diff
changeset
|
249 |
by (blast_tac (!claset delrules [impCE] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
2637
diff
changeset
|
250 |
addSEs sees_Spy_partsEs |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
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parents:
2637
diff
changeset
|
251 |
addIs [impOfSubs analz_subset_parts]) 2); |
3450
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Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
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parents:
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changeset
|
252 |
(*Fake*) |
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Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
253 |
by (spy_analz_tac 1); |
2110 | 254 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
2013 | 255 |
|
256 |
||
3432 | 257 |
(*Final version*) |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
diff
changeset
|
258 |
goal thy |
2516
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|
259 |
"!!evs. [| Says Server A \ |
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Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
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parents:
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changeset
|
260 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, \ |
2516
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changeset
|
261 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
3465 | 262 |
\ : set evs; \ |
263 |
\ Says A Spy {|na, nb, Key K|} ~: set evs; \ |
|
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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parents:
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changeset
|
264 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
265 |
\ ==> Key K ~: analz (sees lost Spy evs)"; |
2013 | 266 |
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
|
267 |
by (blast_tac (!claset addSEs [lemma]) 1); |
2032 | 268 |
qed "Spy_not_see_encrypted_key"; |
2001 | 269 |
|
270 |
||
3432 | 271 |
(*And other agents don't see the key either.*) |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
272 |
goal thy |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
273 |
"!!evs. [| C ~: {A,B,Server}; \ |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
274 |
\ Says Server A \ |
3450
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|
275 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, \ |
2516
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changeset
|
276 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
3465 | 277 |
\ : set evs; \ |
278 |
\ Says A Spy {|na, nb, Key K|} ~: set evs; \ |
|
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
279 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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parents:
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changeset
|
280 |
\ ==> 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
|
281 |
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
|
282 |
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
|
283 |
by (FIRSTGOAL (rtac Spy_not_see_encrypted_key)); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
284 |
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
|
285 |
qed "Agent_not_see_encrypted_key"; |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
286 |
|
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
287 |
|
3444
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Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
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changeset
|
288 |
(*Induction for theorems of the form X ~: analz (sees lost Spy evs) --> ... |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
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changeset
|
289 |
It simplifies the proof by discarding needless information about |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
290 |
analz (insert X (sees lost Spy evs)) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
291 |
*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
292 |
val analz_mono_parts_induct_tac = |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
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parents:
3432
diff
changeset
|
293 |
etac yahalom.induct 1 |
919de2cb3487
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parents:
3432
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|
294 |
THEN |
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parents:
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|
295 |
REPEAT_FIRST |
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Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
296 |
(rtac impI THEN' |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
297 |
dtac (sees_subset_sees_Says RS analz_mono RS contra_subsetD) THEN' |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
298 |
mp_tac) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
299 |
THEN parts_sees_tac; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
300 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
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changeset
|
301 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
302 |
(** Security Guarantee for A upon receiving YM3 **) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
303 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
304 |
(*If the encrypted message appears then it originated with the Server*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
305 |
goal thy |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
306 |
"!!evs. [| Crypt (shrK A) {|Agent B, Key K, na, nb|} \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
307 |
\ : parts (sees lost Spy evs); \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
308 |
\ A ~: lost; evs : yahalom lost |] \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
309 |
\ ==> Says Server A \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
310 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
311 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
3465 | 312 |
\ : set evs"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
313 |
by (etac rev_mp 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
314 |
by parts_induct_tac; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
315 |
by (Fake_parts_insert_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
316 |
qed "A_trusts_YM3"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
317 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
318 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
319 |
(** Security Guarantees for B upon receiving YM4 **) |
2013 | 320 |
|
2110 | 321 |
(*B knows, by the first part of A's message, that the Server distributed |
322 |
the key for A and B. But this part says nothing about nonces.*) |
|
2001 | 323 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
324 |
"!!evs. [| Crypt (shrK B) {|Agent A, Key K|} : parts (sees lost Spy evs); \ |
2051 | 325 |
\ B ~: lost; evs : yahalom lost |] \ |
2001 | 326 |
\ ==> EX NA NB. Says Server A \ |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2377
diff
changeset
|
327 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
328 |
\ Nonce NA, Nonce NB|}, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
329 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
3465 | 330 |
\ : set evs"; |
2032 | 331 |
by (etac rev_mp 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
332 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
333 |
by (Fake_parts_insert_tac 1); |
2110 | 334 |
(*YM3*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
335 |
by (Blast_tac 1); |
2110 | 336 |
qed "B_trusts_YM4_shrK"; |
337 |
||
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
338 |
(*B knows, by the second part of A's message, that the Server distributed |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
339 |
the key quoting nonce NB. This part says nothing about agent names. |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
340 |
Secrecy of NB is crucial.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
341 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
342 |
"!!evs. evs : yahalom lost \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
343 |
\ ==> Nonce NB ~: analz (sees lost Spy evs) --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
344 |
\ Crypt K (Nonce NB) : parts (sees lost Spy evs) --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
345 |
\ (EX A B NA. Says Server A \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
346 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
347 |
\ Nonce NA, Nonce NB|}, \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
348 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
3465 | 349 |
\ : set evs)"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
350 |
by analz_mono_parts_induct_tac; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
351 |
(*YM3 & Fake*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
352 |
by (Blast_tac 2); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
353 |
by (Fake_parts_insert_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
354 |
(*YM4*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
355 |
by (Step_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
356 |
(*A is uncompromised because NB is secure*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
357 |
by (not_lost_tac "A" 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
358 |
(*A's certificate guarantees the existence of the Server message*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
359 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj RS parts.Fst RS |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
360 |
A_trusts_YM3]) 1); |
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
361 |
bind_thm ("B_trusts_YM4_newK", result() RS mp RSN (2, rev_mp)); |
2133 | 362 |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
363 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
364 |
(**** Towards proving secrecy of Nonce NB ****) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
365 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
366 |
(** Lemmas about the predicate KeyWithNonce **) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
367 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
368 |
goalw thy [KeyWithNonce_def] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
369 |
"!!evs. Says Server A \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
370 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|} \ |
3465 | 371 |
\ : set evs ==> KeyWithNonce K NB evs"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
372 |
by (Blast_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
373 |
qed "KeyWithNonceI"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
374 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
375 |
goalw thy [KeyWithNonce_def] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
376 |
"KeyWithNonce K NB (Says S A X # evs) = \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
377 |
\ (Server = S & \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
378 |
\ (EX B n X'. X = {|Crypt (shrK A) {|Agent B, Key K, n, Nonce NB|}, X'|}) \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
379 |
\ | KeyWithNonce K NB evs)"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
380 |
by (Simp_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
381 |
by (Blast_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
382 |
qed "KeyWithNonce_Says"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
383 |
Addsimps [KeyWithNonce_Says]; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
384 |
|
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
385 |
(*A fresh key cannot be associated with any nonce |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
386 |
(with respect to a given trace). *) |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
387 |
goalw thy [KeyWithNonce_def] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
388 |
"!!evs. Key K ~: used evs ==> ~ KeyWithNonce K NB evs"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
389 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
390 |
qed "fresh_not_KeyWithNonce"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
391 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
392 |
(*The Server message associates K with NB' and therefore not with any |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
393 |
other nonce NB.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
394 |
goalw thy [KeyWithNonce_def] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
395 |
"!!evs. [| Says Server A \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
396 |
\ {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB'|}, X|} \ |
3465 | 397 |
\ : set evs; \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
398 |
\ NB ~= NB'; evs : yahalom lost |] \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
399 |
\ ==> ~ KeyWithNonce K NB evs"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
400 |
by (blast_tac (!claset addDs [unique_session_keys]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
401 |
qed "Says_Server_KeyWithNonce"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
402 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
403 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
404 |
(*The only nonces that can be found with the help of session keys are |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
405 |
those distributed as nonce NB by the Server. The form of the theorem |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
406 |
recalls analz_image_freshK, but it is much more complicated.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
407 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
408 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
409 |
(*As with analz_image_freshK, we take some pains to express the property |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
410 |
as a logical equivalence so that the simplifier can apply it.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
411 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
412 |
"!!evs. P --> (X : analz (G Un H)) --> (X : analz H) ==> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
413 |
\ P --> (X : analz (G Un H)) = (X : analz H)"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
414 |
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
415 |
val lemma = result(); |
2133 | 416 |
|
417 |
goal thy |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
418 |
"!!evs. evs : yahalom lost ==> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
419 |
\ (ALL KK. KK <= Compl (range shrK) --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
420 |
\ (ALL K: KK. ~ KeyWithNonce K NB evs) --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
421 |
\ (Nonce NB : analz (Key``KK Un (sees lost Spy evs))) = \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
422 |
\ (Nonce NB : analz (sees lost Spy evs)))"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
423 |
by (etac yahalom.induct 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
424 |
by analz_sees_tac; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
425 |
by (REPEAT_FIRST (resolve_tac [impI RS allI])); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
426 |
by (REPEAT_FIRST (rtac lemma)); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
427 |
(*For Oops, simplification proves NBa~=NB. By Says_Server_KeyWithNonce, |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
428 |
we get (~ KeyWithNonce K NB evsa); then simplification can apply the |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
429 |
induction hypothesis with KK = {K}.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
430 |
by (ALLGOALS (*22 seconds*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
431 |
(asm_simp_tac |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
432 |
(analz_image_freshK_ss addsimps |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
433 |
([all_conj_distrib, not_parts_not_analz, analz_image_freshK, |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
434 |
KeyWithNonce_Says, fresh_not_KeyWithNonce, |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
435 |
imp_disj_not1, (*Moves NBa~=NB to the front*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
436 |
Says_Server_KeyWithNonce] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
437 |
@ pushes)))); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
438 |
(*Base*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
439 |
by (Blast_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
440 |
(*Fake*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
441 |
by (spy_analz_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
442 |
(*YM4*) (** LEVEL 7 **) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
443 |
by (not_lost_tac "A" 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
444 |
by (dtac (Says_imp_sees_Spy' RS parts.Inj RS parts.Fst RS A_trusts_YM3) 1 |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
445 |
THEN REPEAT (assume_tac 1)); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
446 |
by (blast_tac (!claset addIs [KeyWithNonceI]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
447 |
qed_spec_mp "Nonce_secrecy"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
448 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
449 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
450 |
(*Version required below: if NB can be decrypted using a session key then it |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
451 |
was distributed with that key. The more general form above is required |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
452 |
for the induction to carry through.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
453 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
454 |
"!!evs. [| Says Server A \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
455 |
\ {|Crypt (shrK A) {|Agent B, Key KAB, na, Nonce NB'|}, X|} \ |
3465 | 456 |
\ : set evs; \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
457 |
\ NB ~= NB'; KAB ~: range shrK; evs : yahalom lost |] \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
458 |
\ ==> (Nonce NB : analz (insert (Key KAB) (sees lost Spy evs))) = \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
459 |
\ (Nonce NB : analz (sees lost Spy evs))"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
460 |
by (asm_simp_tac (analz_image_freshK_ss addsimps |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
461 |
[Nonce_secrecy, Says_Server_KeyWithNonce]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
462 |
qed "single_Nonce_secrecy"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
463 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
464 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
465 |
(*** The Nonce NB uniquely identifies B's message. ***) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
466 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
467 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
468 |
"!!evs. evs : yahalom lost ==> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
469 |
\ 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
|
470 |
\ Crypt (shrK B) {|Agent A, Nonce NA, NB|} : parts(sees lost Spy evs) \ |
2133 | 471 |
\ --> B ~: lost --> NA = NA' & A = A' & B = B'"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
472 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
473 |
(*Fake*) |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
474 |
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
|
475 |
THEN Fake_parts_insert_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
476 |
by (asm_simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
2133 | 477 |
(*YM2: creation of new Nonce. Move assertion into global context*) |
478 |
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
|
479 |
by (REPEAT (resolve_tac [exI, conjI, impI, refl] 1)); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
480 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1); |
2133 | 481 |
val lemma = result(); |
482 |
||
2110 | 483 |
goal thy |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
484 |
"!!evs.[| Crypt (shrK B) {|Agent A, Nonce NA, NB|} \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
485 |
\ : parts (sees lost Spy evs); \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
486 |
\ Crypt (shrK B') {|Agent A', Nonce NA', NB|} \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
487 |
\ : parts (sees lost Spy evs); \ |
2133 | 488 |
\ evs : yahalom lost; B ~: lost; B' ~: lost |] \ |
489 |
\ ==> NA' = NA & A' = A & B' = B"; |
|
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2377
diff
changeset
|
490 |
by (prove_unique_tac lemma 1); |
2133 | 491 |
qed "unique_NB"; |
492 |
||
493 |
||
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
494 |
(*Variant useful for proving secrecy of NB: the Says... form allows |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
495 |
not_lost_tac to remove the assumption B' ~: lost.*) |
2133 | 496 |
goal thy |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
497 |
"!!evs.[| Says C D {|X, Crypt (shrK B) {|Agent A, Nonce NA, NB|}|} \ |
3465 | 498 |
\ : set evs; B ~: lost; \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
499 |
\ Says C' D' {|X', Crypt (shrK B') {|Agent A', Nonce NA', NB|}|} \ |
3465 | 500 |
\ : set evs; \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
501 |
\ NB ~: analz (sees lost Spy evs); evs : yahalom lost |] \ |
2133 | 502 |
\ ==> NA' = NA & A' = A & B' = B"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
503 |
by (not_lost_tac "B'" 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
504 |
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
|
505 |
addSEs [MPair_parts] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
506 |
addDs [unique_NB]) 1); |
2133 | 507 |
qed "Says_unique_NB"; |
508 |
||
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
509 |
val Says_unique_NB' = read_instantiate [("lost","lost")] Says_unique_NB; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
510 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
511 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
512 |
(** A nonce value is never used both as NA and as NB **) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
513 |
|
2133 | 514 |
goal thy |
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
515 |
"!!evs. [| B ~: lost; evs : yahalom lost |] \ |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
516 |
\ ==> Nonce NB ~: analz (sees lost Spy evs) --> \ |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
517 |
\ Crypt (shrK B') {|Agent A', Nonce NB, NB'|} \ |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
518 |
\ : parts(sees lost Spy evs) \ |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
519 |
\ --> Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|} \ |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
520 |
\ ~: parts(sees lost Spy evs)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
521 |
by analz_mono_parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
522 |
by (Fake_parts_insert_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
523 |
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
|
524 |
addSIs [parts_insertI] |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
525 |
addSEs partsEs) 1); |
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
526 |
bind_thm ("no_nonce_YM1_YM2", result() RS mp RSN (2,rev_mp) RSN (2,rev_notE)); |
2133 | 527 |
|
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
528 |
(*The Server sends YM3 only in response to YM2.*) |
2133 | 529 |
goal thy |
530 |
"!!evs. [| Says Server A \ |
|
3465 | 531 |
\ {|Crypt (shrK A) {|Agent B, k, na, nb|}, X|} : set evs; \ |
2133 | 532 |
\ evs : yahalom lost |] \ |
533 |
\ ==> EX B'. Says B' Server \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
534 |
\ {| Agent B, Crypt (shrK B) {|Agent A, na, nb|} |} \ |
3465 | 535 |
\ : set evs"; |
2133 | 536 |
by (etac rev_mp 1); |
537 |
by (etac yahalom.induct 1); |
|
538 |
by (ALLGOALS Asm_simp_tac); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
539 |
by (ALLGOALS Blast_tac); |
2133 | 540 |
qed "Says_Server_imp_YM2"; |
541 |
||
542 |
||
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
543 |
(*A vital theorem for B, that nonce NB remains secure from the Spy. |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
544 |
Unusually, the Fake case requires Spy:lost.*) |
2133 | 545 |
goal thy |
546 |
"!!evs. [| A ~: lost; B ~: lost; Spy: lost; evs : yahalom lost |] \ |
|
547 |
\ ==> Says B Server \ |
|
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2269
diff
changeset
|
548 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
3465 | 549 |
\ : set evs --> \ |
550 |
\ (ALL k. Says A Spy {|Nonce NA, Nonce NB, k|} ~: set evs) --> \ |
|
2133 | 551 |
\ Nonce NB ~: analz (sees lost Spy evs)"; |
552 |
by (etac yahalom.induct 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
553 |
by analz_sees_tac; |
2133 | 554 |
by (ALLGOALS |
555 |
(asm_simp_tac |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
556 |
(!simpset addsimps ([analz_insert_eq, not_parts_not_analz, |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2454
diff
changeset
|
557 |
analz_insert_freshK] @ pushes) |
2133 | 558 |
setloop split_tac [expand_if]))); |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
559 |
(*Prove YM3 by showing that no NB can also be an NA*) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
560 |
by (blast_tac (!claset addDs [Says_imp_sees_Spy' RS parts.Inj] |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
561 |
addSEs [MPair_parts] |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
562 |
addDs [no_nonce_YM1_YM2, Says_unique_NB']) 4 |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
563 |
THEN flexflex_tac); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
564 |
(*YM2: similar freshness reasoning*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
565 |
by (blast_tac (!claset addSEs partsEs |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
566 |
addDs [Says_imp_sees_Spy' RS analz.Inj, |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
567 |
impOfSubs analz_subset_parts]) 3); |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
568 |
(*YM1: NB=NA is impossible anyway, but NA is secret because it is fresh!*) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
569 |
by (blast_tac (!claset addSIs [parts_insertI] |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3444
diff
changeset
|
570 |
addSEs sees_Spy_partsEs) 2); |
2377 | 571 |
(*Fake*) |
572 |
by (spy_analz_tac 1); |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
573 |
(** LEVEL 7: YM4 and Oops remain **) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
574 |
(*YM4: key K is visible to Spy, contradicting session key secrecy theorem*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
575 |
by (REPEAT (Safe_step_tac 1)); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
576 |
by (not_lost_tac "Aa" 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
577 |
by (dtac (Says_imp_sees_Spy' RS parts.Inj RS parts.Fst RS A_trusts_YM3) 1); |
2133 | 578 |
by (forward_tac [Says_Server_message_form] 3); |
579 |
by (forward_tac [Says_Server_imp_YM2] 4); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
580 |
by (REPEAT_FIRST (eresolve_tac [asm_rl, bexE, exE, disjE])); |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
581 |
(* use Says_unique_NB' to identify message components: Aa=A, Ba=B, NAa=NA *) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
582 |
by (blast_tac (!claset addDs [Says_unique_NB', Spy_not_see_encrypted_key, |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
583 |
impOfSubs Fake_analz_insert]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
584 |
(** LEVEL 14 **) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
585 |
(*Oops case: if the nonce is betrayed now, show that the Oops event is |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
586 |
covered by the quantified Oops assumption.*) |
2133 | 587 |
by (full_simp_tac (!simpset addsimps [all_conj_distrib]) 1); |
588 |
by (step_tac (!claset delrules [disjE, conjI]) 1); |
|
589 |
by (forward_tac [Says_Server_imp_YM2] 1 THEN assume_tac 1 THEN etac exE 1); |
|
590 |
by (expand_case_tac "NB = NBa" 1); |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
591 |
(*If NB=NBa then all other components of the Oops message agree*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
592 |
by (blast_tac (!claset addDs [Says_unique_NB']) 1 THEN flexflex_tac); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
593 |
(*case NB ~= NBa*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
594 |
by (asm_simp_tac (!simpset addsimps [single_Nonce_secrecy]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
595 |
by (blast_tac (!claset addSEs [MPair_parts] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
596 |
addDs [Says_imp_sees_Spy' RS parts.Inj, |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
597 |
no_nonce_YM1_YM2 (*to prove NB~=NAa*) ]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
598 |
bind_thm ("Spy_not_see_NB", result() RSN(2,rev_mp) RSN(2,rev_mp)); |
2133 | 599 |
|
2001 | 600 |
|
3464
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
601 |
(*B's session key guarantee from YM4. The two certificates contribute to a |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
602 |
single conclusion about the Server's message. Note that the "Says A Spy" |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
603 |
assumption must quantify over ALL POSSIBLE keys instead of our particular K. |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
604 |
If this run is broken and the spy substitutes a certificate containing an |
315694e22856
Trivial changes in connection with the Yahalom paper.
paulson
parents:
3450
diff
changeset
|
605 |
old key, B has no means of telling.*) |
2001 | 606 |
goal thy |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
607 |
"!!evs. [| Says B Server \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
608 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
3465 | 609 |
\ : set evs; \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
610 |
\ Says A' B {|Crypt (shrK B) {|Agent A, Key K|}, \ |
3465 | 611 |
\ Crypt K (Nonce NB)|} : set evs; \ |
612 |
\ ALL k. Says A Spy {|Nonce NA, Nonce NB, k|} ~: set evs; \ |
|
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
613 |
\ A ~: lost; B ~: lost; Spy: lost; evs : yahalom lost |] \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
614 |
\ ==> Says Server A \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
615 |
\ {|Crypt (shrK A) {|Agent B, Key K, \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
616 |
\ Nonce NA, Nonce NB|}, \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
617 |
\ Crypt (shrK B) {|Agent A, Key K|}|} \ |
3465 | 618 |
\ : set evs"; |
2133 | 619 |
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
|
620 |
by (etac (Says_imp_sees_Spy' RS parts.Inj RS MPair_parts) 1 THEN |
2133 | 621 |
dtac B_trusts_YM4_shrK 1); |
2170 | 622 |
by (dtac B_trusts_YM4_newK 3); |
2110 | 623 |
by (REPEAT_FIRST (eresolve_tac [asm_rl, exE])); |
2133 | 624 |
by (forward_tac [Says_Server_imp_YM2] 1 THEN assume_tac 1); |
2170 | 625 |
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
|
626 |
by (blast_tac (!claset addDs [Says_unique_NB']) 1); |
2322 | 627 |
qed "B_trusts_YM4"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
628 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
629 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
630 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
631 |
(*** Authenticating B to A ***) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
632 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
633 |
(*The encryption in message YM2 tells us it cannot be faked.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
634 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
635 |
"!!evs. evs : yahalom lost \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
636 |
\ ==> Crypt (shrK B) {|Agent A, Nonce NA, nb|} \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
637 |
\ : parts (sees lost Spy evs) --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
638 |
\ B ~: lost --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
639 |
\ Says B Server {|Agent B, \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
640 |
\ Crypt (shrK B) {|Agent A, Nonce NA, nb|}|} \ |
3465 | 641 |
\ : set evs"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
642 |
by parts_induct_tac; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
643 |
by (Fake_parts_insert_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
644 |
bind_thm ("B_Said_YM2", result() RSN (2, rev_mp) RS mp); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
645 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
646 |
(*If the server sends YM3 then B sent YM2*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
647 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
648 |
"!!evs. evs : yahalom lost \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
649 |
\ ==> Says Server A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, nb|}, X|} \ |
3465 | 650 |
\ : set evs --> \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
651 |
\ B ~: lost --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
652 |
\ Says B Server {|Agent B, \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
653 |
\ Crypt (shrK B) {|Agent A, Nonce NA, nb|}|} \ |
3465 | 654 |
\ : set evs"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
655 |
by (etac yahalom.induct 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
656 |
by (ALLGOALS Asm_simp_tac); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
657 |
(*YM4*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
658 |
by (Blast_tac 2); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
659 |
(*YM3*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
660 |
by (best_tac (!claset addSDs [B_Said_YM2, Says_imp_sees_Spy' RS parts.Inj] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
661 |
addSEs [MPair_parts]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
662 |
val lemma = result() RSN (2, rev_mp) RS mp |> standard; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
663 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
664 |
(*If A receives YM3 then B has used nonce NA (and therefore is alive)*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
665 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
666 |
"!!evs. [| Says S A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, nb|}, X|} \ |
3465 | 667 |
\ : set evs; \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
668 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
669 |
\ ==> Says B Server {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|} \ |
3465 | 670 |
\ : set evs"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
671 |
by (blast_tac (!claset addSDs [A_trusts_YM3, lemma] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
672 |
addEs sees_Spy_partsEs) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
673 |
qed "YM3_auth_B_to_A"; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
674 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
675 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
676 |
(*** Authenticating A to B using the certificate Crypt K (Nonce NB) ***) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
677 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
678 |
(*Induction for theorems of the form X ~: analz (sees lost Spy evs) --> ... |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
679 |
It simplifies the proof by discarding needless information about |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
680 |
analz (insert X (sees lost Spy evs)) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
681 |
*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
682 |
val analz_mono_parts_induct_tac = |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
683 |
etac yahalom.induct 1 |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
684 |
THEN |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
685 |
REPEAT_FIRST |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
686 |
(rtac impI THEN' |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
687 |
dtac (sees_subset_sees_Says RS analz_mono RS contra_subsetD) THEN' |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
688 |
mp_tac) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
689 |
THEN parts_sees_tac; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
690 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
691 |
(*Assuming the session key is secure, if both certificates are present then |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
692 |
A has said NB. We can't be sure about the rest of A's message, but only |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
693 |
NB matters for freshness.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
694 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
695 |
"!!evs. evs : yahalom lost \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
696 |
\ ==> Key K ~: analz (sees lost Spy evs) --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
697 |
\ Crypt K (Nonce NB) : parts (sees lost Spy evs) --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
698 |
\ Crypt (shrK B) {|Agent A, Key K|} \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
699 |
\ : parts (sees lost Spy evs) --> \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
700 |
\ B ~: lost --> \ |
3465 | 701 |
\ (EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs)"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
702 |
by analz_mono_parts_induct_tac; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
703 |
(*Fake*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
704 |
by (Fake_parts_insert_tac 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
705 |
(*YM3: by new_keys_not_used we note that Crypt K (Nonce NB) could not exist*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
706 |
by (fast_tac (!claset addSDs [Crypt_imp_invKey_keysFor] addss (!simpset)) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
707 |
(*YM4: was Crypt K (Nonce NB) the very last message? If not, use ind. hyp.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
708 |
by (asm_simp_tac (!simpset addsimps [ex_disj_distrib]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
709 |
(*yes: apply unicity of session keys*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
710 |
by (not_lost_tac "Aa" 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
711 |
by (blast_tac (!claset addSEs [MPair_parts] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
712 |
addSDs [A_trusts_YM3, B_trusts_YM4_shrK] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
713 |
addDs [Says_imp_sees_Spy' RS parts.Inj, |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
714 |
unique_session_keys]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
715 |
val lemma = normalize_thm [RSspec, RSmp] (result()) |> standard; |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
716 |
|
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
717 |
(*If B receives YM4 then A has used nonce NB (and therefore is alive). |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
718 |
Moreover, A associates K with NB (thus is talking about the same run). |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
719 |
Other premises guarantee secrecy of K.*) |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
720 |
goal thy |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
721 |
"!!evs. [| Says B Server \ |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
722 |
\ {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|} \ |
3465 | 723 |
\ : set evs; \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
724 |
\ Says A' B {|Crypt (shrK B) {|Agent A, Key K|}, \ |
3465 | 725 |
\ Crypt K (Nonce NB)|} : set evs; \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
726 |
\ (ALL NA k. Says A Spy {|Nonce NA, Nonce NB, k|} \ |
3465 | 727 |
\ ~: set evs); \ |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
728 |
\ A ~: lost; B ~: lost; Spy: lost; evs : yahalom lost |] \ |
3465 | 729 |
\ ==> EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs"; |
3444
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
730 |
by (dtac B_trusts_YM4 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
731 |
by (REPEAT_FIRST (eresolve_tac [asm_rl, spec])); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
732 |
by (etac (Says_imp_sees_Spy' RS parts.Inj RS MPair_parts) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
733 |
by (rtac lemma 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
734 |
by (rtac Spy_not_see_encrypted_key 2); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
735 |
by (REPEAT_FIRST assume_tac); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
736 |
by (blast_tac (!claset addSEs [MPair_parts] |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
737 |
addDs [Says_imp_sees_Spy' RS parts.Inj]) 1); |
919de2cb3487
Streamlined proofs of the secrecy of NB and added authentication of A and B
paulson
parents:
3432
diff
changeset
|
738 |
qed_spec_mp "YM4_imp_A_Said_YM3"; |