author | paulson |
Fri, 27 Jun 1997 10:47:13 +0200 | |
changeset 3466 | 30791e5a69c4 |
parent 3465 | e85c24717cad |
child 3501 | 4ab477ffb4c6 |
permissions | -rw-r--r-- |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
1 |
(* Title: HOL/Auth/Yahalom2 |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
2 |
ID: $Id$ |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
4 |
Copyright 1996 University of Cambridge |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
5 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
6 |
Inductive relation "yahalom" for the Yahalom protocol, Variant 2. |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
7 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
8 |
This version trades encryption of NB for additional explicitness in YM3. |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
9 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
10 |
From page 259 of |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
11 |
Burrows, Abadi and Needham. A Logic of Authentication. |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
12 |
Proc. Royal Soc. 426 (1989) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
13 |
*) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
14 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
15 |
open Yahalom2; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
16 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
17 |
proof_timing:=true; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
18 |
HOL_quantifiers := false; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
19 |
|
3432 | 20 |
(*Replacing the variable by a constant improves speed*) |
21 |
val Says_imp_sees_Spy' = read_instantiate [("lost","lost")] Says_imp_sees_Spy; |
|
22 |
||
23 |
||
2323 | 24 |
(*A "possibility property": there are traces that reach the end*) |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
25 |
goal thy |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
26 |
"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
27 |
\ ==> EX X NB K. EX evs: yahalom lost. \ |
3465 | 28 |
\ Says A B {|X, Crypt K (Nonce NB)|} : set evs"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
29 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
30 |
by (rtac (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
31 |
yahalom.YM4) 2); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
32 |
by possibility_tac; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
33 |
result(); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
34 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
35 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
36 |
(**** Inductive proofs about yahalom ****) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
37 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
38 |
(*Monotonicity*) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
39 |
goal thy "!!evs. lost' <= lost ==> yahalom lost' <= yahalom lost"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
40 |
by (rtac subsetI 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
41 |
by (etac yahalom.induct 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
42 |
by (REPEAT_FIRST |
3432 | 43 |
(blast_tac (!claset addIs (impOfSubs(sees_mono RS analz_mono RS synth_mono) |
44 |
:: yahalom.intrs)))); |
|
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
45 |
qed "yahalom_mono"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
46 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
47 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
48 |
(*Nobody sends themselves messages*) |
3465 | 49 |
goal thy "!!evs. evs: yahalom lost ==> ALL A X. Says A A X ~: set evs"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
50 |
by (etac yahalom.induct 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
51 |
by (Auto_tac()); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
52 |
qed_spec_mp "not_Says_to_self"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
53 |
Addsimps [not_Says_to_self]; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
54 |
AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
55 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
56 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
57 |
(** For reasoning about the encrypted portion of messages **) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
58 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
59 |
(*Lets us treat YM4 using a similar argument as for the Fake case.*) |
3465 | 60 |
goal thy "!!evs. Says S A {|NB, Crypt (shrK A) Y, X|} : set evs ==> \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
61 |
\ X : analz (sees lost Spy evs)"; |
3432 | 62 |
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS analz.Inj]) 1); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
63 |
qed "YM4_analz_sees_Spy"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
64 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
65 |
bind_thm ("YM4_parts_sees_Spy", |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
66 |
YM4_analz_sees_Spy RS (impOfSubs analz_subset_parts)); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
67 |
|
2155 | 68 |
(*Relates to both YM4 and Oops*) |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
69 |
goal thy "!!evs. Says S A {|NB, Crypt (shrK A) {|B,K,NA|}, X|} : set evs ==> \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
70 |
\ K : parts (sees lost Spy evs)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
71 |
by (blast_tac (!claset addSEs partsEs |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
72 |
addSDs [Says_imp_sees_Spy' RS parts.Inj]) 1); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
73 |
qed "YM4_Key_parts_sees_Spy"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
74 |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
75 |
(*For proving the easier theorems about X ~: parts (sees lost Spy evs). |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
76 |
We instantiate the variable to "lost" since leaving it as a Var would |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
77 |
interfere with simplification.*) |
3432 | 78 |
val parts_sees_tac = |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
79 |
forw_inst_tac [("lost","lost")] YM4_parts_sees_Spy 6 THEN |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
80 |
forw_inst_tac [("lost","lost")] YM4_Key_parts_sees_Spy 7 THEN |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
81 |
prove_simple_subgoals_tac 1; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
82 |
|
3432 | 83 |
val parts_induct_tac = |
84 |
etac yahalom.induct 1 THEN parts_sees_tac; |
|
85 |
||
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
86 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
87 |
(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
88 |
sends messages containing X! **) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
89 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
90 |
(*Spy never sees another agent's shared key! (unless it's lost at start)*) |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
91 |
goal thy |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
92 |
"!!evs. evs : yahalom lost \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
93 |
\ ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
94 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
95 |
by (Fake_parts_insert_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
96 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
97 |
qed "Spy_see_shrK"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
98 |
Addsimps [Spy_see_shrK]; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
99 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
100 |
goal thy |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
101 |
"!!evs. evs : yahalom lost \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
102 |
\ ==> (Key (shrK A) : analz (sees lost Spy evs)) = (A : lost)"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
103 |
by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset)); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
104 |
qed "Spy_analz_shrK"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
105 |
Addsimps [Spy_analz_shrK]; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
106 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
107 |
goal thy "!!A. [| Key (shrK A) : parts (sees lost Spy evs); \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
108 |
\ evs : yahalom lost |] ==> A:lost"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
109 |
by (blast_tac (!claset addDs [Spy_see_shrK]) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
110 |
qed "Spy_see_shrK_D"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
111 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
112 |
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
113 |
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D]; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
114 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
115 |
|
3432 | 116 |
(*Nobody can have used non-existent keys! Needed to apply analz_insert_Key*) |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
117 |
goal thy "!!evs. evs : yahalom lost ==> \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
118 |
\ Key K ~: used evs --> K ~: keysFor (parts (sees lost Spy evs))"; |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
119 |
by parts_induct_tac; |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
120 |
(*YM4: Key K is not fresh!*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
121 |
by (blast_tac (!claset addSEs sees_Spy_partsEs) 3); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
122 |
(*YM3*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
123 |
by (blast_tac (!claset addss (!simpset)) 2); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
124 |
(*Fake*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
125 |
by (best_tac |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
126 |
(!claset addIs [impOfSubs analz_subset_parts] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
127 |
addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
128 |
impOfSubs (parts_insert_subset_Un RS keysFor_mono)] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
129 |
addss (!simpset)) 1); |
2160 | 130 |
qed_spec_mp "new_keys_not_used"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
131 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
132 |
bind_thm ("new_keys_not_analzd", |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
133 |
[analz_subset_parts RS keysFor_mono, |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
134 |
new_keys_not_used] MRS contra_subsetD); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
135 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
136 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
137 |
|
2155 | 138 |
(*Describes the form of K when the Server sends this message. Useful for |
139 |
Oops as well as main secrecy property.*) |
|
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
140 |
goal thy |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
141 |
"!!evs. [| Says Server A {|NB', Crypt (shrK A) {|Agent B, Key K, NA|}, X|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
142 |
\ : set evs; \ |
2155 | 143 |
\ evs : yahalom lost |] \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
144 |
\ ==> K ~: range shrK & A ~= B"; |
2155 | 145 |
by (etac rev_mp 1); |
146 |
by (etac yahalom.induct 1); |
|
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
147 |
by (ALLGOALS Asm_simp_tac); |
2155 | 148 |
qed "Says_Server_message_form"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
149 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
150 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
151 |
(*For proofs involving analz. We again instantiate the variable to "lost".*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
152 |
val analz_sees_tac = |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
153 |
dres_inst_tac [("lost","lost")] YM4_analz_sees_Spy 6 THEN |
2155 | 154 |
forw_inst_tac [("lost","lost")] Says_Server_message_form 7 THEN |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
155 |
assume_tac 7 THEN |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
156 |
REPEAT ((etac conjE ORELSE' hyp_subst_tac) 7); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
157 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
158 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
159 |
(**** |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
160 |
The following is to prove theorems of the form |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
161 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
162 |
Key K : analz (insert (Key KAB) (sees lost Spy evs)) ==> |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
163 |
Key K : analz (sees lost Spy evs) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
164 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
165 |
A more general formula must be proved inductively. |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
166 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
167 |
****) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
168 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
169 |
(** Session keys are not used to encrypt other session keys **) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
170 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
171 |
goal thy |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
172 |
"!!evs. evs : yahalom lost ==> \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
173 |
\ ALL K KK. KK <= Compl (range shrK) --> \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
174 |
\ (Key K : analz (Key``KK Un (sees lost Spy evs))) = \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
175 |
\ (K : KK | Key K : analz (sees lost Spy evs))"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
176 |
by (etac yahalom.induct 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
177 |
by analz_sees_tac; |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
178 |
by (REPEAT_FIRST (resolve_tac [allI, impI])); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
179 |
by (REPEAT_FIRST (rtac analz_image_freshK_lemma )); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
180 |
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss)); |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
181 |
(*Fake*) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
182 |
by (spy_analz_tac 2); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
183 |
(*Base*) |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
184 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
185 |
qed_spec_mp "analz_image_freshK"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
186 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
187 |
goal thy |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
188 |
"!!evs. [| evs : yahalom lost; KAB ~: range shrK |] ==> \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
189 |
\ Key K : analz (insert (Key KAB) (sees lost Spy evs)) = \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
190 |
\ (K = KAB | Key K : analz (sees lost Spy evs))"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
191 |
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
192 |
qed "analz_insert_freshK"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
193 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
194 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
195 |
(*** The Key K uniquely identifies the Server's message. **) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
196 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
197 |
goal thy |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
198 |
"!!evs. evs : yahalom lost ==> \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
199 |
\ EX A' B' na' nb' X'. ALL A B na nb X. \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
200 |
\ Says Server A \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
201 |
\ {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, X|} \ |
3465 | 202 |
\ : set evs --> A=A' & B=B' & na=na' & nb=nb' & X=X'"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
203 |
by (etac yahalom.induct 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
204 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib]))); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
205 |
by (Step_tac 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
206 |
(*Remaining case: YM3*) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
207 |
by (expand_case_tac "K = ?y" 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
208 |
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2)); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
209 |
(*...we assume X is a recent message and handle this case by contradiction*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
210 |
by (blast_tac (!claset addSEs sees_Spy_partsEs |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
211 |
delrules [conjI] (*prevent split-up into 4 subgoals*) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
212 |
addss (!simpset addsimps [parts_insertI])) 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
213 |
val lemma = result(); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
214 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
215 |
goal thy |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
216 |
"!!evs. [| Says Server A \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
217 |
\ {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, X|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
218 |
\ : set evs; \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
219 |
\ Says Server A' \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
220 |
\ {|nb', Crypt (shrK A') {|Agent B', Key K, na'|}, X'|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
221 |
\ : set evs; \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
222 |
\ evs : yahalom lost |] \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
223 |
\ ==> A=A' & B=B' & na=na' & nb=nb'"; |
2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2377
diff
changeset
|
224 |
by (prove_unique_tac lemma 1); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
225 |
qed "unique_session_keys"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
226 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
227 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
228 |
(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 **) |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
229 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
230 |
goal thy |
2155 | 231 |
"!!evs. [| A ~: lost; B ~: lost; A ~= B; \ |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
232 |
\ evs : yahalom lost |] \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
233 |
\ ==> Says Server A \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
234 |
\ {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
235 |
\ Crypt (shrK B) {|nb, Key K, Agent A|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
236 |
\ : set evs --> \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
237 |
\ Says A Spy {|na, nb, Key K|} ~: set evs --> \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
238 |
\ Key K ~: analz (sees lost Spy evs)"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
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; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
241 |
by (ALLGOALS |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
242 |
(asm_simp_tac |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
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:
3432
diff
changeset
|
244 |
analz_insert_freshK] |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
245 |
setloop split_tac [expand_if]))); |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
246 |
(*Oops*) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
247 |
by (blast_tac (!claset addDs [unique_session_keys]) 3); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
248 |
(*YM3*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
249 |
by (blast_tac (!claset delrules [impCE] |
3432 | 250 |
addSEs sees_Spy_partsEs |
251 |
addIs [impOfSubs analz_subset_parts]) 2); |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
252 |
(*Fake*) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
253 |
by (spy_analz_tac 1); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
254 |
val lemma = result() RS mp RS mp RSN(2,rev_notE); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
255 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
256 |
|
3432 | 257 |
(*Final version*) |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
258 |
goal thy |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
259 |
"!!evs. [| Says Server A \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
260 |
\ {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
261 |
\ Crypt (shrK B) {|nb, Key K, Agent A|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
262 |
\ : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
263 |
\ Says A Spy {|na, nb, Key K|} ~: set evs; \ |
2155 | 264 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
265 |
\ ==> Key K ~: analz (sees lost Spy evs)"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
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); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
268 |
qed "Spy_not_see_encrypted_key"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
269 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
270 |
|
3432 | 271 |
(*And other agents don't see the key either.*) |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
272 |
goal thy |
2155 | 273 |
"!!evs. [| C ~: {A,B,Server}; \ |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
274 |
\ Says Server A \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
275 |
\ {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
276 |
\ Crypt (shrK B) {|nb, Key K, Agent A|}|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
277 |
\ : set evs; \ |
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
278 |
\ Says A Spy {|na, nb, Key K|} ~: set evs; \ |
2155 | 279 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
280 |
\ ==> Key K ~: analz (sees lost C evs)"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
281 |
by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
282 |
by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1); |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
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]))); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
285 |
qed "Agent_not_see_encrypted_key"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
286 |
|
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
287 |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
288 |
(** Security Guarantee for A upon receiving YM3 **) |
2155 | 289 |
|
3432 | 290 |
(*If the encrypted message appears then it originated with the Server. |
291 |
May now apply Spy_not_see_encrypted_key, subject to its conditions.*) |
|
2155 | 292 |
goal thy |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
293 |
"!!evs. [| Crypt (shrK A) {|Agent B, Key K, na|} \ |
2155 | 294 |
\ : parts (sees lost Spy evs); \ |
295 |
\ A ~: lost; evs : yahalom lost |] \ |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
296 |
\ ==> EX nb. Says Server A \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
297 |
\ {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
298 |
\ Crypt (shrK B) {|nb, Key K, Agent A|}|} \ |
3465 | 299 |
\ : set evs"; |
2155 | 300 |
by (etac rev_mp 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
301 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
302 |
by (Fake_parts_insert_tac 1); |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
303 |
by (Blast_tac 1); |
2323 | 304 |
qed "A_trusts_YM3"; |
2155 | 305 |
|
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
306 |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
307 |
(** Security Guarantee for B upon receiving YM4 **) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
308 |
|
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
309 |
(*B knows, by the first part of A's message, that the Server distributed |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
310 |
the key for A and B, and has associated it with NB. *) |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
311 |
goal thy |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
312 |
"!!evs. [| Crypt (shrK B) {|Nonce NB, Key K, Agent A|} \ |
2155 | 313 |
\ : parts (sees lost Spy evs); \ |
314 |
\ B ~: lost; evs : yahalom lost |] \ |
|
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
315 |
\ ==> EX NA. Says Server A \ |
2155 | 316 |
\ {|Nonce NB, \ |
2284
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
317 |
\ Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, \ |
80ebd1a213fd
Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents:
2264
diff
changeset
|
318 |
\ Crypt (shrK B) {|Nonce NB, Key K, Agent A|}|} \ |
3465 | 319 |
\ : set evs"; |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
320 |
by (etac rev_mp 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
321 |
by parts_induct_tac; |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
322 |
by (Fake_parts_insert_tac 1); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
323 |
(*YM3*) |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
324 |
by (Blast_tac 1); |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
325 |
qed "B_trusts_YM4_shrK"; |
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
326 |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
327 |
|
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
328 |
(*With this protocol variant, we don't need the 2nd part of YM4 at all: |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
329 |
Nonce NB is available in the first part.*) |
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
330 |
|
2155 | 331 |
(*What can B deduce from receipt of YM4? Stronger and simpler than Yahalom |
332 |
because we do not have to show that NB is secret. *) |
|
2111
81c8d46edfa3
New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff
changeset
|
333 |
goal thy |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
334 |
"!!evs. [| Says A' B {|Crypt (shrK B) {|Nonce NB, Key K, Agent A|}, X|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
335 |
\ : set evs; \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
336 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
337 |
\ ==> EX NA. Says Server A \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
338 |
\ {|Nonce NB, \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
339 |
\ Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
340 |
\ Crypt (shrK B) {|Nonce NB, Key K, Agent A|}|} \ |
3465 | 341 |
\ : set evs"; |
3432 | 342 |
by (etac (Says_imp_sees_Spy' RS parts.Inj RS MPair_parts) 1); |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
343 |
by (blast_tac (!claset addSDs [B_trusts_YM4_shrK]) 1); |
2323 | 344 |
qed "B_trusts_YM4"; |
3432 | 345 |
|
346 |
||
347 |
||
348 |
(*** Authenticating B to A ***) |
|
349 |
||
350 |
(*The encryption in message YM2 tells us it cannot be faked.*) |
|
351 |
goal thy |
|
352 |
"!!evs. evs : yahalom lost \ |
|
353 |
\ ==> Crypt (shrK B) {|Agent A, Nonce NA|} : parts (sees lost Spy evs) --> \ |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
354 |
\ B ~: lost --> \ |
3432 | 355 |
\ (EX NB. Says B Server {|Agent B, Nonce NB, \ |
356 |
\ Crypt (shrK B) {|Agent A, Nonce NA|}|} \ |
|
3465 | 357 |
\ : set evs)"; |
3432 | 358 |
by parts_induct_tac; |
359 |
by (Fake_parts_insert_tac 1); |
|
360 |
(*YM2*) |
|
361 |
by (Blast_tac 1); |
|
362 |
bind_thm ("B_Said_YM2", result() RSN (2, rev_mp) RS mp); |
|
363 |
||
364 |
(*If the server sends YM3 then B sent YM2, perhaps with a different NB*) |
|
365 |
goal thy |
|
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
366 |
"!!evs. evs : yahalom lost \ |
3432 | 367 |
\ ==> Says Server A {|nb, Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, X|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
368 |
\ : set evs --> \ |
3432 | 369 |
\ B ~: lost --> \ |
370 |
\ (EX nb'. Says B Server {|Agent B, nb', \ |
|
371 |
\ Crypt (shrK B) {|Agent A, Nonce NA|}|} \ |
|
3465 | 372 |
\ : set evs)"; |
3432 | 373 |
by (etac yahalom.induct 1); |
374 |
by (ALLGOALS Asm_simp_tac); |
|
375 |
(*YM3*) |
|
376 |
by (blast_tac (!claset addSDs [B_Said_YM2] |
|
377 |
addSEs [MPair_parts] |
|
378 |
addDs [Says_imp_sees_Spy' RS parts.Inj]) 3); |
|
379 |
(*Fake, YM2*) |
|
380 |
by (ALLGOALS Blast_tac); |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
381 |
val lemma = result() RSN (2, rev_mp) RS mp |> standard; |
3432 | 382 |
|
383 |
(*If A receives YM3 then B has used nonce NA (and therefore is alive)*) |
|
384 |
goal thy |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
385 |
"!!evs. [| Says S A {|nb, Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, X|} \ |
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
386 |
\ : set evs; \ |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
387 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
388 |
\ ==> EX nb'. Says B Server \ |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
389 |
\ {|Agent B, nb', Crypt (shrK B) {|Agent A, Nonce NA|}|} \ |
3465 | 390 |
\ : set evs"; |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
391 |
by (blast_tac (!claset addSDs [A_trusts_YM3, lemma] |
3432 | 392 |
addEs sees_Spy_partsEs) 1); |
393 |
qed "YM3_auth_B_to_A"; |
|
394 |
||
395 |
||
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
396 |
(*** Authenticating A to B using the certificate Crypt K (Nonce NB) ***) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
397 |
|
3432 | 398 |
(*Induction for theorems of the form X ~: analz (sees lost Spy evs) --> ... |
399 |
It simplifies the proof by discarding needless information about |
|
400 |
analz (insert X (sees lost Spy evs)) |
|
401 |
*) |
|
402 |
val analz_mono_parts_induct_tac = |
|
403 |
etac yahalom.induct 1 |
|
404 |
THEN |
|
405 |
REPEAT_FIRST |
|
406 |
(rtac impI THEN' |
|
407 |
dtac (sees_subset_sees_Says RS analz_mono RS contra_subsetD) THEN' |
|
408 |
mp_tac) |
|
409 |
THEN parts_sees_tac; |
|
410 |
||
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
411 |
(*Assuming the session key is secure, if both certificates are present then |
3432 | 412 |
A has said NB. We can't be sure about the rest of A's message, but only |
413 |
NB matters for freshness.*) |
|
414 |
goal thy |
|
415 |
"!!evs. evs : yahalom lost \ |
|
416 |
\ ==> Key K ~: analz (sees lost Spy evs) --> \ |
|
417 |
\ Crypt K (Nonce NB) : parts (sees lost Spy evs) --> \ |
|
418 |
\ Crypt (shrK B) {|Nonce NB, Key K, Agent A|} \ |
|
419 |
\ : parts (sees lost Spy evs) --> \ |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
420 |
\ B ~: lost --> \ |
3465 | 421 |
\ (EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs)"; |
3432 | 422 |
by analz_mono_parts_induct_tac; |
423 |
(*Fake*) |
|
424 |
by (Fake_parts_insert_tac 1); |
|
425 |
(*YM3: by new_keys_not_used we note that Crypt K (Nonce NB) could not exist*) |
|
426 |
by (fast_tac (!claset addSDs [Crypt_imp_invKey_keysFor] addss (!simpset)) 1); |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
427 |
(*YM4: was Crypt K (Nonce NB) the very last message? If not, use ind. hyp.*) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
428 |
by (asm_simp_tac (!simpset addsimps [ex_disj_distrib]) 1); |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
429 |
(*yes: apply unicity of session keys*) |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
430 |
by (not_lost_tac "Aa" 1); |
3432 | 431 |
by (blast_tac (!claset addSEs [MPair_parts] |
432 |
addSDs [A_trusts_YM3, B_trusts_YM4_shrK] |
|
433 |
addDs [Says_imp_sees_Spy' RS parts.Inj, |
|
434 |
unique_session_keys]) 1); |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
435 |
val lemma = normalize_thm [RSspec, RSmp] (result()) |> standard; |
3432 | 436 |
|
437 |
(*If B receives YM4 then A has used nonce NB (and therefore is alive). |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
438 |
Moreover, A associates K with NB (thus is talking about the same run). |
3432 | 439 |
Other premises guarantee secrecy of K.*) |
440 |
goal thy |
|
441 |
"!!evs. [| Says A' B {|Crypt (shrK B) {|Nonce NB, Key K, Agent A|}, \ |
|
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
442 |
\ Crypt K (Nonce NB)|} : set evs; \ |
3465 | 443 |
\ (ALL NA. Says A Spy {|Nonce NA, Nonce NB, Key K|} ~: set evs); \ |
3432 | 444 |
\ A ~: lost; B ~: lost; evs : yahalom lost |] \ |
3465 | 445 |
\ ==> EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs"; |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
446 |
by (etac (Says_imp_sees_Spy' RS parts.Inj RS MPair_parts) 1); |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
447 |
by (dtac B_trusts_YM4_shrK 1); |
3432 | 448 |
by (safe_tac (!claset)); |
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
449 |
by (rtac lemma 1); |
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
450 |
by (rtac Spy_not_see_encrypted_key 2); |
3432 | 451 |
by (REPEAT_FIRST assume_tac); |
452 |
by (ALLGOALS (blast_tac (!claset addSEs [MPair_parts] |
|
3450
cd73bc206d87
Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents:
3432
diff
changeset
|
453 |
addDs [Says_imp_sees_Spy' RS parts.Inj]))); |
3432 | 454 |
qed_spec_mp "YM4_imp_A_Said_YM3"; |