author | nipkow |
Fri, 17 Oct 1997 15:25:12 +0200 | |
changeset 3919 | c036caebfc75 |
parent 3908 | 4f19a40a9343 |
child 3961 | 6a8996fb7d99 |
permissions | -rw-r--r-- |
2320 | 1 |
(* Title: HOL/Auth/Shared |
1934 | 2 |
ID: $Id$ |
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
4 |
Copyright 1996 University of Cambridge |
|
5 |
||
6 |
Theory of Shared Keys (common to all symmetric-key protocols) |
|
7 |
||
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8 |
Shared, long-term keys; initial states of agents |
2032 | 9 |
*) |
10 |
||
1934 | 11 |
|
12 |
open Shared; |
|
13 |
||
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|
14 |
(*** Basic properties of shrK ***) |
1934 | 15 |
|
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16 |
(*Injectiveness: Agents' long-term keys are distinct.*) |
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|
17 |
AddIffs [inj_shrK RS inj_eq]; |
2376
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Temporary additions (random) for the nested Otway-Rees protocol
paulson
parents:
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|
18 |
|
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|
19 |
(* invKey(shrK A) = shrK A *) |
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|
20 |
Addsimps [rewrite_rule [isSymKey_def] isSym_keys]; |
2320 | 21 |
|
1934 | 22 |
(** Rewrites should not refer to initState(Friend i) |
23 |
-- not in normal form! **) |
|
24 |
||
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25 |
goalw thy [keysFor_def] "keysFor (parts (initState C)) = {}"; |
3667 | 26 |
by (induct_tac "C" 1); |
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|
27 |
by (Auto_tac ()); |
1934 | 28 |
qed "keysFor_parts_initState"; |
29 |
Addsimps [keysFor_parts_initState]; |
|
30 |
||
2032 | 31 |
|
3683 | 32 |
(*** Function "spies" ***) |
1934 | 33 |
|
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34 |
(*Spy sees shared keys of agents!*) |
3683 | 35 |
goal thy "!!A. A: bad ==> Key (shrK A) : spies evs"; |
3667 | 36 |
by (induct_tac "evs" 1); |
3683 | 37 |
by (ALLGOALS (asm_simp_tac |
38 |
(!simpset addsimps [imageI, spies_Cons] |
|
3919 | 39 |
addsplits [expand_event_case, expand_if]))); |
3683 | 40 |
qed "Spy_spies_bad"; |
1934 | 41 |
|
3683 | 42 |
AddSIs [Spy_spies_bad]; |
2032 | 43 |
|
3683 | 44 |
(*For not_bad_tac*) |
45 |
goal thy "!!A. [| Crypt (shrK A) X : analz (spies evs); A: bad |] \ |
|
46 |
\ ==> X : analz (spies evs)"; |
|
3443 | 47 |
by (fast_tac (!claset addSDs [analz.Decrypt] addss (!simpset)) 1); |
3683 | 48 |
qed "Crypt_Spy_analz_bad"; |
2072 | 49 |
|
3443 | 50 |
(*Prove that the agent is uncompromised by the confidentiality of |
51 |
a component of a message she's said.*) |
|
3683 | 52 |
fun not_bad_tac s = |
53 |
case_tac ("(" ^ s ^ ") : bad") THEN' |
|
3443 | 54 |
SELECT_GOAL |
3683 | 55 |
(REPEAT_DETERM (dtac (Says_imp_spies RS analz.Inj) 1) THEN |
3443 | 56 |
REPEAT_DETERM (etac MPair_analz 1) THEN |
57 |
THEN_BEST_FIRST |
|
3683 | 58 |
(dres_inst_tac [("A", s)] Crypt_Spy_analz_bad 1 THEN assume_tac 1) |
3443 | 59 |
(has_fewer_prems 1, size_of_thm) |
60 |
(Step_tac 1)); |
|
1934 | 61 |
|
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|
62 |
|
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|
63 |
(** Fresh keys never clash with long-term shared keys **) |
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64 |
|
3683 | 65 |
(*Agents see their own shared keys!*) |
66 |
goal thy "Key (shrK A) : initState A"; |
|
67 |
by (induct_tac "A" 1); |
|
68 |
by (Auto_tac()); |
|
69 |
qed "shrK_in_initState"; |
|
70 |
AddIffs [shrK_in_initState]; |
|
71 |
||
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|
72 |
goal thy "Key (shrK A) : used evs"; |
3683 | 73 |
br initState_into_used 1; |
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74 |
by (Blast_tac 1); |
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|
75 |
qed "shrK_in_used"; |
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|
76 |
AddIffs [shrK_in_used]; |
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|
77 |
|
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|
78 |
(*Used in parts_induct_tac and analz_Fake_tac to distinguish session keys |
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|
79 |
from long-term shared keys*) |
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|
80 |
goal thy "!!K. Key K ~: used evs ==> K ~: range shrK"; |
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|
81 |
by (Blast_tac 1); |
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|
82 |
qed "Key_not_used"; |
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|
83 |
|
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|
84 |
(*A session key cannot clash with a long-term shared key*) |
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|
85 |
goal thy "!!K. K ~: range shrK ==> shrK B ~= K"; |
2891 | 86 |
by (Blast_tac 1); |
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|
87 |
qed "shrK_neq"; |
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|
88 |
|
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|
89 |
Addsimps [Key_not_used, shrK_neq, shrK_neq RS not_sym]; |
3908
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Removed image_eqI from simpset because of clash with neq_shrK.
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|
90 |
Delsimps [image_eqI]; (* loops together with shrK_neq *) |
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|
91 |
|
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|
92 |
(*** Fresh nonces ***) |
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|
93 |
|
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|
94 |
goal thy "Nonce N ~: parts (initState B)"; |
3667 | 95 |
by (induct_tac "B" 1); |
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|
96 |
by (Auto_tac ()); |
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|
97 |
qed "Nonce_notin_initState"; |
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|
98 |
AddIffs [Nonce_notin_initState]; |
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|
99 |
|
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|
100 |
goal thy "Nonce N ~: used []"; |
3683 | 101 |
by (simp_tac (!simpset addsimps [used_Nil]) 1); |
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|
102 |
qed "Nonce_notin_used_empty"; |
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|
103 |
Addsimps [Nonce_notin_used_empty]; |
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|
104 |
|
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|
105 |
|
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|
106 |
(*** Supply fresh nonces for possibility theorems. ***) |
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|
107 |
|
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|
108 |
(*In any trace, there is an upper bound N on the greatest nonce in use.*) |
3683 | 109 |
goal thy "EX N. ALL n. N<=n --> Nonce n ~: used evs"; |
3667 | 110 |
by (induct_tac "evs" 1); |
2516
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|
111 |
by (res_inst_tac [("x","0")] exI 1); |
3683 | 112 |
by (ALLGOALS (asm_simp_tac |
113 |
(!simpset addsimps [used_Cons] |
|
3919 | 114 |
addsplits [expand_event_case, expand_if]))); |
3730 | 115 |
by Safe_tac; |
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|
116 |
by (ALLGOALS (rtac (msg_Nonce_supply RS exE))); |
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|
117 |
by (ALLGOALS (blast_tac (!claset addSEs [add_leE]))); |
2516
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118 |
val lemma = result(); |
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|
119 |
|
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|
120 |
goal thy "EX N. Nonce N ~: used evs"; |
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|
121 |
by (rtac (lemma RS exE) 1); |
2891 | 122 |
by (Blast_tac 1); |
2516
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|
123 |
qed "Nonce_supply1"; |
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|
124 |
|
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|
125 |
goal thy "EX N N'. Nonce N ~: used evs & Nonce N' ~: used evs' & N ~= N'"; |
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|
126 |
by (cut_inst_tac [("evs","evs")] lemma 1); |
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|
127 |
by (cut_inst_tac [("evs","evs'")] lemma 1); |
3708 | 128 |
by (Clarify_tac 1); |
2516
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|
129 |
by (res_inst_tac [("x","N")] exI 1); |
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|
130 |
by (res_inst_tac [("x","Suc (N+Na)")] exI 1); |
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|
131 |
by (asm_simp_tac (!simpset addsimps [less_not_refl2 RS not_sym, |
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|
132 |
le_add2, le_add1, |
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|
133 |
le_eq_less_Suc RS sym]) 1); |
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|
134 |
qed "Nonce_supply2"; |
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|
135 |
|
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|
136 |
goal thy "EX N N' N''. Nonce N ~: used evs & Nonce N' ~: used evs' & \ |
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|
137 |
\ Nonce N'' ~: used evs'' & N ~= N' & N' ~= N'' & N ~= N''"; |
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|
138 |
by (cut_inst_tac [("evs","evs")] lemma 1); |
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|
139 |
by (cut_inst_tac [("evs","evs'")] lemma 1); |
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|
140 |
by (cut_inst_tac [("evs","evs''")] lemma 1); |
3708 | 141 |
by (Clarify_tac 1); |
2516
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|
142 |
by (res_inst_tac [("x","N")] exI 1); |
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|
143 |
by (res_inst_tac [("x","Suc (N+Na)")] exI 1); |
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|
144 |
by (res_inst_tac [("x","Suc (Suc (N+Na+Nb))")] exI 1); |
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|
145 |
by (asm_simp_tac (!simpset addsimps [less_not_refl2 RS not_sym, |
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|
146 |
le_add2, le_add1, |
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|
147 |
le_eq_less_Suc RS sym]) 1); |
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|
148 |
by (rtac (less_trans RS less_not_refl2 RS not_sym) 1); |
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|
149 |
by (stac (le_eq_less_Suc RS sym) 1); |
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|
150 |
by (asm_simp_tac (!simpset addsimps [le_eq_less_Suc RS sym]) 2); |
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|
151 |
by (REPEAT (rtac le_add1 1)); |
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|
152 |
qed "Nonce_supply3"; |
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|
153 |
|
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|
154 |
goal thy "Nonce (@ N. Nonce N ~: used evs) ~: used evs"; |
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|
155 |
by (rtac (lemma RS exE) 1); |
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|
156 |
by (rtac selectI 1); |
2891 | 157 |
by (Blast_tac 1); |
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|
158 |
qed "Nonce_supply"; |
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|
159 |
|
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|
160 |
(*** Supply fresh keys for possibility theorems. ***) |
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|
161 |
|
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|
162 |
goal thy "EX K. Key K ~: used evs"; |
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Modified a few defs and proofs because of the changes to theory Finite.thy.
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|
163 |
by (rtac (Finites.emptyI RS Key_supply_ax RS exE) 1); |
2891 | 164 |
by (Blast_tac 1); |
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|
165 |
qed "Key_supply1"; |
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|
166 |
|
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|
167 |
goal thy "EX K K'. Key K ~: used evs & Key K' ~: used evs' & K ~= K'"; |
3414
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Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
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|
168 |
by (cut_inst_tac [("evs","evs")] (Finites.emptyI RS Key_supply_ax) 1); |
2516
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|
169 |
by (etac exE 1); |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
170 |
by (cut_inst_tac [("evs","evs'")] |
3414
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Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
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changeset
|
171 |
(Finites.emptyI RS Finites.insertI RS Key_supply_ax) 1); |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
172 |
by (Auto_tac()); |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
173 |
qed "Key_supply2"; |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
174 |
|
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
175 |
goal thy "EX K K' K''. Key K ~: used evs & Key K' ~: used evs' & \ |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
176 |
\ Key K'' ~: used evs'' & K ~= K' & K' ~= K'' & K ~= K''"; |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
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changeset
|
177 |
by (cut_inst_tac [("evs","evs")] (Finites.emptyI RS Key_supply_ax) 1); |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
178 |
by (etac exE 1); |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
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changeset
|
179 |
by (cut_inst_tac [("evs","evs'")] |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
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changeset
|
180 |
(Finites.emptyI RS Finites.insertI RS Key_supply_ax) 1); |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
181 |
by (etac exE 1); |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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changeset
|
182 |
by (cut_inst_tac [("evs","evs''")] |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
183 |
(Finites.emptyI RS Finites.insertI RS Finites.insertI RS Key_supply_ax) 1); |
3708 | 184 |
by (Clarify_tac 1); |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
185 |
by (Full_simp_tac 1); |
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
186 |
by (fast_tac (!claset addSEs [allE]) 1); |
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|
187 |
qed "Key_supply3"; |
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|
188 |
|
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
189 |
goal thy "Key (@ K. Key K ~: used evs) ~: used evs"; |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
190 |
by (rtac (Finites.emptyI RS Key_supply_ax RS exE) 1); |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
191 |
by (rtac selectI 1); |
2891 | 192 |
by (Blast_tac 1); |
2516
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
193 |
qed "Key_supply"; |
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|
194 |
|
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Now with Andy Gordon's treatment of freshness to replace newN/K
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|
195 |
(*** Tactics for possibility theorems ***) |
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|
196 |
|
3673
3b06747c3f37
Having "addcongs [if_weak_cong]" in analz_image_..._ss makes simplification
paulson
parents:
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|
197 |
(*Omitting used_Says makes the tactic much faster: it leaves expressions |
3b06747c3f37
Having "addcongs [if_weak_cong]" in analz_image_..._ss makes simplification
paulson
parents:
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changeset
|
198 |
such as Nonce ?N ~: used evs that match Nonce_supply*) |
3542
db5e9aceea49
Now possibility_tac and basic_possibility_tac are explicit functions, in order
paulson
parents:
3519
diff
changeset
|
199 |
fun possibility_tac st = st |> |
3673
3b06747c3f37
Having "addcongs [if_weak_cong]" in analz_image_..._ss makes simplification
paulson
parents:
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|
200 |
(REPEAT |
3512
9dcb4daa15e8
Moving common declarations and proofs from theories "Shared"
paulson
parents:
3479
diff
changeset
|
201 |
(ALLGOALS (simp_tac (!simpset delsimps [used_Says] setSolver safe_solver)) |
2516
4d68fbe6378b
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|
202 |
THEN |
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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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|
203 |
REPEAT_FIRST (eq_assume_tac ORELSE' |
3542
db5e9aceea49
Now possibility_tac and basic_possibility_tac are explicit functions, in order
paulson
parents:
3519
diff
changeset
|
204 |
resolve_tac [refl, conjI, Nonce_supply, Key_supply]))); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
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changeset
|
205 |
|
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
206 |
(*For harder protocols (such as Recur) where we have to set up some |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
207 |
nonces and keys initially*) |
3542
db5e9aceea49
Now possibility_tac and basic_possibility_tac are explicit functions, in order
paulson
parents:
3519
diff
changeset
|
208 |
fun basic_possibility_tac st = st |> |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
209 |
REPEAT |
2637
e9b203f854ae
reflecting my recent changes of the simplifier and classical reasoner
oheimb
parents:
2516
diff
changeset
|
210 |
(ALLGOALS (asm_simp_tac (!simpset setSolver safe_solver)) |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
211 |
THEN |
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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
|
212 |
REPEAT_FIRST (resolve_tac [refl, conjI])); |
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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
|
213 |
|
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
214 |
|
3472
fb3c38c88c08
Deleted the obsolete operators newK, newN and nPair
paulson
parents:
3465
diff
changeset
|
215 |
(*** Specialized rewriting for analz_insert_freshK ***) |
2320 | 216 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
217 |
goal thy "!!A. A <= Compl (range shrK) ==> shrK x ~: A"; |
2891 | 218 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
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parents:
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diff
changeset
|
219 |
qed "subset_Compl_range"; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
220 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
221 |
goal thy "insert (Key K) H = Key `` {K} Un H"; |
2891 | 222 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
223 |
qed "insert_Key_singleton"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
224 |
|
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
225 |
goal thy "insert (Key K) (Key``KK Un C) = Key `` (insert K KK) Un C"; |
2891 | 226 |
by (Blast_tac 1); |
227 |
qed "insert_Key_image"; |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
228 |
|
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3443
diff
changeset
|
229 |
(*Reverse the normal simplification of "image" to build up (not break down) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3443
diff
changeset
|
230 |
the set of keys. Use analz_insert_eq with (Un_upper2 RS analz_mono) to |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3443
diff
changeset
|
231 |
erase occurrences of forwarded message components (X).*) |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
232 |
val analz_image_freshK_ss = |
3673
3b06747c3f37
Having "addcongs [if_weak_cong]" in analz_image_..._ss makes simplification
paulson
parents:
3667
diff
changeset
|
233 |
!simpset addcongs [if_weak_cong] |
3b06747c3f37
Having "addcongs [if_weak_cong]" in analz_image_..._ss makes simplification
paulson
parents:
3667
diff
changeset
|
234 |
delsimps [image_insert, image_Un] |
3680
7588653475b2
Removed the simprule imp_disjL from the analz_image_..._ss to boost speed
paulson
parents:
3673
diff
changeset
|
235 |
delsimps [imp_disjL] (*reduces blow-up*) |
3479
2aacd6f10654
Reordered rules in analz_image_freshK_ss to improve clarity
paulson
parents:
3472
diff
changeset
|
236 |
addsimps ([image_insert RS sym, image_Un RS sym, |
2aacd6f10654
Reordered rules in analz_image_freshK_ss to improve clarity
paulson
parents:
3472
diff
changeset
|
237 |
analz_insert_eq, impOfSubs (Un_upper2 RS analz_mono), |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
238 |
insert_Key_singleton, subset_Compl_range, |
3479
2aacd6f10654
Reordered rules in analz_image_freshK_ss to improve clarity
paulson
parents:
3472
diff
changeset
|
239 |
Key_not_used, insert_Key_image, Un_assoc RS sym] |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
240 |
@disj_comms) |
3919 | 241 |
addsplits [expand_if]; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
242 |
|
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
243 |
(*Lemma for the trivial direction of the if-and-only-if*) |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
244 |
goal thy |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
245 |
"!!evs. (Key K : analz (Key``nE Un H)) --> (K : nE | Key K : analz H) ==> \ |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
246 |
\ (Key K : analz (Key``nE Un H)) = (K : nE | Key K : analz H)"; |
2922 | 247 |
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
248 |
qed "analz_image_freshK_lemma"; |