author | paulson |
Thu, 29 Mar 2001 10:44:37 +0200 | |
changeset 11230 | 756c5034f08b |
parent 11219 | c4c210e7c89c |
child 11270 | a315a3862bb4 |
permissions | -rw-r--r-- |
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1 |
(* Title: HOL/Auth/Shared |
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2 |
ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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4 |
Copyright 1996 University of Cambridge |
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5 |
|
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6 |
Theory of Shared Keys (common to all symmetric-key protocols) |
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8 |
Shared, long-term keys; initial states of agents |
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9 |
*) |
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10 |
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val inj_shrK = thm "inj_shrK"; |
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12 |
val isSym_keys = thm "isSym_keys"; |
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val Key_supply_ax = thm "Key_supply_ax"; |
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14 |
|
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(*** Basic properties of shrK ***) |
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16 |
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(*Injectiveness: Agents' long-term keys are distinct.*) |
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18 |
AddIffs [inj_shrK RS inj_eq]; |
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Goal "invKey K = K"; |
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by (cut_facts_tac [rewrite_rule [symKeys_def] isSym_keys] 1); |
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by Auto_tac; |
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qed "invKey_K"; |
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Addsimps [invKey_K]; |
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27 |
Goal "[| Crypt K X \\<in> analz H; Key K \\<in> analz H |] ==> X \\<in> analz H"; |
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28 |
by Auto_tac; |
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29 |
qed "analz_Decrypt'"; |
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30 |
AddDs [analz_Decrypt']; |
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31 |
Delrules [analz.Decrypt]; |
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32 |
||
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(** Rewrites should not refer to initState(Friend i) |
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-- not in normal form! **) |
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35 |
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Goalw [keysFor_def] "keysFor (parts (initState C)) = {}"; |
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37 |
by (induct_tac "C" 1); |
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by Auto_tac; |
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qed "keysFor_parts_initState"; |
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40 |
Addsimps [keysFor_parts_initState]; |
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41 |
|
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42 |
(*Specialized to shared-key model: no need for addss in protocol proofs*) |
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Goal "[| K: keysFor (parts (insert X H)); X : synth (analz H) |] \ |
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\ ==> K : keysFor (parts H) | Key K : parts H"; |
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by (force_tac |
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(claset() addSDs [impOfSubs (parts_insert_subset_Un RS keysFor_mono), |
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impOfSubs (analz_subset_parts RS keysFor_mono)] |
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addIs [impOfSubs analz_subset_parts], |
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simpset()) 1); |
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qed "keysFor_parts_insert"; |
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51 |
|
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Goal "Crypt K X : H ==> K : keysFor H"; |
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by (dtac Crypt_imp_invKey_keysFor 1); |
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54 |
by (Asm_full_simp_tac 1); |
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55 |
qed "Crypt_imp_keysFor"; |
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|
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57 |
|
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(*** Function "knows" ***) |
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59 |
|
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(*Spy sees shared keys of agents!*) |
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61 |
Goal "A: bad ==> Key (shrK A) : knows Spy evs"; |
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62 |
by (induct_tac "evs" 1); |
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63 |
by (ALLGOALS (asm_simp_tac |
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(simpset() addsimps [imageI, knows_Cons] |
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65 |
addsplits [expand_event_case]))); |
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qed "Spy_knows_Spy_bad"; |
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AddSIs [Spy_knows_Spy_bad]; |
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(*For case analysis on whether or not an agent is compromised*) |
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Goal "[| Crypt (shrK A) X : analz (knows Spy evs); A: bad |] \ |
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\ ==> X : analz (knows Spy evs)"; |
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by (force_tac (claset() addSDs [analz.Decrypt], simpset()) 1); |
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qed "Crypt_Spy_analz_bad"; |
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75 |
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(** Fresh keys never clash with long-term shared keys **) |
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|
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(*Agents see their own shared keys!*) |
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Goal "Key (shrK A) : initState A"; |
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by (induct_tac "A" 1); |
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81 |
by Auto_tac; |
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82 |
qed "shrK_in_initState"; |
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83 |
AddIffs [shrK_in_initState]; |
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84 |
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85 |
Goal "Key (shrK A) : used evs"; |
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by (rtac initState_into_used 1); |
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by (Blast_tac 1); |
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qed "shrK_in_used"; |
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AddIffs [shrK_in_used]; |
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|
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(*Used in parts_induct_tac and analz_Fake_tac to distinguish session keys |
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from long-term shared keys*) |
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Goal "Key K \\<notin> used evs ==> K \\<notin> range shrK"; |
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by (Blast_tac 1); |
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95 |
qed "Key_not_used"; |
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Goal "Key K \\<notin> used evs ==> shrK B \\<noteq> K"; |
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by (Blast_tac 1); |
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qed "shrK_neq"; |
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101 |
Addsimps [Key_not_used, shrK_neq, shrK_neq RS not_sym]; |
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102 |
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103 |
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104 |
(*** Fresh nonces ***) |
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105 |
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106 |
Goal "Nonce N \\<notin> parts (initState B)"; |
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107 |
by (induct_tac "B" 1); |
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108 |
by Auto_tac; |
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109 |
qed "Nonce_notin_initState"; |
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110 |
AddIffs [Nonce_notin_initState]; |
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111 |
|
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Goal "Nonce N \\<notin> used []"; |
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113 |
by (simp_tac (simpset() addsimps [used_Nil]) 1); |
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114 |
qed "Nonce_notin_used_empty"; |
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115 |
Addsimps [Nonce_notin_used_empty]; |
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116 |
|
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117 |
|
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118 |
(*** Supply fresh nonces for possibility theorems. ***) |
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119 |
|
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120 |
(*In any trace, there is an upper bound N on the greatest nonce in use.*) |
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121 |
Goal "EX N. ALL n. N<=n --> Nonce n \\<notin> used evs"; |
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122 |
by (induct_tac "evs" 1); |
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123 |
by (res_inst_tac [("x","0")] exI 1); |
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124 |
by (ALLGOALS (asm_simp_tac |
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125 |
(simpset() addsimps [used_Cons] |
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126 |
addsplits [expand_event_case]))); |
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127 |
by Safe_tac; |
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128 |
by (ALLGOALS (rtac (msg_Nonce_supply RS exE))); |
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|
129 |
by (ALLGOALS (blast_tac (claset() addSEs [add_leE]))); |
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|
130 |
val lemma = result(); |
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|
131 |
|
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|
132 |
Goal "EX N. Nonce N \\<notin> used evs"; |
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changeset
|
133 |
by (rtac (lemma RS exE) 1); |
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parents:
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changeset
|
134 |
by (Blast_tac 1); |
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changeset
|
135 |
qed "Nonce_supply1"; |
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changeset
|
136 |
|
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|
137 |
Goal "EX N N'. Nonce N \\<notin> used evs & Nonce N' \\<notin> used evs' & N \\<noteq> N'"; |
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changeset
|
138 |
by (cut_inst_tac [("evs","evs")] lemma 1); |
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parents:
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changeset
|
139 |
by (cut_inst_tac [("evs","evs'")] lemma 1); |
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parents:
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changeset
|
140 |
by (Clarify_tac 1); |
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parents:
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changeset
|
141 |
by (res_inst_tac [("x","N")] exI 1); |
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parents:
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changeset
|
142 |
by (res_inst_tac [("x","Suc (N+Na)")] exI 1); |
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parents:
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changeset
|
143 |
by (asm_simp_tac (simpset() addsimps [less_not_refl3, le_add1, le_add2, |
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parents:
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changeset
|
144 |
less_Suc_eq_le]) 1); |
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|
145 |
qed "Nonce_supply2"; |
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changeset
|
146 |
|
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|
147 |
Goal "EX N N' N''. Nonce N \\<notin> used evs & Nonce N' \\<notin> used evs' & \ |
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|
148 |
\ Nonce N'' \\<notin> used evs'' & N \\<noteq> N' & N' \\<noteq> N'' & N \\<noteq> N''"; |
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|
149 |
by (cut_inst_tac [("evs","evs")] lemma 1); |
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changeset
|
150 |
by (cut_inst_tac [("evs","evs'")] lemma 1); |
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parents:
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changeset
|
151 |
by (cut_inst_tac [("evs","evs''")] lemma 1); |
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parents:
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changeset
|
152 |
by (Clarify_tac 1); |
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parents:
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changeset
|
153 |
by (res_inst_tac [("x","N")] exI 1); |
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parents:
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changeset
|
154 |
by (res_inst_tac [("x","Suc (N+Na)")] exI 1); |
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parents:
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changeset
|
155 |
by (res_inst_tac [("x","Suc (Suc (N+Na+Nb))")] exI 1); |
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parents:
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changeset
|
156 |
by (asm_simp_tac (simpset() addsimps [less_not_refl3, le_add1, le_add2, |
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changeset
|
157 |
less_Suc_eq_le]) 1); |
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changeset
|
158 |
qed "Nonce_supply3"; |
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changeset
|
159 |
|
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|
160 |
Goal "Nonce (@ N. Nonce N \\<notin> used evs) \\<notin> used evs"; |
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changeset
|
161 |
by (rtac (lemma RS exE) 1); |
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parents:
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changeset
|
162 |
by (rtac someI 1); |
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parents:
diff
changeset
|
163 |
by (Blast_tac 1); |
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parents:
diff
changeset
|
164 |
qed "Nonce_supply"; |
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parents:
diff
changeset
|
165 |
|
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parents:
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changeset
|
166 |
(*** Supply fresh keys for possibility theorems. ***) |
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changeset
|
167 |
|
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|
168 |
Goal "EX K. Key K \\<notin> used evs"; |
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changeset
|
169 |
by (rtac (Finites.emptyI RS Key_supply_ax RS exE) 1); |
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changeset
|
170 |
by (Blast_tac 1); |
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changeset
|
171 |
qed "Key_supply1"; |
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changeset
|
172 |
|
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changeset
|
173 |
Goal "EX K K'. Key K \\<notin> used evs & Key K' \\<notin> used evs' & K \\<noteq> K'"; |
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parents:
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changeset
|
174 |
by (cut_inst_tac [("evs","evs")] (Finites.emptyI RS Key_supply_ax) 1); |
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parents:
diff
changeset
|
175 |
by (etac exE 1); |
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parents:
diff
changeset
|
176 |
by (cut_inst_tac [("evs","evs'")] |
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parents:
diff
changeset
|
177 |
(Finites.emptyI RS Finites.insertI RS Key_supply_ax) 1); |
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parents:
diff
changeset
|
178 |
by (Asm_full_simp_tac 1 THEN depth_tac (claset()) 2 1); (* replaces Auto_tac *) |
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parents:
diff
changeset
|
179 |
qed "Key_supply2"; |
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parents:
diff
changeset
|
180 |
|
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changeset
|
181 |
Goal "EX K K' K''. Key K \\<notin> used evs & Key K' \\<notin> used evs' & \ |
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changeset
|
182 |
\ Key K'' \\<notin> used evs'' & K \\<noteq> K' & K' \\<noteq> K'' & K \\<noteq> K''"; |
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parents:
diff
changeset
|
183 |
by (cut_inst_tac [("evs","evs")] (Finites.emptyI RS Key_supply_ax) 1); |
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paulson
parents:
diff
changeset
|
184 |
by (etac exE 1); |
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parents:
diff
changeset
|
185 |
(*Blast_tac requires instantiation of the keys for some reason*) |
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parents:
diff
changeset
|
186 |
by (cut_inst_tac [("evs","evs'"), ("a1","K")] |
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parents:
diff
changeset
|
187 |
(Finites.emptyI RS Finites.insertI RS Key_supply_ax) 1); |
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parents:
diff
changeset
|
188 |
by (etac exE 1); |
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paulson
parents:
diff
changeset
|
189 |
by (cut_inst_tac [("evs","evs''"), ("a1","Ka"), ("a2","K")] |
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parents:
diff
changeset
|
190 |
(Finites.emptyI RS Finites.insertI RS Finites.insertI RS Key_supply_ax) 1); |
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paulson
parents:
diff
changeset
|
191 |
by (Blast_tac 1); |
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paulson
parents:
diff
changeset
|
192 |
qed "Key_supply3"; |
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parents:
diff
changeset
|
193 |
|
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changeset
|
194 |
Goal "Key (@ K. Key K \\<notin> used evs) \\<notin> used evs"; |
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parents:
diff
changeset
|
195 |
by (rtac (Finites.emptyI RS Key_supply_ax RS exE) 1); |
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paulson
parents:
diff
changeset
|
196 |
by (rtac someI 1); |
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paulson
parents:
diff
changeset
|
197 |
by (Blast_tac 1); |
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paulson
parents:
diff
changeset
|
198 |
qed "Key_supply"; |
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paulson
parents:
diff
changeset
|
199 |
|
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paulson
parents:
diff
changeset
|
200 |
(*** Tactics for possibility theorems ***) |
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paulson
parents:
diff
changeset
|
201 |
|
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paulson
parents:
diff
changeset
|
202 |
(*Omitting used_Says makes the tactic much faster: it leaves expressions |
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|
203 |
such as Nonce ?N \\<notin> used evs that match Nonce_supply*) |
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diff
changeset
|
204 |
fun possibility_tac st = st |> |
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parents:
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changeset
|
205 |
(REPEAT |
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paulson
parents:
diff
changeset
|
206 |
(ALLGOALS (simp_tac (simpset() delsimps [used_Says, used_Notes, used_Gets] |
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paulson
parents:
diff
changeset
|
207 |
setSolver safe_solver)) |
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parents:
diff
changeset
|
208 |
THEN |
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parents:
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changeset
|
209 |
REPEAT_FIRST (eq_assume_tac ORELSE' |
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parents:
diff
changeset
|
210 |
resolve_tac [refl, conjI, Nonce_supply, Key_supply]))); |
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paulson
parents:
diff
changeset
|
211 |
|
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paulson
parents:
diff
changeset
|
212 |
(*For harder protocols (such as Recur) where we have to set up some |
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paulson
parents:
diff
changeset
|
213 |
nonces and keys initially*) |
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paulson
parents:
diff
changeset
|
214 |
fun basic_possibility_tac st = st |> |
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parents:
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changeset
|
215 |
REPEAT |
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parents:
diff
changeset
|
216 |
(ALLGOALS (asm_simp_tac (simpset() setSolver safe_solver)) |
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parents:
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changeset
|
217 |
THEN |
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parents:
diff
changeset
|
218 |
REPEAT_FIRST (resolve_tac [refl, conjI])); |
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paulson
parents:
diff
changeset
|
219 |
|
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paulson
parents:
diff
changeset
|
220 |
|
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paulson
parents:
diff
changeset
|
221 |
(*** Specialized rewriting for analz_insert_freshK ***) |
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paulson
parents:
diff
changeset
|
222 |
|
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changeset
|
223 |
Goal "A <= - (range shrK) ==> shrK x \\<notin> A"; |
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paulson
parents:
diff
changeset
|
224 |
by (Blast_tac 1); |
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paulson
parents:
diff
changeset
|
225 |
qed "subset_Compl_range"; |
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parents:
diff
changeset
|
226 |
|
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parents:
diff
changeset
|
227 |
Goal "insert (Key K) H = Key ` {K} Un H"; |
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paulson
parents:
diff
changeset
|
228 |
by (Blast_tac 1); |
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paulson
parents:
diff
changeset
|
229 |
qed "insert_Key_singleton"; |
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paulson
parents:
diff
changeset
|
230 |
|
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paulson
parents:
diff
changeset
|
231 |
Goal "insert (Key K) (Key`KK Un C) = Key ` (insert K KK) Un C"; |
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paulson
parents:
diff
changeset
|
232 |
by (Blast_tac 1); |
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paulson
parents:
diff
changeset
|
233 |
qed "insert_Key_image"; |
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paulson
parents:
diff
changeset
|
234 |
|
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paulson
parents:
diff
changeset
|
235 |
(** Reverse the normal simplification of "image" to build up (not break down) |
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paulson
parents:
diff
changeset
|
236 |
the set of keys. Use analz_insert_eq with (Un_upper2 RS analz_mono) to |
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parents:
diff
changeset
|
237 |
erase occurrences of forwarded message components (X). **) |
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parents:
diff
changeset
|
238 |
|
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paulson
parents:
diff
changeset
|
239 |
bind_thms ("analz_image_freshK_simps", |
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parents:
diff
changeset
|
240 |
simp_thms @ mem_simps @ (*these two allow its use with only:*) |
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paulson
parents:
diff
changeset
|
241 |
disj_comms @ |
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paulson
parents:
diff
changeset
|
242 |
[image_insert RS sym, image_Un RS sym, empty_subsetI, insert_subset, |
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paulson
parents:
diff
changeset
|
243 |
analz_insert_eq, impOfSubs (Un_upper2 RS analz_mono), |
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parents:
diff
changeset
|
244 |
insert_Key_singleton, subset_Compl_range, |
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Key_not_used, insert_Key_image, Un_assoc RS sym]); |
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|
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val analz_image_freshK_ss = |
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simpset() delsimps [image_insert, image_Un] |
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delsimps [imp_disjL] (*reduces blow-up*) |
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addsimps analz_image_freshK_simps; |
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|
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(*Lemma for the trivial direction of the if-and-only-if*) |
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Goal "(Key K : analz (Key`nE Un H)) --> (K : nE | Key K : analz H) ==> \ |
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\ (Key K : analz (Key`nE Un H)) = (K : nE | Key K : analz H)"; |
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by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1); |
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qed "analz_image_freshK_lemma"; |
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257 |