author | paulson |
Tue, 13 Feb 2001 16:02:53 +0100 | |
changeset 11106 | 83d03e966c68 |
child 11116 | ac51bafd1afb |
permissions | -rw-r--r-- |
11106
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1 |
(* Title: HOL/Auth/Public_lemmas |
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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 Public Keys (common to all symmetric-key protocols) |
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7 |
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8 |
Server keys; initial states of agents; new nonces and keys; function "sees" |
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9 |
*) |
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10 |
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11 |
val inj_pubK = thm "inj_pubK"; |
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val priK_neq_pubK = thm "priK_neq_pubK"; |
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14 |
(*** Basic properties of pubK & priK ***) |
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AddIffs [inj_pubK RS inj_eq]; |
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Goal "(priK A = priK B) = (A=B)"; |
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19 |
by Safe_tac; |
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20 |
by (dres_inst_tac [("f","invKey")] arg_cong 1); |
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21 |
by (Full_simp_tac 1); |
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qed "priK_inj_eq"; |
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AddIffs [priK_inj_eq]; |
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AddIffs [priK_neq_pubK, priK_neq_pubK RS not_sym]; |
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Goalw [isSymKey_def] "~ isSymKey (pubK A)"; |
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by (Simp_tac 1); |
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29 |
qed "not_isSymKey_pubK"; |
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|
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31 |
Goalw [isSymKey_def] "~ isSymKey (priK A)"; |
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32 |
by (Simp_tac 1); |
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33 |
qed "not_isSymKey_priK"; |
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AddIffs [not_isSymKey_pubK, not_isSymKey_priK]; |
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37 |
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38 |
(** "Image" equations that hold for injective functions **) |
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39 |
|
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Goal "(invKey x : invKey`A) = (x:A)"; |
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41 |
by Auto_tac; |
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42 |
qed "invKey_image_eq"; |
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(*holds because invKey is injective*) |
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45 |
Goal "(pubK x : pubK`A) = (x:A)"; |
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by Auto_tac; |
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47 |
qed "pubK_image_eq"; |
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|
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Goal "(priK x ~: pubK`A)"; |
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by Auto_tac; |
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51 |
qed "priK_pubK_image_eq"; |
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52 |
Addsimps [invKey_image_eq, pubK_image_eq, priK_pubK_image_eq]; |
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(** Rewrites should not refer to initState(Friend i) |
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56 |
-- not in normal form! **) |
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57 |
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Goalw [keysFor_def] "keysFor (parts (initState C)) = {}"; |
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by (induct_tac "C" 1); |
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by (auto_tac (claset() addIs [range_eqI], simpset())); |
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qed "keysFor_parts_initState"; |
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Addsimps [keysFor_parts_initState]; |
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64 |
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65 |
(*** Function "spies" ***) |
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66 |
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67 |
(*Agents see their own private keys!*) |
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Goal "Key (priK A) : initState A"; |
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by (induct_tac "A" 1); |
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by Auto_tac; |
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qed "priK_in_initState"; |
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AddIffs [priK_in_initState]; |
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|
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(*All public keys are visible*) |
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Goal "Key (pubK A) : spies evs"; |
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by (induct_tac "evs" 1); |
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by (ALLGOALS (asm_simp_tac |
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(simpset() addsimps [imageI, knows_Cons] |
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addsplits [expand_event_case]))); |
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qed_spec_mp "spies_pubK"; |
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81 |
|
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82 |
(*Spy sees private keys of bad agents!*) |
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Goal "A: bad ==> Key (priK A) : spies evs"; |
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84 |
by (induct_tac "evs" 1); |
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85 |
by (ALLGOALS (asm_simp_tac |
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86 |
(simpset() addsimps [imageI, knows_Cons] |
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87 |
addsplits [expand_event_case]))); |
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qed "Spy_spies_bad"; |
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89 |
|
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90 |
AddIffs [spies_pubK, spies_pubK RS analz.Inj]; |
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91 |
AddSIs [Spy_spies_bad]; |
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92 |
|
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93 |
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94 |
(*For not_bad_tac*) |
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95 |
Goal "[| Crypt (pubK A) X : analz (spies evs); A: bad |] \ |
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\ ==> X : analz (spies evs)"; |
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97 |
by (blast_tac (claset() addSDs [analz.Decrypt]) 1); |
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98 |
qed "Crypt_Spy_analz_bad"; |
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99 |
|
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100 |
(*Prove that the agent is uncompromised by the confidentiality of |
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101 |
a component of a message she's said.*) |
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102 |
fun not_bad_tac s = |
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103 |
case_tac ("(" ^ s ^ ") : bad") THEN' |
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104 |
SELECT_GOAL |
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105 |
(REPEAT_DETERM (dtac (Says_imp_spies RS analz.Inj) 1) THEN |
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106 |
REPEAT_DETERM (etac MPair_analz 1) THEN |
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107 |
THEN_BEST_FIRST |
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108 |
(dres_inst_tac [("A", s)] Crypt_Spy_analz_bad 1 THEN assume_tac 1) |
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109 |
(has_fewer_prems 1, size_of_thm) |
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110 |
Safe_tac); |
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111 |
|
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112 |
|
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113 |
(*** Fresh nonces ***) |
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114 |
|
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115 |
Goal "Nonce N ~: parts (initState B)"; |
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116 |
by (induct_tac "B" 1); |
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117 |
by Auto_tac; |
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118 |
qed "Nonce_notin_initState"; |
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119 |
AddIffs [Nonce_notin_initState]; |
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120 |
|
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121 |
Goal "Nonce N ~: used []"; |
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122 |
by (simp_tac (simpset() addsimps [used_Nil]) 1); |
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123 |
qed "Nonce_notin_used_empty"; |
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124 |
Addsimps [Nonce_notin_used_empty]; |
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125 |
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126 |
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127 |
(*** Supply fresh nonces for possibility theorems. ***) |
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128 |
|
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129 |
(*In any trace, there is an upper bound N on the greatest nonce in use.*) |
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130 |
Goal "EX N. ALL n. N<=n --> Nonce n ~: used evs"; |
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131 |
by (induct_tac "evs" 1); |
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132 |
by (res_inst_tac [("x","0")] exI 1); |
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133 |
by (ALLGOALS (asm_simp_tac |
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134 |
(simpset() addsimps [used_Cons] |
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135 |
addsplits [expand_event_case]))); |
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136 |
by Safe_tac; |
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by (ALLGOALS (rtac (msg_Nonce_supply RS exE))); |
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138 |
by (ALLGOALS (blast_tac (claset() addSEs [add_leE]))); |
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139 |
val lemma = result(); |
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140 |
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141 |
Goal "EX N. Nonce N ~: used evs"; |
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142 |
by (rtac (lemma RS exE) 1); |
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143 |
by (Blast_tac 1); |
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144 |
qed "Nonce_supply1"; |
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145 |
|
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146 |
Goal "Nonce (@ N. Nonce N ~: used evs) ~: used evs"; |
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147 |
by (rtac (lemma RS exE) 1); |
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148 |
by (rtac someI 1); |
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149 |
by (Fast_tac 1); |
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150 |
qed "Nonce_supply"; |
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151 |
|
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152 |
(*Tactic for possibility theorems*) |
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153 |
fun possibility_tac st = st |> |
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154 |
REPEAT (*omit used_Says so that Nonces start from different traces!*) |
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155 |
(ALLGOALS (simp_tac (simpset() delsimps [used_Says])) |
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156 |
THEN |
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157 |
REPEAT_FIRST (eq_assume_tac ORELSE' |
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158 |
resolve_tac [refl, conjI, Nonce_supply])); |
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159 |
|
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160 |
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161 |
(*** Specialized rewriting for the analz_image_... theorems ***) |
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162 |
|
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163 |
Goal "insert (Key K) H = Key ` {K} Un H"; |
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164 |
by (Blast_tac 1); |
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165 |
qed "insert_Key_singleton"; |
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166 |
|
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167 |
Goal "insert (Key K) (Key`KK Un C) = Key ` (insert K KK) Un C"; |
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168 |
by (Blast_tac 1); |
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169 |
qed "insert_Key_image"; |
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170 |
|
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171 |
(*Reverse the normal simplification of "image" to build up (not break down) |
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172 |
the set of keys. Based on analz_image_freshK_ss, but simpler.*) |
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173 |
val analz_image_keys_ss = |
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174 |
simpset() delsimps [image_insert, image_Un] |
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175 |
delsimps [imp_disjL] (*reduces blow-up*) |
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176 |
addsimps [image_insert RS sym, image_Un RS sym, |
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177 |
rangeI, |
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178 |
insert_Key_singleton, |
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179 |
insert_Key_image, Un_assoc RS sym]; |
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180 |