author | paulson |
Mon, 23 Sep 1996 17:41:57 +0200 | |
changeset 2002 | ed423882c6a9 |
parent 1999 | b5efc4108d04 |
child 2014 | 5be4c8ca7b25 |
permissions | -rw-r--r-- |
1941 | 1 |
(* Title: HOL/Auth/OtwayRees |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Inductive relation "otway" for the Otway-Rees protocol. |
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||
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From page 244 of |
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Burrows, Abadi and Needham. A Logic of Authentication. |
|
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Proc. Royal Soc. 426 (1989) |
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*) |
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||
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open OtwayRees; |
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||
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proof_timing:=true; |
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HOL_quantifiers := false; |
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||
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
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33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
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19 |
(** Weak liveness: there are traces that reach the end **) |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
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33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
21 |
goal thy |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
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|
22 |
"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \ |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
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changeset
|
23 |
\ ==> EX K. EX evs: otway. \ |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
24 |
\ Says A B (Crypt (Agent A) K) : set_of_list evs"; |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
25 |
by (REPEAT (resolve_tac [exI,bexI] 1)); |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
26 |
br (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4 RS |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
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changeset
|
27 |
otway.OR5) 2; |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
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diff
changeset
|
28 |
by (ALLGOALS (simp_tac (!simpset setsolver safe_solver))); |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
29 |
by (REPEAT_FIRST (resolve_tac [refl, conjI])); |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
30 |
by (ALLGOALS (fast_tac (!claset addss (!simpset setsolver safe_solver)))); |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
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parents:
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diff
changeset
|
31 |
qed "weak_liveness"; |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
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diff
changeset
|
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|
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
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|
1941 | 34 |
(**** Inductive proofs about otway ****) |
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||
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(*The Enemy can see more than anybody else, except for their initial state*) |
|
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goal thy |
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"!!evs. evs : otway ==> \ |
|
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\ sees A evs <= initState A Un sees Enemy evs"; |
|
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be otway.induct 1; |
|
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by (ALLGOALS (fast_tac (!claset addDs [sees_Says_subset_insert RS subsetD] |
|
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addss (!simpset)))); |
|
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qed "sees_agent_subset_sees_Enemy"; |
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||
45 |
||
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(*Nobody sends themselves messages*) |
|
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goal thy "!!evs. evs : otway ==> ALL A X. Says A A X ~: set_of_list evs"; |
|
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be otway.induct 1; |
|
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by (Auto_tac()); |
|
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qed_spec_mp "not_Says_to_self"; |
|
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Addsimps [not_Says_to_self]; |
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AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
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||
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goal thy "!!evs. evs : otway ==> Notes A X ~: set_of_list evs"; |
|
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be otway.induct 1; |
|
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by (Auto_tac()); |
|
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qed "not_Notes"; |
|
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Addsimps [not_Notes]; |
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AddSEs [not_Notes RSN (2, rev_notE)]; |
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60 |
||
61 |
||
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(** For reasoning about the encrypted portion of messages **) |
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63 |
||
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
64 |
goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set_of_list evs ==> \ |
1941 | 65 |
\ X : analz (sees Enemy evs)"; |
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by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1); |
|
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qed "OR2_analz_sees_Enemy"; |
|
68 |
||
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
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parents:
1967
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|
69 |
goal thy "!!evs. Says S B {|N, X, X'|} : set_of_list evs ==> \ |
1941 | 70 |
\ X : analz (sees Enemy evs)"; |
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by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1); |
|
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qed "OR4_analz_sees_Enemy"; |
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73 |
||
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
74 |
goal thy "!!evs. Says B' A {|N, Crypt {|N,K|} K'|} : set_of_list evs ==> \ |
1941 | 75 |
\ K : parts (sees Enemy evs)"; |
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by (fast_tac (!claset addSEs partsEs |
|
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addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1); |
|
78 |
qed "OR5_parts_sees_Enemy"; |
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79 |
||
80 |
(*OR2_analz... and OR4_analz... let us treat those cases using the same |
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1964 | 81 |
argument as for the Fake case. This is possible for most, but not all, |
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proofs: Fake does not invent new nonces (as in OR2), and of course Fake |
|
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messages originate from the Enemy. *) |
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||
1941 | 85 |
val OR2_OR4_tac = |
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dtac (OR2_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 4 THEN |
|
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dtac (OR4_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 6; |
|
88 |
||
89 |
||
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(*** Shared keys are not betrayed ***) |
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91 |
||
1964 | 92 |
(*Enemy never sees another agent's shared key! (unless it is leaked at start)*) |
1941 | 93 |
goal thy |
1999 | 94 |
"!!evs. [| evs : otway; A ~: bad |] \ |
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\ ==> Key (shrK A) ~: parts (sees Enemy evs)"; |
|
1941 | 96 |
be otway.induct 1; |
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by OR2_OR4_tac; |
|
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by (Auto_tac()); |
|
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(*Deals with Fake message*) |
|
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by (best_tac (!claset addDs [impOfSubs analz_subset_parts, |
|
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impOfSubs Fake_parts_insert]) 1); |
|
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qed "Enemy_not_see_shrK"; |
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103 |
||
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bind_thm ("Enemy_not_analz_shrK", |
|
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[analz_subset_parts, Enemy_not_see_shrK] MRS contra_subsetD); |
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||
1967 | 107 |
Addsimps [Enemy_not_see_shrK, Enemy_not_analz_shrK]; |
1941 | 108 |
|
1964 | 109 |
(*We go to some trouble to preserve R in the 3rd and 4th subgoals |
110 |
As usual fast_tac cannot be used because it uses the equalities too soon*) |
|
1941 | 111 |
val major::prems = |
1964 | 112 |
goal thy "[| Key (shrK A) : parts (sees Enemy evs); \ |
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\ evs : otway; \ |
|
1967 | 114 |
\ A:bad ==> R \ |
1941 | 115 |
\ |] ==> R"; |
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br ccontr 1; |
|
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br ([major, Enemy_not_see_shrK] MRS rev_notE) 1; |
|
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by (swap_res_tac prems 2); |
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1967 | 119 |
by (ALLGOALS (fast_tac (!claset addIs prems))); |
1941 | 120 |
qed "Enemy_see_shrK_E"; |
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||
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bind_thm ("Enemy_analz_shrK_E", |
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analz_subset_parts RS subsetD RS Enemy_see_shrK_E); |
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124 |
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AddSEs [Enemy_see_shrK_E, Enemy_analz_shrK_E]; |
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126 |
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127 |
||
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(*** Future keys can't be seen or used! ***) |
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129 |
||
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(*Nobody can have SEEN keys that will be generated in the future. |
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This has to be proved anew for each protocol description, |
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but should go by similar reasoning every time. Hardest case is the |
|
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standard Fake rule. |
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The length comparison, and Union over C, are essential for the |
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induction! *) |
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goal thy "!!evs. evs : otway ==> \ |
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\ length evs <= length evs' --> \ |
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\ Key (newK evs') ~: (UN C. parts (sees C evs))"; |
|
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be otway.induct 1; |
|
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by OR2_OR4_tac; |
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(*auto_tac does not work here, as it performs safe_tac first*) |
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by (ALLGOALS Asm_simp_tac); |
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by (REPEAT_FIRST (best_tac (!claset addDs [impOfSubs analz_subset_parts, |
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impOfSubs parts_insert_subset_Un, |
|
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Suc_leD] |
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addss (!simpset)))); |
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val lemma = result(); |
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148 |
||
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(*Variant needed for the main theorem below*) |
|
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goal thy |
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1999 | 151 |
"!!evs. [| evs : otway; length evs <= length evs' |] \ |
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\ ==> Key (newK evs') ~: parts (sees C evs)"; |
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1941 | 153 |
by (fast_tac (!claset addDs [lemma]) 1); |
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qed "new_keys_not_seen"; |
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Addsimps [new_keys_not_seen]; |
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156 |
||
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(*Another variant: old messages must contain old keys!*) |
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goal thy |
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"!!evs. [| Says A B X : set_of_list evs; \ |
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\ Key (newK evt) : parts {X}; \ |
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\ evs : otway \ |
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\ |] ==> length evt < length evs"; |
|
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br ccontr 1; |
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by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Enemy] |
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addIs [impOfSubs parts_mono, leI]) 1); |
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qed "Says_imp_old_keys"; |
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167 |
||
168 |
||
169 |
(*Nobody can have USED keys that will be generated in the future. |
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...very like new_keys_not_seen*) |
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goal thy "!!evs. evs : otway ==> \ |
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\ length evs <= length evs' --> \ |
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\ newK evs' ~: keysFor (UN C. parts (sees C evs))"; |
|
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be otway.induct 1; |
|
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by OR2_OR4_tac; |
|
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bd OR5_parts_sees_Enemy 7; |
|
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by (ALLGOALS Asm_simp_tac); |
|
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(*OR1 and OR3*) |
|
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by (EVERY (map (fast_tac (!claset addDs [Suc_leD] addss (!simpset))) [4,2])); |
|
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(*Fake, OR2, OR4: these messages send unknown (X) components*) |
|
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by (EVERY |
|
182 |
(map |
|
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(best_tac |
|
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
184 |
(!claset addDs [impOfSubs (analz_subset_parts RS keysFor_mono), |
1941 | 185 |
impOfSubs (parts_insert_subset_Un RS keysFor_mono), |
186 |
Suc_leD] |
|
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addEs [new_keys_not_seen RS not_parts_not_analz RSN(2,rev_notE)] |
|
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addss (!simpset))) |
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[3,2,1])); |
|
190 |
(*OR5: dummy message*) |
|
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
191 |
by (best_tac (!claset addEs [new_keys_not_seen RSN(2,rev_notE)] |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
192 |
addIs [less_SucI, impOfSubs keysFor_mono] |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
193 |
addss (!simpset addsimps [le_def])) 1); |
1941 | 194 |
val lemma = result(); |
195 |
||
196 |
goal thy |
|
1999 | 197 |
"!!evs. [| evs : otway; length evs <= length evs' |] \ |
198 |
\ ==> newK evs' ~: keysFor (parts (sees C evs))"; |
|
1941 | 199 |
by (fast_tac (!claset addSDs [lemma] addss (!simpset)) 1); |
200 |
qed "new_keys_not_used"; |
|
201 |
||
202 |
bind_thm ("new_keys_not_analzd", |
|
203 |
[analz_subset_parts RS keysFor_mono, |
|
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new_keys_not_used] MRS contra_subsetD); |
|
205 |
||
206 |
Addsimps [new_keys_not_used, new_keys_not_analzd]; |
|
207 |
||
208 |
||
209 |
(** Lemmas concerning the form of items passed in messages **) |
|
210 |
||
211 |
||
212 |
(**** |
|
213 |
The following is to prove theorems of the form |
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214 |
||
1964 | 215 |
Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) ==> |
216 |
Key K : analz (sees Enemy evs) |
|
1941 | 217 |
|
218 |
A more general formula must be proved inductively. |
|
219 |
||
220 |
****) |
|
221 |
||
222 |
||
223 |
(*NOT useful in this form, but it says that session keys are not used |
|
224 |
to encrypt messages containing other keys, in the actual protocol. |
|
225 |
We require that agents should behave like this subsequently also.*) |
|
226 |
goal thy |
|
227 |
"!!evs. evs : otway ==> \ |
|
228 |
\ (Crypt X (newK evt)) : parts (sees Enemy evs) & \ |
|
229 |
\ Key K : parts {X} --> Key K : parts (sees Enemy evs)"; |
|
230 |
be otway.induct 1; |
|
231 |
by OR2_OR4_tac; |
|
232 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps pushes))); |
|
233 |
(*Deals with Faked messages*) |
|
234 |
by (best_tac (!claset addSEs partsEs |
|
235 |
addDs [impOfSubs analz_subset_parts, |
|
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impOfSubs parts_insert_subset_Un] |
|
1964 | 237 |
addss (!simpset)) 2); |
238 |
(*Base case and OR5*) |
|
239 |
by (Auto_tac()); |
|
1941 | 240 |
result(); |
241 |
||
242 |
||
243 |
(** Specialized rewriting for this proof **) |
|
244 |
||
245 |
Delsimps [image_insert]; |
|
246 |
Addsimps [image_insert RS sym]; |
|
247 |
||
1964 | 248 |
Delsimps [image_Un]; |
249 |
Addsimps [image_Un RS sym]; |
|
250 |
||
1941 | 251 |
goal thy "insert (Key (newK x)) (sees A evs) = \ |
252 |
\ Key `` (newK``{x}) Un (sees A evs)"; |
|
253 |
by (Fast_tac 1); |
|
254 |
val insert_Key_singleton = result(); |
|
255 |
||
256 |
goal thy "insert (Key (f x)) (Key``(f``E) Un C) = \ |
|
257 |
\ Key `` (f `` (insert x E)) Un C"; |
|
258 |
by (Fast_tac 1); |
|
259 |
val insert_Key_image = result(); |
|
260 |
||
261 |
||
262 |
(*This lets us avoid analyzing the new message -- unless we have to!*) |
|
263 |
(*NEEDED??*) |
|
264 |
goal thy "synth (analz (sees Enemy evs)) <= \ |
|
265 |
\ synth (analz (sees Enemy (Says A B X # evs)))"; |
|
266 |
by (Simp_tac 1); |
|
267 |
br (subset_insertI RS analz_mono RS synth_mono) 1; |
|
268 |
qed "synth_analz_thin"; |
|
269 |
||
270 |
AddIs [impOfSubs synth_analz_thin]; |
|
271 |
||
272 |
||
273 |
||
274 |
(** Session keys are not used to encrypt other session keys **) |
|
275 |
||
276 |
(*Lemma for the trivial direction of the if-and-only-if*) |
|
277 |
goal thy |
|
1964 | 278 |
"!!evs. (Key K : analz (Key``nE Un sEe)) --> \ |
279 |
\ (K : nE | Key K : analz sEe) ==> \ |
|
280 |
\ (Key K : analz (Key``nE Un sEe)) = (K : nE | Key K : analz sEe)"; |
|
1941 | 281 |
by (fast_tac (!claset addSEs [impOfSubs analz_mono]) 1); |
282 |
val lemma = result(); |
|
283 |
||
1964 | 284 |
|
1941 | 285 |
goal thy |
286 |
"!!evs. evs : otway ==> \ |
|
1964 | 287 |
\ ALL K E. (Key K : analz (Key``(newK``E) Un (sees Enemy evs))) = \ |
288 |
\ (K : newK``E | Key K : analz (sees Enemy evs))"; |
|
1941 | 289 |
be otway.induct 1; |
290 |
bd OR2_analz_sees_Enemy 4; |
|
291 |
bd OR4_analz_sees_Enemy 6; |
|
292 |
by (REPEAT_FIRST (resolve_tac [allI, lemma])); |
|
1964 | 293 |
by (ALLGOALS (*Takes 35 secs*) |
1941 | 294 |
(asm_simp_tac |
295 |
(!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK] |
|
296 |
@ pushes) |
|
297 |
setloop split_tac [expand_if]))); |
|
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
298 |
(*OR4, OR2, Fake*) |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
299 |
by (EVERY (map enemy_analz_tac [5,3,2])); |
1941 | 300 |
(*OR3*) |
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
301 |
by (Fast_tac 2); |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
302 |
(*Base case*) |
1941 | 303 |
by (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1); |
304 |
qed_spec_mp "analz_image_newK"; |
|
305 |
||
306 |
||
307 |
goal thy |
|
308 |
"!!evs. evs : otway ==> \ |
|
1964 | 309 |
\ Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) = \ |
310 |
\ (K = newK evt | Key K : analz (sees Enemy evs))"; |
|
1941 | 311 |
by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK, |
312 |
insert_Key_singleton]) 1); |
|
313 |
by (Fast_tac 1); |
|
314 |
qed "analz_insert_Key_newK"; |
|
315 |
||
316 |
||
317 |
(*Describes the form *and age* of K when the following message is sent*) |
|
318 |
goal thy |
|
319 |
"!!evs. [| Says Server B \ |
|
320 |
\ {|NA, Crypt {|NA, K|} (shrK A), \ |
|
321 |
\ Crypt {|NB, K|} (shrK B)|} : set_of_list evs; \ |
|
322 |
\ evs : otway |] \ |
|
323 |
\ ==> (EX evt:otway. K = Key(newK evt) & \ |
|
324 |
\ length evt < length evs) & \ |
|
325 |
\ (EX i. NA = Nonce i)"; |
|
326 |
be rev_mp 1; |
|
327 |
be otway.induct 1; |
|
328 |
by (ALLGOALS (fast_tac (!claset addIs [less_SucI] addss (!simpset)))); |
|
329 |
qed "Says_Server_message_form"; |
|
330 |
||
331 |
||
332 |
(*Crucial secrecy property: Enemy does not see the keys sent in msg OR3*) |
|
333 |
goal thy |
|
1967 | 334 |
"!!evs. [| Says Server A \ |
335 |
\ {|NA, Crypt {|NA, K|} (shrK B), \ |
|
336 |
\ Crypt {|NB, K|} (shrK A)|} : set_of_list evs; \ |
|
337 |
\ A ~: bad; B ~: bad; evs : otway |] ==> \ |
|
1964 | 338 |
\ K ~: analz (sees Enemy evs)"; |
1941 | 339 |
be rev_mp 1; |
340 |
be otway.induct 1; |
|
341 |
bd OR2_analz_sees_Enemy 4; |
|
342 |
bd OR4_analz_sees_Enemy 6; |
|
343 |
by (ALLGOALS Asm_simp_tac); |
|
344 |
(*Next 3 steps infer that K has the form "Key (newK evs'" ... *) |
|
345 |
by (REPEAT_FIRST (resolve_tac [conjI, impI])); |
|
346 |
by (TRYALL (forward_tac [Says_Server_message_form] THEN' assume_tac)); |
|
347 |
by (REPEAT_FIRST (eresolve_tac [bexE, exE, conjE] ORELSE' hyp_subst_tac)); |
|
1964 | 348 |
by (ALLGOALS |
1941 | 349 |
(asm_full_simp_tac |
350 |
(!simpset addsimps ([analz_subset_parts RS contra_subsetD, |
|
351 |
analz_insert_Key_newK] @ pushes) |
|
352 |
setloop split_tac [expand_if]))); |
|
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
353 |
(*OR4, OR2, Fake*) |
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
354 |
by (EVERY (map enemy_analz_tac [4,2,1])); |
1941 | 355 |
(*OR3*) |
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
356 |
by (fast_tac (!claset addSEs [less_irrefl]) 1); |
1941 | 357 |
qed "Enemy_not_see_encrypted_key"; |
1945 | 358 |
|
359 |
||
360 |
||
361 |
(*** Session keys are issued at most once, and identify the principals ***) |
|
362 |
||
363 |
(** First, two lemmas for the Fake, OR2 and OR4 cases **) |
|
364 |
||
365 |
goal thy |
|
1964 | 366 |
"!!evs. [| X : synth (analz (sees Enemy evs)); \ |
367 |
\ Crypt X' (shrK C) : parts{X}; \ |
|
1967 | 368 |
\ C ~: bad; evs : otway |] \ |
1945 | 369 |
\ ==> Crypt X' (shrK C) : parts (sees Enemy evs)"; |
370 |
by (best_tac (!claset addSEs [impOfSubs analz_subset_parts] |
|
371 |
addDs [impOfSubs parts_insert_subset_Un] |
|
372 |
addss (!simpset)) 1); |
|
373 |
qed "Crypt_Fake_parts"; |
|
374 |
||
375 |
goal thy |
|
376 |
"!!evs. [| Crypt X' K : parts (sees A evs); evs : otway |] \ |
|
377 |
\ ==> EX S S' Y. Says S S' Y : set_of_list evs & \ |
|
378 |
\ Crypt X' K : parts {Y}"; |
|
379 |
bd parts_singleton 1; |
|
380 |
by (fast_tac (!claset addSDs [seesD] addss (!simpset)) 1); |
|
381 |
qed "Crypt_parts_singleton"; |
|
382 |
||
383 |
fun ex_strip_tac i = REPEAT (ares_tac [exI, conjI] i) THEN assume_tac (i+1); |
|
384 |
||
385 |
(*The Key K uniquely identifies a pair of senders in the message encrypted by |
|
386 |
C, but if C=Enemy then he could send all sorts of nonsense.*) |
|
387 |
goal thy |
|
1964 | 388 |
"!!evs. evs : otway ==> \ |
389 |
\ EX A B. ALL C. \ |
|
1967 | 390 |
\ C ~: bad --> \ |
1945 | 391 |
\ (ALL S S' X. Says S S' X : set_of_list evs --> \ |
392 |
\ (EX NA. Crypt {|NA, Key K|} (shrK C) : parts{X}) --> C=A | C=B)"; |
|
393 |
by (Simp_tac 1); |
|
394 |
be otway.induct 1; |
|
395 |
bd OR2_analz_sees_Enemy 4; |
|
396 |
bd OR4_analz_sees_Enemy 6; |
|
397 |
by (ALLGOALS |
|
398 |
(asm_simp_tac (!simpset addsimps [all_conj_distrib, imp_conj_distrib]))); |
|
399 |
by (REPEAT_FIRST (etac exE)); |
|
400 |
(*OR4*) |
|
401 |
by (ex_strip_tac 4); |
|
402 |
by (fast_tac (!claset addSDs [synth.Inj RS Crypt_Fake_parts, |
|
403 |
Crypt_parts_singleton]) 4); |
|
404 |
(*OR3: Case split propagates some context to other subgoal...*) |
|
405 |
(** LEVEL 8 **) |
|
406 |
by (excluded_middle_tac "K = newK evsa" 3); |
|
407 |
by (Asm_simp_tac 3); |
|
408 |
by (REPEAT (ares_tac [exI] 3)); |
|
409 |
(*...we prove this case by contradiction: the key is too new!*) |
|
410 |
by (fast_tac (!claset addIs [impOfSubs (subset_insertI RS parts_mono)] |
|
411 |
addSEs partsEs |
|
412 |
addEs [Says_imp_old_keys RS less_irrefl] |
|
413 |
addss (!simpset)) 3); |
|
414 |
(*OR2*) (** LEVEL 12 **) |
|
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
415 |
(*enemy_analz_tac just does not work here: it is an entirely different proof!*) |
1945 | 416 |
by (ex_strip_tac 2); |
1996
33c42cae3dd0
Uses the improved enemy_analz_tac of Shared.ML, with simpler proofs
paulson
parents:
1967
diff
changeset
|
417 |
by (res_inst_tac [("x1","X")] (insert_commute RS ssubst) 2); |
1945 | 418 |
by (Simp_tac 2); |
419 |
by (fast_tac (!claset addSDs [synth.Inj RS Crypt_Fake_parts, |
|
420 |
Crypt_parts_singleton]) 2); |
|
421 |
(*Fake*) (** LEVEL 16 **) |
|
422 |
by (ex_strip_tac 1); |
|
423 |
by (fast_tac (!claset addSDs [Crypt_Fake_parts, Crypt_parts_singleton]) 1); |
|
424 |
qed "unique_session_keys"; |
|
425 |
||
426 |
(*It seems strange but this theorem is NOT needed to prove the main result!*) |