src/HOL/Auth/Yahalom2.ML
author paulson
Fri, 27 Jun 1997 10:47:13 +0200
changeset 3466 30791e5a69c4
parent 3465 e85c24717cad
child 3501 4ab477ffb4c6
permissions -rw-r--r--
Corrected indentations and margins after the renaming of "set_of_list"
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     1
(*  Title:      HOL/Auth/Yahalom2
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     2
    ID:         $Id$
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     4
    Copyright   1996  University of Cambridge
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     5
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     6
Inductive relation "yahalom" for the Yahalom protocol, Variant 2.
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     7
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     8
This version trades encryption of NB for additional explicitness in YM3.
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     9
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    10
From page 259 of
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    11
  Burrows, Abadi and Needham.  A Logic of Authentication.
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    12
  Proc. Royal Soc. 426 (1989)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    13
*)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    14
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    15
open Yahalom2;
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    16
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    17
proof_timing:=true;
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    18
HOL_quantifiers := false;
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    19
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    20
(*Replacing the variable by a constant improves speed*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    21
val Says_imp_sees_Spy' = read_instantiate [("lost","lost")] Says_imp_sees_Spy;
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    22
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    23
2323
3ae9b0ccee21 Trivial renamings
paulson
parents: 2284
diff changeset
    24
(*A "possibility property": there are traces that reach the end*)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    25
goal thy 
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
    26
 "!!A B. [| A ~= B; A ~= Server; B ~= Server |]        \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    27
\        ==> EX X NB K. EX evs: yahalom lost.          \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
    28
\               Says A B {|X, Crypt K (Nonce NB)|} : set evs";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    29
by (REPEAT (resolve_tac [exI,bexI] 1));
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    30
by (rtac (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS 
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    31
          yahalom.YM4) 2);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    32
by possibility_tac;
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    33
result();
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    34
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    35
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    36
(**** Inductive proofs about yahalom ****)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    37
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    38
(*Monotonicity*)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    39
goal thy "!!evs. lost' <= lost ==> yahalom lost' <= yahalom lost";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    40
by (rtac subsetI 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    41
by (etac yahalom.induct 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    42
by (REPEAT_FIRST
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    43
    (blast_tac (!claset addIs (impOfSubs(sees_mono RS analz_mono RS synth_mono)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    44
			       :: yahalom.intrs))));
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    45
qed "yahalom_mono";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    46
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    47
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    48
(*Nobody sends themselves messages*)
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
    49
goal thy "!!evs. evs: yahalom lost ==> ALL A X. Says A A X ~: set evs";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    50
by (etac yahalom.induct 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    51
by (Auto_tac());
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    52
qed_spec_mp "not_Says_to_self";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    53
Addsimps [not_Says_to_self];
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    54
AddSEs   [not_Says_to_self RSN (2, rev_notE)];
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    55
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    56
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    57
(** For reasoning about the encrypted portion of messages **)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    58
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    59
(*Lets us treat YM4 using a similar argument as for the Fake case.*)
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
    60
goal thy "!!evs. Says S A {|NB, Crypt (shrK A) Y, X|} : set evs ==> \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    61
\                X : analz (sees lost Spy evs)";
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    62
by (blast_tac (!claset addSDs [Says_imp_sees_Spy' RS analz.Inj]) 1);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    63
qed "YM4_analz_sees_Spy";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    64
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    65
bind_thm ("YM4_parts_sees_Spy",
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    66
          YM4_analz_sees_Spy RS (impOfSubs analz_subset_parts));
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    67
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
    68
(*Relates to both YM4 and Oops*)
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
    69
goal thy "!!evs. Says S A {|NB, Crypt (shrK A) {|B,K,NA|}, X|} : set evs ==> \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    70
\                K : parts (sees lost Spy evs)";
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    71
by (blast_tac (!claset addSEs partsEs
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
    72
                       addSDs [Says_imp_sees_Spy' RS parts.Inj]) 1);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    73
qed "YM4_Key_parts_sees_Spy";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    74
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    75
(*For proving the easier theorems about X ~: parts (sees lost Spy evs).
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    76
  We instantiate the variable to "lost" since leaving it as a Var would
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    77
  interfere with simplification.*)
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    78
val parts_sees_tac = 
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    79
    forw_inst_tac [("lost","lost")] YM4_parts_sees_Spy 6     THEN
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    80
    forw_inst_tac [("lost","lost")] YM4_Key_parts_sees_Spy 7 THEN
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    81
    prove_simple_subgoals_tac  1;
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    82
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    83
val parts_induct_tac = 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    84
    etac yahalom.induct 1 THEN parts_sees_tac;
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
    85
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    86
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    87
(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    88
    sends messages containing X! **)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    89
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    90
(*Spy never sees another agent's shared key! (unless it's lost at start)*)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    91
goal thy 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    92
 "!!evs. evs : yahalom lost \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    93
\        ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)";
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    94
by parts_induct_tac;
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    95
by (Fake_parts_insert_tac 1);
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
    96
by (Blast_tac 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    97
qed "Spy_see_shrK";
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    98
Addsimps [Spy_see_shrK];
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    99
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   100
goal thy 
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   101
 "!!evs. evs : yahalom lost \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   102
\        ==> (Key (shrK A) : analz (sees lost Spy evs)) = (A : lost)";
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   103
by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset));
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   104
qed "Spy_analz_shrK";
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   105
Addsimps [Spy_analz_shrK];
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   106
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   107
goal thy  "!!A. [| Key (shrK A) : parts (sees lost Spy evs);       \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   108
\                  evs : yahalom lost |] ==> A:lost";
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   109
by (blast_tac (!claset addDs [Spy_see_shrK]) 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   110
qed "Spy_see_shrK_D";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   111
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   112
bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   113
AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D];
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   114
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   115
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   116
(*Nobody can have used non-existent keys!  Needed to apply analz_insert_Key*)
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   117
goal thy "!!evs. evs : yahalom lost ==>          \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   118
\         Key K ~: used evs --> K ~: keysFor (parts (sees lost Spy evs))";
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   119
by parts_induct_tac;
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   120
(*YM4: Key K is not fresh!*)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   121
by (blast_tac (!claset addSEs sees_Spy_partsEs) 3);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   122
(*YM3*)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   123
by (blast_tac (!claset addss (!simpset)) 2);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   124
(*Fake*)
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   125
by (best_tac
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   126
      (!claset addIs [impOfSubs analz_subset_parts]
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   127
               addDs [impOfSubs (analz_subset_parts RS keysFor_mono),
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   128
                      impOfSubs (parts_insert_subset_Un RS keysFor_mono)]
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   129
               addss (!simpset)) 1);
2160
ad4382e546fc Simplified new_keys_not_seen, etc.: replaced the
paulson
parents: 2155
diff changeset
   130
qed_spec_mp "new_keys_not_used";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   131
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   132
bind_thm ("new_keys_not_analzd",
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   133
          [analz_subset_parts RS keysFor_mono,
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   134
           new_keys_not_used] MRS contra_subsetD);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   135
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   136
Addsimps [new_keys_not_used, new_keys_not_analzd];
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   137
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   138
(*Describes the form of K when the Server sends this message.  Useful for
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   139
  Oops as well as main secrecy property.*)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   140
goal thy 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   141
 "!!evs. [| Says Server A {|NB', Crypt (shrK A) {|Agent B, Key K, NA|}, X|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   142
\            : set evs;                                                 \
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   143
\           evs : yahalom lost |]                                       \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   144
\        ==> K ~: range shrK & A ~= B";
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   145
by (etac rev_mp 1);
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   146
by (etac yahalom.induct 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   147
by (ALLGOALS Asm_simp_tac);
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   148
qed "Says_Server_message_form";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   149
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   150
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   151
(*For proofs involving analz.  We again instantiate the variable to "lost".*)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   152
val analz_sees_tac = 
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   153
    dres_inst_tac [("lost","lost")] YM4_analz_sees_Spy 6 THEN
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   154
    forw_inst_tac [("lost","lost")] Says_Server_message_form 7 THEN
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   155
    assume_tac 7 THEN
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   156
    REPEAT ((etac conjE ORELSE' hyp_subst_tac) 7);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   157
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   158
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   159
(****
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   160
 The following is to prove theorems of the form
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   161
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   162
          Key K : analz (insert (Key KAB) (sees lost Spy evs)) ==>
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   163
          Key K : analz (sees lost Spy evs)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   164
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   165
 A more general formula must be proved inductively.
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   166
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   167
****)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   168
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   169
(** Session keys are not used to encrypt other session keys **)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   170
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   171
goal thy  
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   172
 "!!evs. evs : yahalom lost ==>                                  \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   173
\  ALL K KK. KK <= Compl (range shrK) -->                        \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   174
\            (Key K : analz (Key``KK Un (sees lost Spy evs))) =  \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   175
\            (K : KK | Key K : analz (sees lost Spy evs))";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   176
by (etac yahalom.induct 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   177
by analz_sees_tac;
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   178
by (REPEAT_FIRST (resolve_tac [allI, impI]));
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   179
by (REPEAT_FIRST (rtac analz_image_freshK_lemma ));
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   180
by (ALLGOALS (asm_simp_tac analz_image_freshK_ss));
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   181
(*Fake*) 
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   182
by (spy_analz_tac 2);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   183
(*Base*)
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   184
by (Blast_tac 1);
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   185
qed_spec_mp "analz_image_freshK";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   186
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   187
goal thy
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   188
 "!!evs. [| evs : yahalom lost;  KAB ~: range shrK |] ==>             \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   189
\        Key K : analz (insert (Key KAB) (sees lost Spy evs)) =       \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   190
\        (K = KAB | Key K : analz (sees lost Spy evs))";
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   191
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1);
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   192
qed "analz_insert_freshK";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   193
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   194
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   195
(*** The Key K uniquely identifies the Server's  message. **)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   196
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   197
goal thy 
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   198
 "!!evs. evs : yahalom lost ==>                                     \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   199
\      EX A' B' na' nb' X'. ALL A B na nb X.                        \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   200
\          Says Server A                                            \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   201
\           {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, X|}        \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   202
\          : set evs --> A=A' & B=B' & na=na' & nb=nb' & X=X'";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   203
by (etac yahalom.induct 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   204
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib])));
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   205
by (Step_tac 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   206
(*Remaining case: YM3*)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   207
by (expand_case_tac "K = ?y" 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   208
by (REPEAT (ares_tac [refl,exI,impI,conjI] 2));
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   209
(*...we assume X is a recent message and handle this case by contradiction*)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   210
by (blast_tac (!claset addSEs sees_Spy_partsEs
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   211
                      delrules [conjI]    (*prevent split-up into 4 subgoals*)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   212
                      addss (!simpset addsimps [parts_insertI])) 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   213
val lemma = result();
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   214
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   215
goal thy 
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   216
"!!evs. [| Says Server A                                            \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   217
\           {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, X|}        \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   218
\           : set evs;                                              \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   219
\          Says Server A'                                           \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   220
\           {|nb', Crypt (shrK A') {|Agent B', Key K, na'|}, X'|}   \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   221
\           : set evs;                                              \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   222
\          evs : yahalom lost |]                                    \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   223
\       ==> A=A' & B=B' & na=na' & nb=nb'";
2451
ce85a2aafc7a Extensive tidying and simplification, largely stemming from
paulson
parents: 2377
diff changeset
   224
by (prove_unique_tac lemma 1);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   225
qed "unique_session_keys";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   226
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   227
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   228
(** Crucial secrecy property: Spy does not see the keys sent in msg YM3 **)
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   229
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   230
goal thy 
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   231
 "!!evs. [| A ~: lost;  B ~: lost;  A ~= B;                          \
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   232
\           evs : yahalom lost |]                                    \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   233
\        ==> Says Server A                                           \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   234
\              {|nb, Crypt (shrK A) {|Agent B, Key K, na|},          \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   235
\                    Crypt (shrK B) {|nb, Key K, Agent A|}|}         \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   236
\             : set evs -->                                          \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   237
\            Says A Spy {|na, nb, Key K|} ~: set evs -->             \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   238
\            Key K ~: analz (sees lost Spy evs)";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   239
by (etac yahalom.induct 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   240
by analz_sees_tac;
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   241
by (ALLGOALS
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   242
    (asm_simp_tac 
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   243
     (!simpset addsimps [analz_insert_eq, not_parts_not_analz, 
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   244
			 analz_insert_freshK]
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   245
               setloop split_tac [expand_if])));
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   246
(*Oops*)
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   247
by (blast_tac (!claset addDs [unique_session_keys]) 3);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   248
(*YM3*)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   249
by (blast_tac (!claset delrules [impCE]
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   250
                       addSEs sees_Spy_partsEs
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   251
                       addIs [impOfSubs analz_subset_parts]) 2);
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   252
(*Fake*) 
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   253
by (spy_analz_tac 1);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   254
val lemma = result() RS mp RS mp RSN(2,rev_notE);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   255
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   256
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   257
(*Final version*)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   258
goal thy 
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   259
 "!!evs. [| Says Server A                                         \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   260
\              {|nb, Crypt (shrK A) {|Agent B, Key K, na|},       \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   261
\                    Crypt (shrK B) {|nb, Key K, Agent A|}|}      \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   262
\           : set evs;                                            \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   263
\           Says A Spy {|na, nb, Key K|} ~: set evs;              \
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   264
\           A ~: lost;  B ~: lost;  evs : yahalom lost |]         \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   265
\        ==> Key K ~: analz (sees lost Spy evs)";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   266
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   267
by (blast_tac (!claset addSEs [lemma]) 1);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   268
qed "Spy_not_see_encrypted_key";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   269
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   270
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   271
(*And other agents don't see the key either.*)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   272
goal thy 
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   273
 "!!evs. [| C ~: {A,B,Server};                                    \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   274
\           Says Server A                                         \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   275
\              {|nb, Crypt (shrK A) {|Agent B, Key K, na|},       \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   276
\                    Crypt (shrK B) {|nb, Key K, Agent A|}|}      \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   277
\           : set evs;                                            \
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   278
\           Says A Spy {|na, nb, Key K|} ~: set evs;              \
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   279
\           A ~: lost;  B ~: lost;  evs : yahalom lost |]         \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
   280
\        ==> Key K ~: analz (sees lost C evs)";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   281
by (rtac (subset_insertI RS sees_mono RS analz_mono RS contra_subsetD) 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   282
by (rtac (sees_lost_agent_subset_sees_Spy RS analz_mono RS contra_subsetD) 1);
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   283
by (FIRSTGOAL (rtac Spy_not_see_encrypted_key));
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   284
by (REPEAT_FIRST (blast_tac (!claset addIs [yahalom_mono RS subsetD])));
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   285
qed "Agent_not_see_encrypted_key";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   286
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   287
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   288
(** Security Guarantee for A upon receiving YM3 **)
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   289
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   290
(*If the encrypted message appears then it originated with the Server.
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   291
  May now apply Spy_not_see_encrypted_key, subject to its conditions.*)
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   292
goal thy
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   293
 "!!evs. [| Crypt (shrK A) {|Agent B, Key K, na|}                      \
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   294
\            : parts (sees lost Spy evs);                              \
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   295
\           A ~: lost;  evs : yahalom lost |]                          \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   296
\         ==> EX nb. Says Server A                                     \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   297
\                      {|nb, Crypt (shrK A) {|Agent B, Key K, na|},    \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   298
\                            Crypt (shrK B) {|nb, Key K, Agent A|}|}   \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   299
\                    : set evs";
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   300
by (etac rev_mp 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   301
by parts_induct_tac;
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   302
by (Fake_parts_insert_tac 1);
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   303
by (Blast_tac 1);
2323
3ae9b0ccee21 Trivial renamings
paulson
parents: 2284
diff changeset
   304
qed "A_trusts_YM3";
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   305
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   306
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   307
(** Security Guarantee for B upon receiving YM4 **)
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   308
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   309
(*B knows, by the first part of A's message, that the Server distributed 
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   310
  the key for A and B, and has associated it with NB. *)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   311
goal thy 
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   312
 "!!evs. [| Crypt (shrK B) {|Nonce NB, Key K, Agent A|}              \
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   313
\            : parts (sees lost Spy evs);                            \
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   314
\           B ~: lost;  evs : yahalom lost |]                        \
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   315
\        ==> EX NA. Says Server A                                    \
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   316
\                    {|Nonce NB,                                     \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   317
\                      Crypt (shrK A) {|Agent B, Key K, Nonce NA|},  \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2264
diff changeset
   318
\                      Crypt (shrK B) {|Nonce NB, Key K, Agent A|}|} \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   319
\                       : set evs";
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   320
by (etac rev_mp 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   321
by parts_induct_tac;
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   322
by (Fake_parts_insert_tac 1);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   323
(*YM3*)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   324
by (Blast_tac 1);
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   325
qed "B_trusts_YM4_shrK";
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   326
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   327
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   328
(*With this protocol variant, we don't need the 2nd part of YM4 at all:
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   329
  Nonce NB is available in the first part.*)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   330
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   331
(*What can B deduce from receipt of YM4?  Stronger and simpler than Yahalom
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
   332
  because we do not have to show that NB is secret. *)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   333
goal thy 
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   334
 "!!evs. [| Says A' B {|Crypt (shrK B) {|Nonce NB, Key K, Agent A|}, X|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   335
\             : set evs;                                                 \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   336
\           A ~: lost;  B ~: lost;  evs : yahalom lost |]                \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   337
\        ==> EX NA. Says Server A                                        \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   338
\                    {|Nonce NB,                                         \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   339
\                      Crypt (shrK A) {|Agent B, Key K, Nonce NA|},      \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   340
\                      Crypt (shrK B) {|Nonce NB, Key K, Agent A|}|}     \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   341
\                   : set evs";
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   342
by (etac (Says_imp_sees_Spy' RS parts.Inj RS MPair_parts) 1);
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 2637
diff changeset
   343
by (blast_tac (!claset addSDs [B_trusts_YM4_shrK]) 1);
2323
3ae9b0ccee21 Trivial renamings
paulson
parents: 2284
diff changeset
   344
qed "B_trusts_YM4";
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   345
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   346
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   347
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   348
(*** Authenticating B to A ***)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   349
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   350
(*The encryption in message YM2 tells us it cannot be faked.*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   351
goal thy 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   352
 "!!evs. evs : yahalom lost                                            \
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   353
\  ==> Crypt (shrK B) {|Agent A, Nonce NA|} : parts (sees lost Spy evs) -->  \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   354
\      B ~: lost -->                                                   \
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   355
\      (EX NB. Says B Server {|Agent B, Nonce NB,                      \
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   356
\                              Crypt (shrK B) {|Agent A, Nonce NA|}|}  \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   357
\         : set evs)";
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   358
by parts_induct_tac;
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   359
by (Fake_parts_insert_tac 1);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   360
(*YM2*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   361
by (Blast_tac 1);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   362
bind_thm ("B_Said_YM2", result() RSN (2, rev_mp) RS mp);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   363
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   364
(*If the server sends YM3 then B sent YM2, perhaps with a different NB*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   365
goal thy 
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   366
 "!!evs. evs : yahalom lost                                              \
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   367
\  ==> Says Server A {|nb, Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, X|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   368
\         : set evs -->                                                  \
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   369
\      B ~: lost -->                                                     \
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   370
\      (EX nb'. Says B Server {|Agent B, nb',                            \
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   371
\                               Crypt (shrK B) {|Agent A, Nonce NA|}|}   \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   372
\                 : set evs)";
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   373
by (etac yahalom.induct 1);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   374
by (ALLGOALS Asm_simp_tac);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   375
(*YM3*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   376
by (blast_tac (!claset addSDs [B_Said_YM2]
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   377
		       addSEs [MPair_parts]
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   378
		       addDs [Says_imp_sees_Spy' RS parts.Inj]) 3);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   379
(*Fake, YM2*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   380
by (ALLGOALS Blast_tac);
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   381
val lemma = result() RSN (2, rev_mp) RS mp |> standard;
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   382
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   383
(*If A receives YM3 then B has used nonce NA (and therefore is alive)*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   384
goal thy
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   385
 "!!evs. [| Says S A {|nb, Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, X|} \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   386
\             : set evs;                                                    \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   387
\           A ~: lost;  B ~: lost;  evs : yahalom lost |]                   \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   388
\   ==> EX nb'. Says B Server                                               \
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   389
\                    {|Agent B, nb', Crypt (shrK B) {|Agent A, Nonce NA|}|} \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   390
\                 : set evs";
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   391
by (blast_tac (!claset addSDs [A_trusts_YM3, lemma]
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   392
		       addEs sees_Spy_partsEs) 1);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   393
qed "YM3_auth_B_to_A";
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   394
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   395
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   396
(*** Authenticating A to B using the certificate Crypt K (Nonce NB) ***)
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   397
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   398
(*Induction for theorems of the form X ~: analz (sees lost Spy evs) --> ...
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   399
  It simplifies the proof by discarding needless information about
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   400
	analz (insert X (sees lost Spy evs)) 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   401
*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   402
val analz_mono_parts_induct_tac = 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   403
    etac yahalom.induct 1 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   404
    THEN 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   405
    REPEAT_FIRST  
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   406
      (rtac impI THEN' 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   407
       dtac (sees_subset_sees_Says RS analz_mono RS contra_subsetD) THEN'
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   408
       mp_tac)  
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   409
    THEN  parts_sees_tac;
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   410
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   411
(*Assuming the session key is secure, if both certificates are present then
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   412
  A has said NB.  We can't be sure about the rest of A's message, but only
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   413
  NB matters for freshness.*)  
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   414
goal thy 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   415
 "!!evs. evs : yahalom lost                                             \
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   416
\        ==> Key K ~: analz (sees lost Spy evs) -->                     \
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   417
\            Crypt K (Nonce NB) : parts (sees lost Spy evs) -->         \
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   418
\            Crypt (shrK B) {|Nonce NB, Key K, Agent A|}                \
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   419
\              : parts (sees lost Spy evs) -->                          \
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   420
\            B ~: lost -->                                              \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   421
\             (EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs)";
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   422
by analz_mono_parts_induct_tac;
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   423
(*Fake*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   424
by (Fake_parts_insert_tac 1);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   425
(*YM3: by new_keys_not_used we note that Crypt K (Nonce NB) could not exist*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   426
by (fast_tac (!claset addSDs [Crypt_imp_invKey_keysFor] addss (!simpset)) 1); 
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   427
(*YM4: was Crypt K (Nonce NB) the very last message?  If not, use ind. hyp.*)
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   428
by (asm_simp_tac (!simpset addsimps [ex_disj_distrib]) 1);
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   429
(*yes: apply unicity of session keys*)
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   430
by (not_lost_tac "Aa" 1);
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   431
by (blast_tac (!claset addSEs [MPair_parts]
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   432
                       addSDs [A_trusts_YM3, B_trusts_YM4_shrK]
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   433
		       addDs  [Says_imp_sees_Spy' RS parts.Inj,
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   434
			       unique_session_keys]) 1);
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   435
val lemma = normalize_thm [RSspec, RSmp] (result()) |> standard;
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   436
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   437
(*If B receives YM4 then A has used nonce NB (and therefore is alive).
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   438
  Moreover, A associates K with NB (thus is talking about the same run).
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   439
  Other premises guarantee secrecy of K.*)
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   440
goal thy 
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   441
 "!!evs. [| Says A' B {|Crypt (shrK B) {|Nonce NB, Key K, Agent A|},    \
3466
30791e5a69c4 Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents: 3465
diff changeset
   442
\                       Crypt K (Nonce NB)|} : set evs;                 \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   443
\           (ALL NA. Says A Spy {|Nonce NA, Nonce NB, Key K|} ~: set evs); \
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   444
\           A ~: lost;  B ~: lost;  evs : yahalom lost |]               \
3465
e85c24717cad set_of_list -> set
nipkow
parents: 3450
diff changeset
   445
\        ==> EX X. Says A B {|X, Crypt K (Nonce NB)|} : set evs";
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   446
by (etac (Says_imp_sees_Spy' RS parts.Inj RS MPair_parts) 1);
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   447
by (dtac B_trusts_YM4_shrK 1);
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   448
by (safe_tac (!claset));
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   449
by (rtac lemma 1);
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   450
by (rtac Spy_not_see_encrypted_key 2);
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   451
by (REPEAT_FIRST assume_tac);
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   452
by (ALLGOALS (blast_tac (!claset addSEs [MPair_parts]
3450
cd73bc206d87 Proof tidying and variable renaming (NA->na, NB->nb when of type msg)
paulson
parents: 3432
diff changeset
   453
			         addDs [Says_imp_sees_Spy' RS parts.Inj])));
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 3121
diff changeset
   454
qed_spec_mp "YM4_imp_A_Said_YM3";