src/HOL/Auth/Yahalom2.thy
author berghofe
Wed, 11 Jul 2007 11:14:51 +0200
changeset 23746 a455e69c31cc
parent 16417 9bc16273c2d4
child 32960 69916a850301
permissions -rw-r--r--
Adapted to new inductive definition package.
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
3445
96fcfbfa4fb5 Corrected Title in header lines
paulson
parents: 3432
diff changeset
     1
(*  Title:      HOL/Auth/Yahalom2
2111
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
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
     5
*)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
     6
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
     7
header{*The Yahalom Protocol, Variant 2*}
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
     8
16417
9bc16273c2d4 migrated theory headers to new format
haftmann
parents: 14207
diff changeset
     9
theory Yahalom2 imports Public begin
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
    10
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
    11
text{*
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    12
This version trades encryption of NB for additional explicitness in YM3.
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 2516
diff changeset
    13
Also in YM3, care is taken to make the two certificates distinct.
2111
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
From page 259 of
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
    16
  Burrows, Abadi and Needham (1989).  A Logic of Authentication.
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
    17
  Proc. Royal Soc. 426
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    18
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
    19
This theory has the prototypical example of a secrecy relation, KeyCryptNonce.
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
    20
*}
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    21
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    22
inductive_set yahalom :: "event list set"
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    23
  where
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    24
         (*Initial trace is empty*)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    25
   Nil:  "[] \<in> yahalom"
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    26
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    27
         (*The spy MAY say anything he CAN say.  We do not expect him to
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    28
           invent new nonces here, but he can also use NS1.  Common to
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    29
           all similar protocols.*)
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    30
 | Fake: "[| evsf \<in> yahalom;  X \<in> synth (analz (knows Spy evsf)) |]
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    31
          ==> Says Spy B X  # evsf \<in> yahalom"
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    32
6335
7e4bffaa2a3e updating both Yahalom protocols to the Gets model
paulson
parents: 5434
diff changeset
    33
         (*A message that has been sent can be received by the
7e4bffaa2a3e updating both Yahalom protocols to the Gets model
paulson
parents: 5434
diff changeset
    34
           intended recipient.*)
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    35
 | Reception: "[| evsr \<in> yahalom;  Says A B X \<in> set evsr |]
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    36
               ==> Gets B X # evsr \<in> yahalom"
6335
7e4bffaa2a3e updating both Yahalom protocols to the Gets model
paulson
parents: 5434
diff changeset
    37
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    38
         (*Alice initiates a protocol run*)
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    39
 | YM1:  "[| evs1 \<in> yahalom;  Nonce NA \<notin> used evs1 |]
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    40
          ==> Says A B {|Agent A, Nonce NA|} # evs1 \<in> yahalom"
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    41
6335
7e4bffaa2a3e updating both Yahalom protocols to the Gets model
paulson
parents: 5434
diff changeset
    42
         (*Bob's response to Alice's message.*)
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    43
 | YM2:  "[| evs2 \<in> yahalom;  Nonce NB \<notin> used evs2;
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    44
             Gets B {|Agent A, Nonce NA|} \<in> set evs2 |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    45
          ==> Says B Server
3432
04412cfe6861 Strengthened and streamlined the Yahalom proofs
paulson
parents: 2516
diff changeset
    46
                  {|Agent B, Nonce NB, Crypt (shrK B) {|Agent A, Nonce NA|}|}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    47
                # evs2 \<in> yahalom"
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    48
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    49
         (*The Server receives Bob's message.  He responds by sending a
3659
eddedfe2f3f8 Renamed "evs" to "evs1", "evs2", etc. in protocol inductive definition
paulson
parents: 3519
diff changeset
    50
           new session key to Alice, with a certificate for forwarding to Bob.
5066
30271d90644f Changed format of Bob's certificate from Nb,K,A to A,B,K,Nb.
paulson
parents: 4537
diff changeset
    51
           Both agents are quoted in the 2nd certificate to prevent attacks!*)
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    52
 | YM3:  "[| evs3 \<in> yahalom;  Key KAB \<notin> used evs3;
6335
7e4bffaa2a3e updating both Yahalom protocols to the Gets model
paulson
parents: 5434
diff changeset
    53
             Gets Server {|Agent B, Nonce NB,
7e4bffaa2a3e updating both Yahalom protocols to the Gets model
paulson
parents: 5434
diff changeset
    54
			   Crypt (shrK B) {|Agent A, Nonce NA|}|}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    55
               \<in> set evs3 |]
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    56
          ==> Says Server A
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    57
               {|Nonce NB,
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2451
diff changeset
    58
                 Crypt (shrK A) {|Agent B, Key KAB, Nonce NA|},
5066
30271d90644f Changed format of Bob's certificate from Nb,K,A to A,B,K,Nb.
paulson
parents: 4537
diff changeset
    59
                 Crypt (shrK B) {|Agent A, Agent B, Key KAB, Nonce NB|}|}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    60
                 # evs3 \<in> yahalom"
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    61
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    62
         (*Alice receives the Server's (?) message, checks her Nonce, and
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    63
           uses the new session key to send Bob his Nonce.*)
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    64
 | YM4:  "[| evs4 \<in> yahalom;
6335
7e4bffaa2a3e updating both Yahalom protocols to the Gets model
paulson
parents: 5434
diff changeset
    65
             Gets A {|Nonce NB, Crypt (shrK A) {|Agent B, Key K, Nonce NA|},
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    66
                      X|}  \<in> set evs4;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    67
             Says A B {|Agent A, Nonce NA|} \<in> set evs4 |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    68
          ==> Says A B {|X, Crypt K (Nonce NB)|} # evs4 \<in> yahalom"
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
    69
2155
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
    70
         (*This message models possible leaks of session keys.  The nonces
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
    71
           identify the protocol run.  Quoting Server here ensures they are
dc85854810eb New version with simpler disambiguation in YM3,
paulson
parents: 2111
diff changeset
    72
           correct. *)
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    73
 | Oops: "[| evso \<in> yahalom;
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    74
             Says Server A {|Nonce NB,
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2155
diff changeset
    75
                             Crypt (shrK A) {|Agent B, Key K, Nonce NA|},
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    76
                             X|}  \<in> set evso |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    77
          ==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso \<in> yahalom"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    78
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    79
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    80
declare Says_imp_knows_Spy [THEN analz.Inj, dest]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    81
declare parts.Body  [dest]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    82
declare Fake_parts_insert_in_Un  [dest]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    83
declare analz_into_parts [dest]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    84
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
    85
text{*A "possibility property": there are traces that reach the end*}
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 13956
diff changeset
    86
lemma "Key K \<notin> used []
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 13956
diff changeset
    87
       ==> \<exists>X NB. \<exists>evs \<in> yahalom.
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    88
             Says A B {|X, Crypt K (Nonce NB)|} \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    89
apply (intro exI bexI)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    90
apply (rule_tac [2] yahalom.Nil
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    91
                    [THEN yahalom.YM1, THEN yahalom.Reception,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    92
                     THEN yahalom.YM2, THEN yahalom.Reception,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    93
                     THEN yahalom.YM3, THEN yahalom.Reception,
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 13956
diff changeset
    94
                     THEN yahalom.YM4])
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
    95
apply (possibility, simp add: used_Cons)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    96
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    97
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    98
lemma Gets_imp_Says:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
    99
     "[| Gets B X \<in> set evs; evs \<in> yahalom |] ==> \<exists>A. Says A B X \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   100
by (erule rev_mp, erule yahalom.induct, auto)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   101
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   102
text{*Must be proved separately for each protocol*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   103
lemma Gets_imp_knows_Spy:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   104
     "[| Gets B X \<in> set evs; evs \<in> yahalom |]  ==> X \<in> knows Spy evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   105
by (blast dest!: Gets_imp_Says Says_imp_knows_Spy)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   106
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   107
declare Gets_imp_knows_Spy [THEN analz.Inj, dest]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   108
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   109
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   110
subsection{*Inductive Proofs*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   111
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   112
text{*Result for reasoning about the encrypted portion of messages.
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   113
Lets us treat YM4 using a similar argument as for the Fake case.*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   114
lemma YM4_analz_knows_Spy:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   115
     "[| Gets A {|NB, Crypt (shrK A) Y, X|} \<in> set evs;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   116
      ==> X \<in> analz (knows Spy evs)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   117
by blast
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   118
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   119
lemmas YM4_parts_knows_Spy =
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   120
       YM4_analz_knows_Spy [THEN analz_into_parts, standard]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   121
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   122
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   123
(** Theorems of the form X \<notin> parts (knows Spy evs) imply that NOBODY
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   124
    sends messages containing X! **)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   125
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   126
text{*Spy never sees a good agent's shared key!*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   127
lemma Spy_see_shrK [simp]:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   128
     "evs \<in> yahalom ==> (Key (shrK A) \<in> parts (knows Spy evs)) = (A \<in> bad)"
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   129
by (erule yahalom.induct, force,
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   130
    drule_tac [6] YM4_parts_knows_Spy, simp_all, blast+)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   131
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   132
lemma Spy_analz_shrK [simp]:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   133
     "evs \<in> yahalom ==> (Key (shrK A) \<in> analz (knows Spy evs)) = (A \<in> bad)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   134
by auto
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   135
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   136
lemma Spy_see_shrK_D [dest!]:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   137
     "[|Key (shrK A) \<in> parts (knows Spy evs);  evs \<in> yahalom|] ==> A \<in> bad"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   138
by (blast dest: Spy_see_shrK)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   139
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   140
text{*Nobody can have used non-existent keys!  
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   141
    Needed to apply @{text analz_insert_Key}*}
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   142
lemma new_keys_not_used [simp]:
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   143
    "[|Key K \<notin> used evs; K \<in> symKeys; evs \<in> yahalom|]
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   144
     ==> K \<notin> keysFor (parts (spies evs))"
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   145
apply (erule rev_mp)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   146
apply (erule yahalom.induct, force,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   147
       frule_tac [6] YM4_parts_knows_Spy, simp_all)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13907
diff changeset
   148
txt{*Fake*}
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13907
diff changeset
   149
apply (force dest!: keysFor_parts_insert)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   150
txt{*YM3*}
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   151
apply blast
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   152
txt{*YM4*}
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   153
apply auto
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   154
apply (blast dest!: Gets_imp_knows_Spy [THEN parts.Inj])
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   155
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   156
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   157
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   158
text{*Describes the form of K when the Server sends this message.  Useful for
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   159
  Oops as well as main secrecy property.*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   160
lemma Says_Server_message_form:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   161
     "[| Says Server A {|nb', Crypt (shrK A) {|Agent B, Key K, na|}, X|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   162
          \<in> set evs;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   163
      ==> K \<notin> range shrK"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   164
by (erule rev_mp, erule yahalom.induct, simp_all)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   165
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   166
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   167
(****
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   168
 The following is to prove theorems of the form
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   169
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   170
          Key K \<in> analz (insert (Key KAB) (knows Spy evs)) ==>
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   171
          Key K \<in> analz (knows Spy evs)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   172
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   173
 A more general formula must be proved inductively.
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   174
****)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   175
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   176
(** Session keys are not used to encrypt other session keys **)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   177
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   178
lemma analz_image_freshK [rule_format]:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   179
 "evs \<in> yahalom ==>
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   180
   \<forall>K KK. KK <= - (range shrK) -->
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   181
          (Key K \<in> analz (Key`KK Un (knows Spy evs))) =
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   182
          (K \<in> KK | Key K \<in> analz (knows Spy evs))"
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   183
apply (erule yahalom.induct)
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   184
apply (frule_tac [8] Says_Server_message_form)
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   185
apply (drule_tac [7] YM4_analz_knows_Spy, analz_freshK, spy_analz, blast)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   186
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   187
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   188
lemma analz_insert_freshK:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   189
     "[| evs \<in> yahalom;  KAB \<notin> range shrK |] ==>
11655
923e4d0d36d5 tuned parentheses in relational expressions;
wenzelm
parents: 11251
diff changeset
   190
      (Key K \<in> analz (insert (Key KAB) (knows Spy evs))) =
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   191
      (K = KAB | Key K \<in> analz (knows Spy evs))"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   192
by (simp only: analz_image_freshK analz_image_freshK_simps)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   193
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   194
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   195
text{*The Key K uniquely identifies the Server's  message*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   196
lemma unique_session_keys:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   197
     "[| Says Server A
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   198
          {|nb, Crypt (shrK A) {|Agent B, Key K, na|}, X|} \<in> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   199
        Says Server A'
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   200
          {|nb', Crypt (shrK A') {|Agent B', Key K, na'|}, X'|} \<in> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   201
        evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   202
     ==> A=A' & B=B' & na=na' & nb=nb'"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   203
apply (erule rev_mp, erule rev_mp)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   204
apply (erule yahalom.induct, simp_all)
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   205
txt{*YM3, by freshness*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   206
apply blast
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   207
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   208
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   209
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   210
subsection{*Crucial Secrecy Property: Spy Does Not See Key @{term KAB}*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   211
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   212
lemma secrecy_lemma:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   213
     "[| A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   214
      ==> Says Server A
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   215
            {|nb, Crypt (shrK A) {|Agent B, Key K, na|},
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   216
                  Crypt (shrK B) {|Agent A, Agent B, Key K, nb|}|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   217
           \<in> set evs -->
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   218
          Notes Spy {|na, nb, Key K|} \<notin> set evs -->
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   219
          Key K \<notin> analz (knows Spy evs)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   220
apply (erule yahalom.induct, force, frule_tac [7] Says_Server_message_form,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   221
       drule_tac [6] YM4_analz_knows_Spy)
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   222
apply (simp_all add: pushes analz_insert_eq analz_insert_freshK, spy_analz)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   223
apply (blast dest: unique_session_keys)+  (*YM3, Oops*)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   224
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   225
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   226
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   227
text{*Final version*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   228
lemma Spy_not_see_encrypted_key:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   229
     "[| Says Server A
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   230
            {|nb, Crypt (shrK A) {|Agent B, Key K, na|},
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   231
                  Crypt (shrK B) {|Agent A, Agent B, Key K, nb|}|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   232
         \<in> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   233
         Notes Spy {|na, nb, Key K|} \<notin> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   234
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   235
      ==> Key K \<notin> analz (knows Spy evs)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   236
by (blast dest: secrecy_lemma Says_Server_message_form)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   237
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   238
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   239
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   240
text{*This form is an immediate consequence of the previous result.  It is
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   241
similar to the assertions established by other methods.  It is equivalent
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   242
to the previous result in that the Spy already has @{term analz} and
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   243
@{term synth} at his disposal.  However, the conclusion
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   244
@{term "Key K \<notin> knows Spy evs"} appears not to be inductive: all the cases
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   245
other than Fake are trivial, while Fake requires
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   246
@{term "Key K \<notin> analz (knows Spy evs)"}. *}
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   247
lemma Spy_not_know_encrypted_key:
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   248
     "[| Says Server A
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   249
            {|nb, Crypt (shrK A) {|Agent B, Key K, na|},
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   250
                  Crypt (shrK B) {|Agent A, Agent B, Key K, nb|}|}
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   251
         \<in> set evs;
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   252
         Notes Spy {|na, nb, Key K|} \<notin> set evs;
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   253
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom |]
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   254
      ==> Key K \<notin> knows Spy evs"
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   255
by (blast dest: Spy_not_see_encrypted_key)
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   256
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   257
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   258
subsection{*Security Guarantee for A upon receiving YM3*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   259
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   260
text{*If the encrypted message appears then it originated with the Server.
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   261
  May now apply @{text Spy_not_see_encrypted_key}, subject to its conditions.*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   262
lemma A_trusts_YM3:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   263
     "[| Crypt (shrK A) {|Agent B, Key K, na|} \<in> parts (knows Spy evs);
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   264
         A \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   265
      ==> \<exists>nb. Says Server A
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   266
                    {|nb, Crypt (shrK A) {|Agent B, Key K, na|},
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   267
                          Crypt (shrK B) {|Agent A, Agent B, Key K, nb|}|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   268
                  \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   269
apply (erule rev_mp)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   270
apply (erule yahalom.induct, force,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   271
       frule_tac [6] YM4_parts_knows_Spy, simp_all)
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   272
txt{*Fake, YM3*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   273
apply blast+
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   274
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   275
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   276
text{*The obvious combination of @{text A_trusts_YM3} with 
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   277
@{text Spy_not_see_encrypted_key}*}
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   278
theorem A_gets_good_key:
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   279
     "[| Crypt (shrK A) {|Agent B, Key K, na|} \<in> parts (knows Spy evs);
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   280
         \<forall>nb. Notes Spy {|na, nb, Key K|} \<notin> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   281
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   282
      ==> Key K \<notin> analz (knows Spy evs)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   283
by (blast dest!: A_trusts_YM3 Spy_not_see_encrypted_key)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   284
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   285
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   286
subsection{*Security Guarantee for B upon receiving YM4*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   287
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   288
text{*B knows, by the first part of A's message, that the Server distributed
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   289
  the key for A and B, and has associated it with NB.*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   290
lemma B_trusts_YM4_shrK:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   291
     "[| Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   292
           \<in> parts (knows Spy evs);
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   293
         B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   294
  ==> \<exists>NA. Says Server A
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   295
             {|Nonce NB,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   296
               Crypt (shrK A) {|Agent B, Key K, Nonce NA|},
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   297
               Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   298
             \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   299
apply (erule rev_mp)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   300
apply (erule yahalom.induct, force,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   301
       frule_tac [6] YM4_parts_knows_Spy, simp_all)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   302
txt{*Fake, YM3*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   303
apply blast+
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   304
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   305
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   306
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   307
text{*With this protocol variant, we don't need the 2nd part of YM4 at all:
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   308
  Nonce NB is available in the first part.*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   309
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   310
text{*What can B deduce from receipt of YM4?  Stronger and simpler than Yahalom
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   311
  because we do not have to show that NB is secret. *}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   312
lemma B_trusts_YM4:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   313
     "[| Gets B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|},  X|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   314
           \<in> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   315
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   316
  ==> \<exists>NA. Says Server A
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   317
             {|Nonce NB,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   318
               Crypt (shrK A) {|Agent B, Key K, Nonce NA|},
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   319
               Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   320
            \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   321
by (blast dest!: B_trusts_YM4_shrK)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   322
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   323
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   324
text{*The obvious combination of @{text B_trusts_YM4} with 
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   325
@{text Spy_not_see_encrypted_key}*}
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   326
theorem B_gets_good_key:
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   327
     "[| Gets B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}, X|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   328
           \<in> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   329
         \<forall>na. Notes Spy {|na, Nonce NB, Key K|} \<notin> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   330
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   331
      ==> Key K \<notin> analz (knows Spy evs)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   332
by (blast dest!: B_trusts_YM4 Spy_not_see_encrypted_key)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   333
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   334
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   335
subsection{*Authenticating B to A*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   336
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   337
text{*The encryption in message YM2 tells us it cannot be faked.*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   338
lemma B_Said_YM2:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   339
     "[| Crypt (shrK B) {|Agent A, Nonce NA|} \<in> parts (knows Spy evs);
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   340
         B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   341
      ==> \<exists>NB. Says B Server {|Agent B, Nonce NB,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   342
                               Crypt (shrK B) {|Agent A, Nonce NA|}|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   343
                      \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   344
apply (erule rev_mp)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   345
apply (erule yahalom.induct, force,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   346
       frule_tac [6] YM4_parts_knows_Spy, simp_all)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   347
txt{*Fake, YM2*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   348
apply blast+
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   349
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   350
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   351
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   352
text{*If the server sends YM3 then B sent YM2, perhaps with a different NB*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   353
lemma YM3_auth_B_to_A_lemma:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   354
     "[| Says Server A {|nb, Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, X|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   355
           \<in> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   356
         B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   357
      ==> \<exists>nb'. Says B Server {|Agent B, nb',
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   358
                                   Crypt (shrK B) {|Agent A, Nonce NA|}|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   359
                       \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   360
apply (erule rev_mp)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   361
apply (erule yahalom.induct, simp_all)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   362
txt{*Fake, YM2, YM3*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   363
apply (blast dest!: B_Said_YM2)+
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   364
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   365
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   366
text{*If A receives YM3 then B has used nonce NA (and therefore is alive)*}
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   367
theorem YM3_auth_B_to_A:
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   368
     "[| Gets A {|nb, Crypt (shrK A) {|Agent B, Key K, Nonce NA|}, X|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   369
           \<in> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   370
         A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   371
 ==> \<exists>nb'. Says B Server
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   372
                  {|Agent B, nb', Crypt (shrK B) {|Agent A, Nonce NA|}|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   373
               \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   374
by (blast dest!: A_trusts_YM3 YM3_auth_B_to_A_lemma)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   375
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   376
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   377
subsection{*Authenticating A to B*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   378
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   379
text{*using the certificate @{term "Crypt K (Nonce NB)"}*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   380
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   381
text{*Assuming the session key is secure, if both certificates are present then
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   382
  A has said NB.  We can't be sure about the rest of A's message, but only
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   383
  NB matters for freshness.  Note that @{term "Key K \<notin> analz (knows Spy evs)"}
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   384
  must be the FIRST antecedent of the induction formula.*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   385
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   386
text{*This lemma allows a use of @{text unique_session_keys} in the next proof,
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   387
  which otherwise is extremely slow.*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   388
lemma secure_unique_session_keys:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   389
     "[| Crypt (shrK A) {|Agent B, Key K, na|} \<in> analz (spies evs);
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   390
         Crypt (shrK A') {|Agent B', Key K, na'|} \<in> analz (spies evs);
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   391
         Key K \<notin> analz (knows Spy evs);  evs \<in> yahalom |]
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   392
     ==> A=A' & B=B'"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   393
by (blast dest!: A_trusts_YM3 dest: unique_session_keys Crypt_Spy_analz_bad)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   394
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   395
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   396
lemma Auth_A_to_B_lemma [rule_format]:
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   397
     "evs \<in> yahalom
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   398
      ==> Key K \<notin> analz (knows Spy evs) -->
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   399
          K \<in> symKeys -->
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   400
          Crypt K (Nonce NB) \<in> parts (knows Spy evs) -->
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   401
          Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|}
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   402
            \<in> parts (knows Spy evs) -->
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   403
          B \<notin> bad -->
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   404
          (\<exists>X. Says A B {|X, Crypt K (Nonce NB)|} \<in> set evs)"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   405
apply (erule yahalom.induct, force,
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   406
       frule_tac [6] YM4_parts_knows_Spy)
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   407
apply (analz_mono_contra, simp_all)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   408
txt{*Fake*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   409
apply blast
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   410
txt{*YM3: by @{text new_keys_not_used}, the message
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   411
   @{term "Crypt K (Nonce NB)"} could not exist*}
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   412
apply (force dest!: Crypt_imp_keysFor)
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   413
txt{*YM4: was   @{term "Crypt K (Nonce NB)"} the very last message?  If so, 
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   414
    apply unicity of session keys; if not, use the induction hypothesis*}
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   415
apply (blast dest!: B_trusts_YM4_shrK dest: secure_unique_session_keys)
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   416
done
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   417
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   418
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   419
text{*If B receives YM4 then A has used nonce NB (and therefore is alive).
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   420
  Moreover, A associates K with NB (thus is talking about the same run).
13907
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   421
  Other premises guarantee secrecy of K.*}
2bc462b99e70 tidying
paulson
parents: 13507
diff changeset
   422
theorem YM4_imp_A_Said_YM3 [rule_format]:
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   423
     "[| Gets B {|Crypt (shrK B) {|Agent A, Agent B, Key K, Nonce NB|},
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   424
                  Crypt K (Nonce NB)|} \<in> set evs;
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   425
         (\<forall>NA. Notes Spy {|Nonce NA, Nonce NB, Key K|} \<notin> set evs);
14207
f20fbb141673 Conversion of all main protocols from "Shared" to "Public".
paulson
parents: 14200
diff changeset
   426
         K \<in> symKeys;  A \<notin> bad;  B \<notin> bad;  evs \<in> yahalom |]
11251
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   427
      ==> \<exists>X. Says A B {|X, Crypt K (Nonce NB)|} \<in> set evs"
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   428
by (blast intro: Auth_A_to_B_lemma
a6816d47f41d converted many HOL/Auth theories to Isar scripts
paulson
parents: 11185
diff changeset
   429
          dest: Spy_not_see_encrypted_key B_trusts_YM4_shrK)
2111
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   430
81c8d46edfa3 New version of Yahalom, as recommended on p 259 of BAN paper
paulson
parents:
diff changeset
   431
end