src/HOL/Auth/Message.thy
author paulson
Fri Oct 16 12:20:41 1998 +0200 (1998-10-16)
changeset 5652 fe5f5510aef4
parent 5234 701fa0ed77b7
child 6807 6737af18317e
permissions -rw-r--r--
parent is Main
     1 (*  Title:      HOL/Auth/Message
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1996  University of Cambridge
     5 
     6 Datatypes of agents and messages;
     7 Inductive relations "parts", "analz" and "synth"
     8 *)
     9 
    10 Message = Main +
    11 
    12 types 
    13   key = nat
    14 
    15 consts
    16   invKey :: key=>key
    17 
    18 rules
    19   invKey "invKey (invKey K) = K"
    20 
    21   (*The inverse of a symmetric key is itself;
    22     that of a public key is the private key and vice versa*)
    23 
    24 constdefs
    25   isSymKey :: key=>bool
    26   "isSymKey K == (invKey K = K)"
    27 
    28 datatype  (*We allow any number of friendly agents*)
    29   agent = Server | Friend nat | Spy
    30 
    31 
    32 (*Datatype msg is (awkwardly) split into two parts to avoid having freeness
    33   expressed using natural numbers.*)
    34 datatype  
    35   atomic = AGENT  agent	(*Agent names*)
    36          | NUMBER nat   (*Ordinary integers, timestamps, ...*)
    37          | NONCE  nat   (*Unguessable nonces*)
    38          | KEY    key   (*Crypto keys*)
    39 
    40 datatype
    41      msg = Atomic atomic
    42 	 | Hash   msg       (*Hashing*)
    43 	 | MPair  msg msg   (*Compound messages*)
    44 	 | Crypt  key msg   (*Encryption, public- or shared-key*)
    45 
    46 (*These translations complete the illustion that "msg" has seven constructors*)
    47 syntax
    48   Agent       :: agent => msg
    49   Number      :: nat   => msg
    50   Nonce       :: nat   => msg
    51   Key         :: key   => msg
    52 
    53 translations
    54   "Agent x"   == "Atomic (AGENT x)"
    55   "Number x"  == "Atomic (NUMBER x)"
    56   "Nonce x"   == "Atomic (NONCE x)"
    57   "Key x"     == "Atomic (KEY x)"
    58   "Key``x"    == "Atomic `` (KEY `` x)"
    59 
    60 
    61 (*Concrete syntax: messages appear as {|A,B,NA|}, etc...*)
    62 syntax
    63   "@MTuple"      :: "['a, args] => 'a * 'b"       ("(2{|_,/ _|})")
    64 
    65 translations
    66   "{|x, y, z|}"   == "{|x, {|y, z|}|}"
    67   "{|x, y|}"      == "MPair x y"
    68 
    69 
    70 constdefs
    71   (*Message Y, paired with a MAC computed with the help of X*)
    72   HPair :: "[msg,msg]=>msg"                       ("(4Hash[_] /_)" [0, 1000])
    73     "Hash[X] Y == {| Hash{|X,Y|}, Y|}"
    74 
    75   (*Keys useful to decrypt elements of a message set*)
    76   keysFor :: msg set => key set
    77   "keysFor H == invKey `` {K. EX X. Crypt K X : H}"
    78 
    79 (** Inductive definition of all "parts" of a message.  **)
    80 
    81 consts  parts   :: msg set => msg set
    82 inductive "parts H"
    83   intrs 
    84     Inj     "X: H  ==>  X: parts H"
    85     Fst     "{|X,Y|}   : parts H ==> X : parts H"
    86     Snd     "{|X,Y|}   : parts H ==> Y : parts H"
    87     Body    "Crypt K X : parts H ==> X : parts H"
    88 
    89 
    90 (** Inductive definition of "analz" -- what can be broken down from a set of
    91     messages, including keys.  A form of downward closure.  Pairs can
    92     be taken apart; messages decrypted with known keys.  **)
    93 
    94 consts  analz   :: msg set => msg set
    95 inductive "analz H"
    96   intrs 
    97     Inj     "X: H ==> X: analz H"
    98     Fst     "{|X,Y|} : analz H ==> X : analz H"
    99     Snd     "{|X,Y|} : analz H ==> Y : analz H"
   100     Decrypt "[| Crypt K X : analz H; Key(invKey K): analz H |] ==> X : analz H"
   101 
   102 
   103 (** Inductive definition of "synth" -- what can be built up from a set of
   104     messages.  A form of upward closure.  Pairs can be built, messages
   105     encrypted with known keys.  Agent names are public domain.
   106     Numbers can be guessed, but Nonces cannot be.  **)
   107 
   108 consts  synth   :: msg set => msg set
   109 inductive "synth H"
   110   intrs 
   111     Inj     "X: H ==> X: synth H"
   112     Agent   "Agent agt : synth H"
   113     Number  "Number n  : synth H"
   114     Hash    "X: synth H ==> Hash X : synth H"
   115     MPair   "[| X: synth H;  Y: synth H |] ==> {|X,Y|} : synth H"
   116     Crypt   "[| X: synth H;  Key(K) : H |] ==> Crypt K X : synth H"
   117 
   118 end