author paulson
Fri, 29 Nov 1996 18:03:21 +0100
changeset 2284 80ebd1a213fd
parent 2121 7e118eb32bdc
child 2373 490ffa16952e
permissions -rw-r--r--
Swapped arguments of Crypt (for clarity and because it is conventional)

(*  Title:      HOL/Auth/Message
    ID:         $Id$
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1996  University of Cambridge

Datatypes of agents and messages;
Inductive relations "parts", "analz" and "synth"

Message = Arith +

(*Is there a difference between a nonce and arbitrary numerical data?
  Do we need a type of nonces?*)

  key = nat

  invKey :: key=>key

  invKey "invKey (invKey K) = K"

  (*The inverse of a symmetric key is itself;
    that of a public key is the private key and vice versa*)

  isSymKey :: key=>bool
  "isSymKey K == (invKey K = K)"

  (*We do not assume  Crypt (invKey K) (Crypt K X) = X
    because Crypt a is constructor!  We assume that encryption is injective,
    which is not true in the real world.  The alternative is to take
    Crypt an as uninterpreted function symbol satisfying the equation
    above.  This seems to require moving to ZF and regarding msg as an
    inductive definition instead of a datatype.*) 

datatype  (*We allow any number of friendly agents*)
  agent = Server | Friend nat | Spy

datatype  (*Messages are agent names, nonces, keys, pairs and encryptions*)
  msg = Agent agent
      | Nonce nat
      | Key   key
      | MPair msg msg
      | Crypt key msg

(*Allows messages of the form {|A,B,NA|}, etc...*)
  "@MTuple"      :: "['a, args] => 'a * 'b"            ("(2{|_,/ _|})")

  "{|x, y, z|}"   == "{|x, {|y, z|}|}"
  "{|x, y|}"      == "MPair x y"

constdefs  (*Keys useful to decrypt elements of a message set*)
  keysFor :: msg set => key set
  "keysFor H == invKey `` {K. EX X. Crypt K X : H}"

(** Inductive definition of all "parts" of a message.  **)

consts  parts   :: msg set => msg set
inductive "parts H"
    Inj     "X: H ==> X: parts H"
    Fst     "{|X,Y|} : parts H ==> X : parts H"
    Snd     "{|X,Y|} : parts H ==> Y : parts H"
    Body    "Crypt K X : parts H ==> X : parts H"

(** Inductive definition of "analz" -- what can be broken down from a set of
    messages, including keys.  A form of downward closure.  Pairs can
    be taken apart; messages decrypted with known keys.  **)

consts  analz   :: msg set => msg set
inductive "analz H"
    Inj     "X: H ==> X: analz H"
    Fst     "{|X,Y|} : analz H ==> X : analz H"
    Snd     "{|X,Y|} : analz H ==> Y : analz H"
    Decrypt "[| Crypt K X : analz H; Key(invKey K): analz H |] ==> X : analz H"

(** Inductive definition of "synth" -- what can be built up from a set of
    messages.  A form of upward closure.  Pairs can be built, messages
    encrypted with known keys.  Agent names may be quoted.  **)

consts  synth   :: msg set => msg set
inductive "synth H"
    Inj     "X: H ==> X: synth H"
    Agent   "Agent agt : synth H"
    MPair   "[| X: synth H;  Y: synth H |] ==> {|X,Y|} : synth H"
    Crypt   "[| X: synth H; Key(K): H |] ==> Crypt K X : synth H"