(* 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?*)
types
key = nat
consts
invKey :: key=>key
rules
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*)
constdefs
isSymKey :: key=>bool
"isSymKey K == (invKey K = K)"
(*We do not assume Crypt (Crypt X K) (invKey K) = X
because Crypt is a constructor! We assume that encryption is injective,
which is not true in the real world. The alternative is to take
Crypt as an 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 | Enemy
consts
isEnemy :: agent => bool
primrec isEnemy agent
isEnemy_Server "isEnemy Server = False"
isEnemy_Friend "isEnemy (Friend i) = False"
isEnemy_Enemy "isEnemy Enemy = True"
datatype (*Messages are agent names, nonces, keys, pairs and encryptions*)
msg = Agent agent
| Nonce nat
| Key key
| MPair msg msg
| Crypt msg key
(*Allows messages of the form {|A,B,NA|}, etc...*)
syntax
"@MTuple" :: "['a, args] => 'a * 'b" ("(2{|_,/ _|})")
translations
"{|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 X K : H}"
(** Inductive definition of all "parts" of a message. **)
consts parts :: msg set => msg set
inductive "parts H"
intrs
Inj "X: H ==> X: parts H"
Fst "{|X,Y|} : parts H ==> X : parts H"
Snd "{|X,Y|} : parts H ==> Y : parts H"
Body "Crypt X K : 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"
intrs
Inj "X: H ==> X: analz H"
Fst "{|X,Y|} : analz H ==> X : analz H"
Snd "{|X,Y|} : analz H ==> Y : analz H"
Decrypt "[| Crypt X K : 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"
intrs
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 X K : synth H"
end