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src/HOL/Auth/Message.thy

author | paulson |

Mon, 23 Sep 1996 18:18:18 +0200 | |

changeset 2010 | 0a22b9d63a18 |

parent 1947 | f19a801a2bca |

child 2032 | 1bbf1bdcaf56 |

permissions | -rw-r--r-- |

Simplification of definition of synth

(* 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