src/HOL/Auth/Shared.thy

Changing "lost" from a parameter of protocol definitions to a constant.

Advantages: no "lost" argument everywhere; fewer Vars in subgoals;
less need for specially instantiated rules
Disadvantage: can no longer prove "Agent_not_see_encrypted_key", but this
theorem was never used, and its original proof was also broken
the introduction of the "Notes" constructor.

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

Theory of Shared Keys (common to all symmetric-key protocols)

Shared, long-term keys; initial states of agents
*)

Shared = Event + Finite +

consts
  shrK    :: agent => key  (*symmetric keys*)

rules
  isSym_keys "isSymKey K"	(*All keys are symmetric*)
  inj_shrK   "inj shrK"		(*No two agents have the same long-term key*)

primrec initState agent
        (*Server knows all long-term keys; other agents know only their own*)
  initState_Server  "initState Server     = Key `` range shrK"
  initState_Friend  "initState (Friend i) = {Key (shrK (Friend i))}"
  initState_Spy     "initState Spy        = Key``shrK``lost"


rules
  (*Unlike the corresponding property of nonces, this cannot be proved.
    We have infinitely many agents and there is nothing to stop their
    long-term keys from exhausting all the natural numbers.  The axiom
    assumes that their keys are dispersed so as to leave room for infinitely
    many fresh session keys.  We could, alternatively, restrict agents to
    an unspecified finite number.*)
  Key_supply_ax  "finite KK ==> EX K. K ~: KK & Key K ~: used evs"

end