(* 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
(*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``bad"
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