(* 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)
Server keys; initial states of agents; new nonces and keys; function "sees"
*)
Shared = Message + List + Finite +
consts
shrK :: agent => key (*symmetric keys*)
rules
(*ALL keys are symmetric*)
isSym_keys "isSymKey K"
consts (*Initial states of agents -- parameter of the construction*)
initState :: [agent set, agent] => msg set
primrec initState agent
(*Server knows all long-term keys; other agents know only their own*)
initState_Server "initState lost Server = Key `` range shrK"
initState_Friend "initState lost (Friend i) = {Key (shrK (Friend i))}"
initState_Spy "initState lost Spy = Key``shrK``lost"
datatype (*Messages, and components of agent stores*)
event = Says agent agent msg
consts
sees1 :: [agent, event] => msg set
primrec sees1 event
(*Spy reads all traffic whether addressed to him or not*)
sees1_Says "sees1 A (Says A' B X) = (if A:{B,Spy} then {X} else {})"
consts
sees :: [agent set, agent, event list] => msg set
primrec sees list
sees_Nil "sees lost A [] = initState lost A"
sees_Cons "sees lost A (ev#evs) = sees1 A ev Un sees lost A evs"
constdefs
(*Set of items that might be visible to somebody: complement of the set
of fresh items*)
used :: event list => msg set
"used evs == parts (UN lost B. sees lost B evs)"
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"
(*Agents generate random (symmetric) keys and nonces.
The numeric argument is typically the length of the current trace.
An injective pairing function allows multiple keys/nonces to be generated
in one protocol round. A typical candidate for npair(i,j) is
2^j(2i+1)
*)
consts
nPair :: "nat*nat => nat"
newN :: "nat => nat"
newK :: "nat => key"
rules
inj_shrK "inj shrK"
inj_nPair "inj nPair"
inj_newN "inj newN"
inj_newK "inj newK"
newK_neq_shrK "newK i ~= shrK A"
end