(* Title: HOL/Auth/Message
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1996 University of Cambridge
Datatype of events;
inductive relation "traces" for Needham-Schroeder (shared keys)
WHAT ABOUT ASYMMETRIC KEYS? NOBODY'S PRIVATE KEY CAN EQUAL SOMEBODY ELSE'S
PUBLIC KEY...
*)
Event = Message + List +
consts
publicKey :: agent => key
serverKey :: agent => key (*symmetric keys*)
rules
isSym_serverKey "isSymKey (serverKey A)"
consts (*Initial states of agents -- parameter of the construction*)
initState :: agent => msg set
primrec initState agent
(*Server knows all keys; other agents know only their own*)
initState_Server "initState Server = range (Key o serverKey)"
initState_Friend "initState (Friend i) = {Key (serverKey (Friend i))}"
initState_Enemy "initState Enemy = {Key (serverKey Enemy)}"
(**
For asymmetric keys: server knows all public and private keys,
others know their private key and perhaps all public keys
**)
datatype (*Messages, and components of agent stores*)
event = Says agent agent msg
| Notes agent msg
consts
sees1 :: [agent, event] => msg set
primrec sees1 event
(*First agent recalls all that it says, but NOT everything
that is sent to it; it must note such things if/when received*)
sees1_Says "sees1 A (Says A' B X) = (if A:{A',Enemy} then {X} else {})"
(*part of A's internal state*)
sees1_Notes "sees1 A (Notes A' X) = (if A=A' then {X} else {})"
consts
sees :: [agent, event list] => msg set
primrec sees list
(*Initial knowledge includes all public keys and own private key*)
sees_Nil "sees A [] = initState A"
sees_Cons "sees A (ev#evs) = sees1 A ev Un sees A evs"
constdefs
knownBy :: [event list, msg] => agent set
"knownBy evs X == {A. X: analyze (sees A evs)}"
(*Agents generate "random" nonces. Different agents always generate
different nonces. Different traces also yield different nonces. Same
applies for keys.*)
(*newK NEEDS AN ARGUMENT TO ALLOW ASYMMETRIC KEYS. REMOVE AGENT ARGUMENT?
NEED AXIOM SAYING THAT NEW KEYS CANNOT EQUAL THE INVERSE OF A PREVIOUS KEY*)
consts
newN :: "agent * event list => nat"
newK :: "agent * event list => key"
rules
inj_serverKey "inj serverKey"
inj_newN "inj(newN)"
fresh_newN "Nonce (newN(A,evs)) ~: parts (initState B)"
inj_newK "inj(newK)"
fresh_newK "Key (newK(A,evs)) ~: parts (initState B)"
isSym_newK "isSymKey (newK(A,evs))"
consts traces :: "event list set"
inductive traces
intrs
Nil "[]: traces"
(*The enemy MAY say anything he CAN say. We do not expect him to
invent new nonces here, but he can also use NS1.*)
Fake "[| evs: traces; X: synthesize(analyze(sees Enemy evs))
|] ==> (Says Enemy B X) # evs : traces"
NS1 "[| evs: traces; A ~= Server
|] ==> (Says A Server {|Agent A, Agent B, Nonce (newN(A,evs))|})
# evs : traces"
NS2 "[| evs: traces;
evs = (Says A Server {|Agent A, Agent B, Nonce NA|}) # evs'
|] ==> (Says Server A
(Crypt {|Agent A, Agent B,
Key (newK(Server,evs)), Nonce NA|}
(serverKey A))) # evs : traces"
end