(* Title: HOL/Auth/NS_Shared
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1996 University of Cambridge
Inductive relation "ns_shared" for Needham-Schroeder Shared-Key protocol.
From page 247 of
Burrows, Abadi and Needham. A Logic of Authentication.
Proc. Royal Soc. 426 (1989)
*)
NS_Shared = Shared +
consts ns_shared :: "event list set"
inductive ns_shared
intrs
(*Initial trace is empty*)
Nil "[]: ns_shared"
(*The enemy MAY say anything he CAN say. We do not expect him to
invent new nonces here, but he can also use NS1. Common to
all similar protocols.*)
Fake "[| evs: ns_shared; B ~= Enemy; X: synth (analz (sees Enemy evs))
|] ==> Says Enemy B X # evs : ns_shared"
(*Alice initiates a protocol run, requesting to talk to any B*)
NS1 "[| evs: ns_shared; A ~= Server
|] ==> Says A Server {|Agent A, Agent B, Nonce (newN evs)|} # evs
: ns_shared"
(*Server's response to Alice's message.
!! It may respond more than once to A's request !!
Server doesn't know who the true sender is, hence the A' in
the sender field.*)
NS2 "[| evs: ns_shared; A ~= B; A ~= Server;
Says A' Server {|Agent A, Agent B, Nonce NA|} : set_of_list evs
|] ==> Says Server A
(Crypt {|Nonce NA, Agent B, Key (newK evs),
(Crypt {|Key (newK evs), Agent A|} (shrK B))|}
(shrK A)) # evs : ns_shared"
(*We can't assume S=Server. Agent A "remembers" her nonce.
May assume WLOG that she is NOT the Enemy: the Fake rule
covers this case. Can inductively show A ~= Server*)
NS3 "[| evs: ns_shared; A ~= B;
Says S A (Crypt {|Nonce NA, Agent B, Key K, X|} (shrK A))
: set_of_list evs;
A = Friend i;
Says A Server {|Agent A, Agent B, Nonce NA|} : set_of_list evs
|] ==> Says A B X # evs : ns_shared"
(*Bob's nonce exchange. He does not know who the message came
from, but responds to A because she is mentioned inside.*)
NS4 "[| evs: ns_shared; A ~= B;
Says A' B (Crypt {|Key K, Agent A|} (shrK B)) : set_of_list evs
|] ==> Says B A (Crypt (Nonce (newN evs)) K) # evs : ns_shared"
(*Alice responds with the Nonce, if she has seen the key before.
We do NOT use N-1 or similar as the Enemy cannot spoof such things.
Allowing the Enemy to add or subtract 1 allows him to send ALL
nonces. Instead we distinguish the messages by sending the
nonce twice.*)
NS5 "[| evs: ns_shared; A ~= B;
Says B' A (Crypt (Nonce N) K) : set_of_list evs;
Says S A (Crypt {|Nonce NA, Agent B, Key K, X|} (shrK A))
: set_of_list evs
|] ==> Says A B (Crypt {|Nonce N, Nonce N|} K) # evs : ns_shared"
end