(* 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 :: agent set => event list set
inductive "ns_shared lost"
intrs
(*Initial trace is empty*)
Nil "[]: ns_shared lost"
(*The spy 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 lost; B ~= Spy;
X: synth (analz (sees lost Spy evs)) |]
==> Says Spy B X # evs : ns_shared lost"
(*Alice initiates a protocol run, requesting to talk to any B*)
NS1 "[| evs: ns_shared lost; A ~= Server |]
==> Says A Server {|Agent A, Agent B, Nonce (newN evs)|} # evs
: ns_shared lost"
(*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 lost; A ~= B; A ~= Server;
Says A' Server {|Agent A, Agent B, Nonce NA|} : set_of_list evs |]
==> Says Server A (Crypt (shrK A)
{|Nonce NA, Agent B, Key (newK evs),
(Crypt (shrK B) {|Key (newK evs), Agent A|})|})
# evs : ns_shared lost"
(*We can't assume S=Server. Agent A "remembers" her nonce.
Can inductively show A ~= Server*)
NS3 "[| evs: ns_shared lost; A ~= B;
Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})
: set_of_list evs;
Says A Server {|Agent A, Agent B, Nonce NA|} : set_of_list evs |]
==> Says A B X # evs : ns_shared lost"
(*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 lost; A ~= B;
Says A' B (Crypt (shrK B) {|Key K, Agent A|}) : set_of_list evs |]
==> Says B A (Crypt K (Nonce (newN evs))) # evs : ns_shared lost"
(*Alice responds with Nonce NB if she has seen the key before.
Maybe should somehow check Nonce NA again.
We do NOT send NB-1 or similar as the Spy cannot spoof such things.
Letting the Spy add or subtract 1 lets him send ALL nonces.
Instead we distinguish the messages by sending the nonce twice.*)
NS5 "[| evs: ns_shared lost; A ~= B;
Says B' A (Crypt K (Nonce NB)) : set_of_list evs;
Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})
: set_of_list evs |]
==> Says A B (Crypt K {|Nonce NB, Nonce NB|}) # evs : ns_shared lost"
(*This message models possible leaks of session keys.
The two Nonces identify the protocol run: the rule insists upon
the true senders in order to make them accurate.*)
Oops "[| evs: ns_shared lost; A ~= Spy;
Says B A (Crypt K (Nonce NB)) : set_of_list evs;
Says Server A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})
: set_of_list evs |]
==> Says A Spy {|Nonce NA, Nonce NB, Key K|} # evs : ns_shared lost"
end