(* 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 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; X: synth (analz (spies evs)) |]
==> Says Spy B X # evs : ns_shared"
(*Alice initiates a protocol run, requesting to talk to any B*)
NS1 "[| evs1: ns_shared; Nonce NA ~: used evs1 |]
==> Says A Server {|Agent A, Agent B, Nonce NA|} # evs1
: 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 "[| evs2: ns_shared; Key KAB ~: used evs2;
Says A' Server {|Agent A, Agent B, Nonce NA|} : set evs2 |]
==> Says Server A
(Crypt (shrK A)
{|Nonce NA, Agent B, Key KAB,
(Crypt (shrK B) {|Key KAB, Agent A|})|})
# evs2 : ns_shared"
(*We can't assume S=Server. Agent A "remembers" her nonce.
Need A ~= Server because we allow messages to self.*)
NS3 "[| evs3: ns_shared; A ~= Server;
Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})
: set evs3;
Says A Server {|Agent A, Agent B, Nonce NA|} : set evs3 |]
==> Says A B X # evs3 : 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 "[| evs4: ns_shared; Nonce NB ~: used evs4;
Says A' B (Crypt (shrK B) {|Key K, Agent A|}) : set evs4 |]
==> Says B A (Crypt K (Nonce NB)) # evs4
: ns_shared"
(*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 "[| evs5: ns_shared;
Says B' A (Crypt K (Nonce NB)) : set evs5;
Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})
: set evs5 |]
==> Says A B (Crypt K {|Nonce NB, Nonce NB|}) # evs5 : ns_shared"
(*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 "[| evso: ns_shared; Says B A (Crypt K (Nonce NB)) : set evso;
Says Server A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})
: set evso |]
==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso : ns_shared"
end