Some X-symbols for <notin>, <noteq>, <forall>, <exists>
Streamlining of Yahalom proofs
Removal of redundant proofs
(* Title: HOL/Auth/OtwayRees_Bad
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1996 University of Cambridge
Inductive relation "otway" for the Otway-Rees protocol.
The FAULTY version omitting encryption of Nonce NB, as suggested on page 247 of
Burrows, Abadi and Needham. A Logic of Authentication.
Proc. Royal Soc. 426 (1989)
*)
OtwayRees_Bad = Shared +
consts otway :: event list set
inductive otway
intrs
(*Initial trace is empty*)
Nil "[] \\<in> otway"
(*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 "[| evsf \\<in> otway; X \\<in> synth (analz (knows Spy evsf)) |]
==> Says Spy B X # evsf \\<in> otway"
(*A message that has been sent can be received by the
intended recipient.*)
Reception "[| evsr \\<in> otway; Says A B X \\<in> set evsr |]
==> Gets B X # evsr \\<in> otway"
(*Alice initiates a protocol run*)
OR1 "[| evs1 \\<in> otway; Nonce NA \\<notin> used evs1 |]
==> Says A B {|Nonce NA, Agent A, Agent B,
Crypt (shrK A) {|Nonce NA, Agent A, Agent B|} |}
# evs1 \\<in> otway"
(*Bob's response to Alice's message.
This variant of the protocol does NOT encrypt NB.*)
OR2 "[| evs2 \\<in> otway; Nonce NB \\<notin> used evs2;
Gets B {|Nonce NA, Agent A, Agent B, X|} \\<in> set evs2 |]
==> Says B Server
{|Nonce NA, Agent A, Agent B, X, Nonce NB,
Crypt (shrK B) {|Nonce NA, Agent A, Agent B|}|}
# evs2 \\<in> otway"
(*The Server receives Bob's message and checks that the three NAs
match. Then he sends a new session key to Bob with a packet for
forwarding to Alice.*)
OR3 "[| evs3 \\<in> otway; Key KAB \\<notin> used evs3;
Gets Server
{|Nonce NA, Agent A, Agent B,
Crypt (shrK A) {|Nonce NA, Agent A, Agent B|},
Nonce NB,
Crypt (shrK B) {|Nonce NA, Agent A, Agent B|}|}
\\<in> set evs3 |]
==> Says Server B
{|Nonce NA,
Crypt (shrK A) {|Nonce NA, Key KAB|},
Crypt (shrK B) {|Nonce NB, Key KAB|}|}
# evs3 \\<in> otway"
(*Bob receives the Server's (?) message and compares the Nonces with
those in the message he previously sent the Server.
Need B ~= Server because we allow messages to self.*)
OR4 "[| evs4 \\<in> otway; B ~= Server;
Says B Server {|Nonce NA, Agent A, Agent B, X', Nonce NB,
Crypt (shrK B) {|Nonce NA, Agent A, Agent B|}|}
\\<in> set evs4;
Gets B {|Nonce NA, X, Crypt (shrK B) {|Nonce NB, Key K|}|}
\\<in> set evs4 |]
==> Says B A {|Nonce NA, X|} # evs4 \\<in> otway"
(*This message models possible leaks of session keys. The nonces
identify the protocol run.*)
Oops "[| evso \\<in> otway;
Says Server B {|Nonce NA, X, Crypt (shrK B) {|Nonce NB, Key K|}|}
\\<in> set evso |]
==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso \\<in> otway"
end