Some X-symbols for <notin>, <noteq>, <forall>, <exists>
Streamlining of Yahalom proofs
Removal of redundant proofs
(* Title: HOL/Auth/Yahalom
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1996 University of Cambridge
Inductive relation "yahalom" for the Yahalom protocol.
From page 257 of
Burrows, Abadi and Needham. A Logic of Authentication.
Proc. Royal Soc. 426 (1989)
*)
Yahalom = Shared +
consts yahalom :: event list set
inductive "yahalom"
intrs
(*Initial trace is empty*)
Nil "[] \\<in> yahalom"
(*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> yahalom; X \\<in> synth (analz (knows Spy evsf)) |]
==> Says Spy B X # evsf \\<in> yahalom"
(*A message that has been sent can be received by the
intended recipient.*)
Reception "[| evsr \\<in> yahalom; Says A B X \\<in> set evsr |]
==> Gets B X # evsr \\<in> yahalom"
(*Alice initiates a protocol run*)
YM1 "[| evs1 \\<in> yahalom; Nonce NA \\<notin> used evs1 |]
==> Says A B {|Agent A, Nonce NA|} # evs1 \\<in> yahalom"
(*Bob's response to Alice's message.*)
YM2 "[| evs2 \\<in> yahalom; Nonce NB \\<notin> used evs2;
Gets B {|Agent A, Nonce NA|} \\<in> set evs2 |]
==> Says B Server
{|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
# evs2 \\<in> yahalom"
(*The Server receives Bob's message. He responds by sending a
new session key to Alice, with a packet for forwarding to Bob.*)
YM3 "[| evs3 \\<in> yahalom; Key KAB \\<notin> used evs3;
Gets Server
{|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
\\<in> set evs3 |]
==> Says Server A
{|Crypt (shrK A) {|Agent B, Key KAB, Nonce NA, Nonce NB|},
Crypt (shrK B) {|Agent A, Key KAB|}|}
# evs3 \\<in> yahalom"
(*Alice receives the Server's (?) message, checks her Nonce, and
uses the new session key to send Bob his Nonce. The premise
A \\<noteq> Server is needed to prove Says_Server_not_range.*)
YM4 "[| evs4 \\<in> yahalom; A \\<noteq> Server;
Gets A {|Crypt(shrK A) {|Agent B, Key K, Nonce NA, Nonce NB|}, X|}
\\<in> set evs4;
Says A B {|Agent A, Nonce NA|} \\<in> set evs4 |]
==> Says A B {|X, Crypt K (Nonce NB)|} # evs4 \\<in> yahalom"
(*This message models possible leaks of session keys. The Nonces
identify the protocol run. Quoting Server here ensures they are
correct.*)
Oops "[| evso \\<in> yahalom;
Says Server A {|Crypt (shrK A)
{|Agent B, Key K, Nonce NA, Nonce NB|},
X|} \\<in> set evso |]
==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso \\<in> yahalom"
constdefs
KeyWithNonce :: [key, nat, event list] => bool
"KeyWithNonce K NB evs ==
\\<exists>A B na X.
Says Server A {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|}
\\<in> set evs"
end