(* 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 "[]: 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 "[| evs: yahalom; X: synth (analz (spies evs)) |]
==> Says Spy B X # evs : yahalom"
(*Alice initiates a protocol run*)
YM1 "[| evs1: yahalom; Nonce NA ~: used evs1 |]
==> Says A B {|Agent A, Nonce NA|} # evs1 : yahalom"
(*Bob's response to Alice's message. Bob doesn't know who
the sender is, hence the A' in the sender field.*)
YM2 "[| evs2: yahalom; Nonce NB ~: used evs2;
Says A' B {|Agent A, Nonce NA|} : set evs2 |]
==> Says B Server
{|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
# evs2 : 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: yahalom; Key KAB ~: used evs3;
Says B' Server
{|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
: set evs3 |]
==> Says Server A
{|Crypt (shrK A) {|Agent B, Key KAB, Nonce NA, Nonce NB|},
Crypt (shrK B) {|Agent A, Key KAB|}|}
# evs3 : yahalom"
(*Alice receives the Server's (?) message, checks her Nonce, and
uses the new session key to send Bob his Nonce. The premise
A ~= Server is needed to prove Says_Server_not_range.*)
YM4 "[| evs4: yahalom; A ~= Server;
Says S A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, Nonce NB|},
X|} : set evs4;
Says A B {|Agent A, Nonce NA|} : set evs4 |]
==> Says A B {|X, Crypt K (Nonce NB)|} # evs4 : yahalom"
(*This message models possible leaks of session keys. The Nonces
identify the protocol run. Quoting Server here ensures they are
correct.*)
Oops "[| evso: yahalom;
Says Server A {|Crypt (shrK A)
{|Agent B, Key K, Nonce NA, Nonce NB|},
X|} : set evso |]
==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso : yahalom"
constdefs
KeyWithNonce :: [key, nat, event list] => bool
"KeyWithNonce K NB evs ==
EX A B na X.
Says Server A {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|}
: set evs"
end