(* 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 :: agent set => event list set
inductive "yahalom lost"
intrs
(*Initial trace is empty*)
Nil "[]: yahalom 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: yahalom lost; B ~= Spy;
X: synth (analz (sees lost Spy evs)) |]
==> Says Spy B X # evs : yahalom lost"
(*Alice initiates a protocol run*)
YM1 "[| evs: yahalom lost; A ~= B; Nonce NA ~: used evs |]
==> Says A B {|Agent A, Nonce NA|} # evs : yahalom lost"
(*Bob's response to Alice's message. Bob doesn't know who
the sender is, hence the A' in the sender field.*)
YM2 "[| evs: yahalom lost; B ~= Server; Nonce NB ~: used evs;
Says A' B {|Agent A, Nonce NA|} : set evs |]
==> Says B Server
{|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
# evs : yahalom lost"
(*The Server receives Bob's message. He responds by sending a
new session key to Alice, with a packet for forwarding to Bob.*)
YM3 "[| evs: yahalom lost; A ~= Server; Key KAB ~: used evs;
Says B' Server
{|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
: set evs |]
==> Says Server A
{|Crypt (shrK A) {|Agent B, Key KAB, Nonce NA, Nonce NB|},
Crypt (shrK B) {|Agent A, Key KAB|}|}
# evs : yahalom lost"
(*Alice receives the Server's (?) message, checks her Nonce, and
uses the new session key to send Bob his Nonce.*)
YM4 "[| evs: yahalom lost; A ~= Server; A ~= B;
Says S A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, Nonce NB|},
X|} : set evs;
Says A B {|Agent A, Nonce NA|} : set evs |]
==> Says A B {|X, Crypt K (Nonce NB)|} # evs : yahalom lost"
(*This message models possible leaks of session keys. The Nonces
identify the protocol run. Quoting Server here ensures they are
correct.*)
Oops "[| evs: yahalom lost; A ~= Spy;
Says Server A {|Crypt (shrK A)
{|Agent B, Key K, Nonce NA, Nonce NB|},
X|} : set evs |]
==> Says A Spy {|Nonce NA, Nonce NB, Key K|} # evs : yahalom lost"
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