(* Title: HOL/Auth/WooLam
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1996 University of Cambridge
Inductive relation "woolam" for the Woo-Lam protocol.
Simplified version from page 11 of
Abadi and Needham. Prudent Engineering Practice for Cryptographic Protocols.
IEEE Trans. S.E. 22(1), 1996, pages 6-15.
*)
open WooLam;
set proof_timing;
HOL_quantifiers := false;
AddEs spies_partsEs;
AddDs [impOfSubs analz_subset_parts];
AddDs [impOfSubs Fake_parts_insert];
(*A "possibility property": there are traces that reach the end*)
Goal "[| A ~= B; A ~= Server; B ~= Server |] \
\ ==> EX NB. EX evs: woolam. \
\ Says Server B (Crypt (shrK B) {|Agent A, Nonce NB|}) : set evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
by (rtac (woolam.Nil RS woolam.WL1 RS woolam.WL2 RS woolam.WL3 RS
woolam.WL4 RS woolam.WL5) 2);
by possibility_tac;
result();
(**** Inductive proofs about woolam ****)
(*Nobody sends themselves messages*)
Goal "evs : woolam ==> ALL A X. Says A A X ~: set evs";
by (etac woolam.induct 1);
by Auto_tac;
qed_spec_mp "not_Says_to_self";
Addsimps [not_Says_to_self];
AddSEs [not_Says_to_self RSN (2, rev_notE)];
(** For reasoning about the encrypted portion of messages **)
Goal "Says A' B X : set evs ==> X : analz (spies evs)";
by (etac (Says_imp_spies RS analz.Inj) 1);
qed "WL4_analz_spies";
bind_thm ("WL4_parts_spies",
WL4_analz_spies RS (impOfSubs analz_subset_parts));
(*For proving the easier theorems about X ~: parts (spies evs) *)
fun parts_induct_tac i =
etac woolam.induct i THEN
forward_tac [WL4_parts_spies] (i+5) THEN
prove_simple_subgoals_tac 1;
(** Theorems of the form X ~: parts (spies evs) imply that NOBODY
sends messages containing X! **)
(*Spy never sees another agent's shared key! (unless it's bad at start)*)
Goal "evs : woolam ==> (Key (shrK A) : parts (spies evs)) = (A : bad)";
by (parts_induct_tac 1);
by (Blast_tac 1);
qed "Spy_see_shrK";
Addsimps [Spy_see_shrK];
Goal "evs : woolam ==> (Key (shrK A) : analz (spies evs)) = (A : bad)";
by Auto_tac;
qed "Spy_analz_shrK";
Addsimps [Spy_analz_shrK];
AddSDs [Spy_see_shrK RSN (2, rev_iffD1),
Spy_analz_shrK RSN (2, rev_iffD1)];
(**** Autheticity properties for Woo-Lam ****)
(*** WL4 ***)
(*If the encrypted message appears then it originated with Alice*)
Goal "[| Crypt (shrK A) (Nonce NB) : parts (spies evs); \
\ A ~: bad; evs : woolam |] \
\ ==> EX B. Says A B (Crypt (shrK A) (Nonce NB)) : set evs";
by (etac rev_mp 1);
by (parts_induct_tac 1);
by (ALLGOALS Blast_tac);
qed "NB_Crypt_imp_Alice_msg";
(*Guarantee for Server: if it gets a message containing a certificate from
Alice, then she originated that certificate. But we DO NOT know that B
ever saw it: the Spy may have rerouted the message to the Server.*)
Goal "[| Says B' Server {|Agent A, Agent B, Crypt (shrK A) (Nonce NB)|} \
\ : set evs; \
\ A ~: bad; evs : woolam |] \
\ ==> EX B. Says A B (Crypt (shrK A) (Nonce NB)) : set evs";
by (blast_tac (claset() addSIs [NB_Crypt_imp_Alice_msg]) 1);
qed "Server_trusts_WL4";
AddDs [Server_trusts_WL4];
(*** WL5 ***)
(*Server sent WL5 only if it received the right sort of message*)
Goal "[| Says Server B (Crypt (shrK B) {|Agent A, NB|}) : set evs; \
\ evs : woolam |] \
\ ==> EX B'. Says B' Server {|Agent A, Agent B, Crypt (shrK A) NB|} \
\ : set evs";
by (etac rev_mp 1);
by (parts_induct_tac 1);
by (ALLGOALS Blast_tac);
qed "Server_sent_WL5";
AddDs [Server_sent_WL5];
(*If the encrypted message appears then it originated with the Server!*)
Goal "[| Crypt (shrK B) {|Agent A, NB|} : parts (spies evs); \
\ B ~: bad; evs : woolam |] \
\ ==> Says Server B (Crypt (shrK B) {|Agent A, NB|}) : set evs";
by (etac rev_mp 1);
by (parts_induct_tac 1);
by (Blast_tac 1);
qed_spec_mp "NB_Crypt_imp_Server_msg";
(*Guarantee for B. If B gets the Server's certificate then A has encrypted
the nonce using her key. This event can be no older than the nonce itself.
But A may have sent the nonce to some other agent and it could have reached
the Server via the Spy.*)
Goal "[| Says S B (Crypt (shrK B) {|Agent A, Nonce NB|}): set evs; \
\ A ~: bad; B ~: bad; evs : woolam |] \
\ ==> EX B. Says A B (Crypt (shrK A) (Nonce NB)) : set evs";
by (blast_tac (claset() addSDs [NB_Crypt_imp_Server_msg]) 1);
qed "B_trusts_WL5";
(*B only issues challenges in response to WL1. Not used.*)
Goal "[| Says B A (Nonce NB) : set evs; B ~= Spy; evs : woolam |] \
\ ==> EX A'. Says A' B (Agent A) : set evs";
by (etac rev_mp 1);
by (parts_induct_tac 1);
by (ALLGOALS Blast_tac);
qed "B_said_WL2";
(**CANNOT be proved because A doesn't know where challenges come from...
Goal "[| A ~: bad; B ~= Spy; evs : woolam |] \
\ ==> Crypt (shrK A) (Nonce NB) : parts (spies evs) & \
\ Says B A (Nonce NB) : set evs \
\ --> Says A B (Crypt (shrK A) (Nonce NB)) : set evs";
by (parts_induct_tac 1);
by (Blast_tac 1);
by Safe_tac;
**)