author | paulson |
Sat, 10 Jan 1998 17:58:42 +0100 | |
changeset 4551 | 41fa62c229c3 |
parent 4477 | b3e5857d8d99 |
child 4556 | e7a4683c0026 |
permissions | -rw-r--r-- |
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(* Title: HOL/Auth/NS_Public_Bad |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Inductive relation "ns_public" for the Needham-Schroeder Public-Key protocol. |
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Flawed version, vulnerable to Lowe's attack. |
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From page 260 of |
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Burrows, Abadi and Needham. A Logic of Authentication. |
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Proc. Royal Soc. 426 (1989) |
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*) |
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open NS_Public_Bad; |
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||
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set proof_timing; |
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HOL_quantifiers := false; |
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||
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AddIffs [Spy_in_bad]; |
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(*A "possibility property": there are traces that reach the end*) |
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goal thy |
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"!!A B. A ~= B ==> EX NB. EX evs: ns_public. \ |
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\ Says A B (Crypt (pubK B) (Nonce NB)) : set evs"; |
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by (REPEAT (resolve_tac [exI,bexI] 1)); |
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by (rtac (ns_public.Nil RS ns_public.NS1 RS ns_public.NS2 RS ns_public.NS3) 2); |
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by possibility_tac; |
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result(); |
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(**** Inductive proofs about ns_public ****) |
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(*Nobody sends themselves messages*) |
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goal thy "!!evs. evs : ns_public ==> ALL A X. Says A A X ~: set evs"; |
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by (etac ns_public.induct 1); |
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by Auto_tac; |
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qed_spec_mp "not_Says_to_self"; |
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Addsimps [not_Says_to_self]; |
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AddSEs [not_Says_to_self RSN (2, rev_notE)]; |
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(*Induction for regularity theorems. If induction formula has the form |
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X ~: analz (spies evs) --> ... then it shortens the proof by discarding |
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needless information about analz (insert X (spies evs)) *) |
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fun parts_induct_tac i = |
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etac ns_public.induct i |
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THEN |
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REPEAT (FIRSTGOAL analz_mono_contra_tac) |
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THEN |
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prove_simple_subgoals_tac i; |
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|
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(** Theorems of the form X ~: parts (spies evs) imply that NOBODY |
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sends messages containing X! **) |
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(*Spy never sees another agent's private key! (unless it's bad at start)*) |
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goal thy |
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"!!A. evs: ns_public ==> (Key (priK A) : parts (spies evs)) = (A : bad)"; |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
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qed "Spy_see_priK"; |
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Addsimps [Spy_see_priK]; |
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goal thy |
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"!!A. evs: ns_public ==> (Key (priK A) : analz (spies evs)) = (A : bad)"; |
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by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset())); |
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qed "Spy_analz_priK"; |
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Addsimps [Spy_analz_priK]; |
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AddSDs [Spy_see_priK RSN (2, rev_iffD1), |
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Spy_analz_priK RSN (2, rev_iffD1)]; |
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||
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(**** Authenticity properties obtained from NS2 ****) |
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|
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(*It is impossible to re-use a nonce in both NS1 and NS2, provided the nonce |
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is secret. (Honest users generate fresh nonces.)*) |
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goal thy |
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"!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \ |
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\ Nonce NA ~: analz (spies evs); evs : ns_public |] \ |
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\ ==> Crypt (pubK C) {|NA', Nonce NA|} ~: parts (spies evs)"; |
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by (etac rev_mp 1); |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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(*NS3*) |
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by (blast_tac (claset() addSEs partsEs) 3); |
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(*NS2*) |
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by (blast_tac (claset() addSEs partsEs) 2); |
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by (Fake_parts_insert_tac 1); |
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qed "no_nonce_NS1_NS2"; |
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|
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(*Unicity for NS1: nonce NA identifies agents A and B*) |
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goal thy |
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"!!evs. [| Nonce NA ~: analz (spies evs); evs : ns_public |] \ |
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\ ==> EX A' B'. ALL A B. \ |
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\ Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs) --> \ |
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\ A=A' & B=B'"; |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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by (ALLGOALS |
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(asm_simp_tac (simpset() addsimps [all_conj_distrib, |
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parts_insert_spies]))); |
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(*NS1*) |
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by (expand_case_tac "NA = ?y" 2 THEN blast_tac (claset() addSEs partsEs) 2); |
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(*Fake*) |
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by (Clarify_tac 1); |
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by (ex_strip_tac 1); |
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by (Fake_parts_insert_tac 1); |
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val lemma = result(); |
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|
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goal thy |
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"!!evs. [| Crypt(pubK B) {|Nonce NA, Agent A|} : parts(spies evs); \ |
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\ Crypt(pubK B') {|Nonce NA, Agent A'|} : parts(spies evs); \ |
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\ Nonce NA ~: analz (spies evs); \ |
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\ evs : ns_public |] \ |
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\ ==> A=A' & B=B'"; |
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by (prove_unique_tac lemma 1); |
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qed "unique_NA"; |
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|
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|
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(*Tactic for proving secrecy theorems*) |
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fun analz_induct_tac i = |
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etac ns_public.induct i THEN |
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ALLGOALS (asm_simp_tac (simpset() addsplits [expand_if])); |
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(*Secrecy: Spy does not see the nonce sent in msg NS1 if A and B are secure*) |
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goal thy |
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"!!evs. [| Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs; \ |
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\ A ~: bad; B ~: bad; evs : ns_public |] \ |
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\ ==> Nonce NA ~: analz (spies evs)"; |
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by (etac rev_mp 1); |
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by (analz_induct_tac 1); |
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(*NS3*) |
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by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj] |
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addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)]) 4); |
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(*NS2*) |
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by (blast_tac (claset() addSEs [MPair_parts] |
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addDs [Says_imp_spies RS parts.Inj, |
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parts.Body, unique_NA]) 3); |
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(*NS1*) |
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by (blast_tac (claset() addSEs spies_partsEs |
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addIs [impOfSubs analz_subset_parts]) 2); |
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(*Fake*) |
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by (spy_analz_tac 1); |
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qed "Spy_not_see_NA"; |
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(*Authentication for A: if she receives message 2 and has used NA |
|
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to start a run, then B has sent message 2.*) |
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goal thy |
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"!!evs. [| Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs; \ |
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\ Says B' A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set evs; \ |
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\ A ~: bad; B ~: bad; evs : ns_public |] \ |
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\ ==> Says B A (Crypt(pubK A) {|Nonce NA, Nonce NB|}): set evs"; |
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by (etac rev_mp 1); |
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(*prepare induction over Crypt (pubK A) {|NA,NB|} : parts H*) |
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by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); |
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by (etac ns_public.induct 1); |
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by (ALLGOALS Asm_simp_tac); |
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by (ALLGOALS Clarify_tac); |
163 |
(*NS2*) |
|
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by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, |
3709 | 165 |
Spy_not_see_NA, unique_NA]) 3); |
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(*NS1*) |
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by (blast_tac (claset() addSEs spies_partsEs) 2); |
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(*Fake*) |
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by (blast_tac (claset() addSDs [impOfSubs Fake_parts_insert] |
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addDs [Spy_not_see_NA, |
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impOfSubs analz_subset_parts]) 1); |
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qed "A_trusts_NS2"; |
173 |
||
174 |
(*If the encrypted message appears then it originated with Alice in NS1*) |
|
175 |
goal thy |
|
3683 | 176 |
"!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \ |
177 |
\ Nonce NA ~: analz (spies evs); \ |
|
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\ evs : ns_public |] \ |
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\ ==> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs"; |
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by (etac rev_mp 1); |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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by (Fake_parts_insert_tac 1); |
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qed "B_trusts_NS1"; |
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|
186 |
||
187 |
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(**** Authenticity properties obtained from NS2 ****) |
|
189 |
||
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(*Unicity for NS2: nonce NB identifies agent A and nonce NA |
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[proof closely follows that for unique_NA] *) |
192 |
goal thy |
|
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"!!evs. [| Nonce NB ~: analz (spies evs); evs : ns_public |] \ |
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\ ==> EX A' NA'. ALL A NA. \ |
195 |
\ Crypt (pubK A) {|Nonce NA, Nonce NB|} \ |
|
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\ : parts (spies evs) --> A=A' & NA=NA'"; |
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by (etac rev_mp 1); |
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by (parts_induct_tac 1); |
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199 |
by (ALLGOALS |
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(asm_simp_tac (simpset() addsimps [all_conj_distrib, parts_insert_spies]))); |
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(*NS2*) |
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by (expand_case_tac "NB = ?y" 2 THEN blast_tac (claset() addSEs partsEs) 2); |
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(*Fake*) |
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by (Clarify_tac 1); |
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by (ex_strip_tac 1); |
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206 |
by (Fake_parts_insert_tac 1); |
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val lemma = result(); |
208 |
||
209 |
goal thy |
|
3683 | 210 |
"!!evs. [| Crypt(pubK A) {|Nonce NA, Nonce NB|} : parts(spies evs); \ |
211 |
\ Crypt(pubK A'){|Nonce NA', Nonce NB|} : parts(spies evs); \ |
|
212 |
\ Nonce NB ~: analz (spies evs); \ |
|
3709 | 213 |
\ evs : ns_public |] \ |
2318 | 214 |
\ ==> A=A' & NA=NA'"; |
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset
|
215 |
by (prove_unique_tac lemma 1); |
2318 | 216 |
qed "unique_NB"; |
217 |
||
218 |
||
219 |
(*NB remains secret PROVIDED Alice never responds with round 3*) |
|
220 |
goal thy |
|
3466
30791e5a69c4
Corrected indentations and margins after the renaming of "set_of_list"
paulson
parents:
3465
diff
changeset
|
221 |
"!!evs.[| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs; \ |
3703 | 222 |
\ ALL C. Says A C (Crypt (pubK C) (Nonce NB)) ~: set evs; \ |
223 |
\ A ~: bad; B ~: bad; evs : ns_public |] \ |
|
3683 | 224 |
\ ==> Nonce NB ~: analz (spies evs)"; |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
225 |
by (etac rev_mp 1); |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
226 |
by (etac rev_mp 1); |
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset
|
227 |
by (analz_induct_tac 1); |
4091 | 228 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib]))); |
3709 | 229 |
by (ALLGOALS Clarify_tac); |
3703 | 230 |
(*NS3: because NB determines A*) |
4091 | 231 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, unique_NB]) 4); |
3703 | 232 |
(*NS2: by freshness and unicity of NB*) |
4091 | 233 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj] |
3703 | 234 |
addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)] |
235 |
addEs partsEs |
|
236 |
addIs [impOfSubs analz_subset_parts]) 3); |
|
237 |
(*NS1: by freshness*) |
|
4091 | 238 |
by (blast_tac (claset() addSEs spies_partsEs) 2); |
2318 | 239 |
(*Fake*) |
2497 | 240 |
by (spy_analz_tac 1); |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
241 |
qed "Spy_not_see_NB"; |
2318 | 242 |
|
243 |
||
244 |
||
245 |
(*Authentication for B: if he receives message 3 and has used NB |
|
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
246 |
in message 2, then A has sent message 3--to somebody....*) |
2318 | 247 |
goal thy |
3545 | 248 |
"!!evs. [| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs; \ |
249 |
\ Says A' B (Crypt (pubK B) (Nonce NB)): set evs; \ |
|
3683 | 250 |
\ A ~: bad; B ~: bad; evs : ns_public |] \ |
3465 | 251 |
\ ==> EX C. Says A C (Crypt (pubK C) (Nonce NB)) : set evs"; |
2536
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
252 |
by (etac rev_mp 1); |
1e04eb7f7eb1
Tidied proofs by using "etac rev_mp" instead of applying rev_mp to result()
paulson
parents:
2516
diff
changeset
|
253 |
(*prepare induction over Crypt (pubK B) NB : parts H*) |
3683 | 254 |
by (etac (Says_imp_spies RS parts.Inj RS rev_mp) 1); |
3519
ab0a9fbed4c0
Changing "lost" from a parameter of protocol definitions to a constant.
paulson
parents:
3466
diff
changeset
|
255 |
by (parts_induct_tac 1); |
4091 | 256 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps [ex_disj_distrib]))); |
3709 | 257 |
by (ALLGOALS Clarify_tac); |
4197 | 258 |
(*NS3: because NB determines A (this use of unique_NB is more robust) *) |
259 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, Spy_not_see_NB] |
|
260 |
addIs [unique_NB RS conjunct1]) 3); |
|
3703 | 261 |
(*NS1: by freshness*) |
4091 | 262 |
by (blast_tac (claset() addSEs spies_partsEs) 2); |
2318 | 263 |
(*Fake*) |
4091 | 264 |
by (blast_tac (claset() addSDs [impOfSubs Fake_parts_insert] |
3121
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
265 |
addDs [Spy_not_see_NB, |
cbb6c0c1c58a
Conversion to use blast_tac (with other improvements)
paulson
parents:
2637
diff
changeset
|
266 |
impOfSubs analz_subset_parts]) 1); |
2318 | 267 |
qed "B_trusts_NS3"; |
268 |
||
269 |
||
270 |
(*Can we strengthen the secrecy theorem? NO*) |
|
271 |
goal thy |
|
3683 | 272 |
"!!evs. [| A ~: bad; B ~: bad; evs : ns_public |] \ |
3465 | 273 |
\ ==> Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs \ |
3683 | 274 |
\ --> Nonce NB ~: analz (spies evs)"; |
2418
6b6a92d05fb2
New tactics: prove_unique_tac and analz_induct_tac
paulson
parents:
2374
diff
changeset
|
275 |
by (analz_induct_tac 1); |
3709 | 276 |
by (ALLGOALS Clarify_tac); |
3703 | 277 |
(*NS2: by freshness and unicity of NB*) |
4091 | 278 |
by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj] |
3703 | 279 |
addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)] |
280 |
addEs partsEs |
|
281 |
addIs [impOfSubs analz_subset_parts]) 3); |
|
282 |
(*NS1: by freshness*) |
|
4091 | 283 |
by (blast_tac (claset() addSEs spies_partsEs) 2); |
2318 | 284 |
(*Fake*) |
2497 | 285 |
by (spy_analz_tac 1); |
3703 | 286 |
(*NS3: unicity of NB identifies A and NA, but not B*) |
3683 | 287 |
by (forw_inst_tac [("A'","A")] (Says_imp_spies RS parts.Inj RS unique_NB) 1 |
288 |
THEN REPEAT (eresolve_tac [asm_rl, Says_imp_spies RS parts.Inj] 1)); |
|
4477
b3e5857d8d99
New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents:
4476
diff
changeset
|
289 |
by Auto_tac; |
3703 | 290 |
by (rename_tac "C B' evs3" 1); |
2318 | 291 |
|
292 |
(* |
|
293 |
THIS IS THE ATTACK! |
|
3703 | 294 |
Level 8 |
3683 | 295 |
!!evs. [| A ~: bad; B ~: bad; evs : ns_public |] |
3703 | 296 |
==> Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs --> |
3683 | 297 |
Nonce NB ~: analz (spies evs) |
3703 | 298 |
1. !!C B' evs3. |
299 |
[| A ~: bad; B ~: bad; evs3 : ns_public; |
|
300 |
Says A C (Crypt (pubK C) {|Nonce NA, Agent A|}) : set evs3; |
|
301 |
Says B' A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs3; C : bad; |
|
302 |
Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB|}) : set evs3; |
|
303 |
Nonce NB ~: analz (spies evs3) |] |
|
2318 | 304 |
==> False |
305 |
*) |