src/HOL/Auth/TLS.thy
author paulson
Fri Sep 19 18:27:31 1997 +0200 (1997-09-19)
changeset 3686 4b484805b4c4
parent 3685 5b8c0c8f576e
child 3687 fb7d096d7884
permissions -rw-r--r--
First working version with Oops event for session keys
     1 (*  Title:      HOL/Auth/TLS
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1997  University of Cambridge
     5 
     6 Inductive relation "tls" for the baby TLS (Transport Layer Security) protocol.
     7 This protocol is essentially the same as SSL 3.0.
     8 
     9 Abstracted from "The TLS Protocol, Version 1.0" by Tim Dierks and Christopher
    10 Allen, Transport Layer Security Working Group, 21 May 1997,
    11 INTERNET-DRAFT draft-ietf-tls-protocol-03.txt.  Section numbers below refer
    12 to that memo.
    13 
    14 An RSA cryptosystem is assumed, and X.509v3 certificates are abstracted down
    15 to the trivial form {A, publicKey(A)}privateKey(Server), where Server is a
    16 global signing authority.
    17 
    18 A is the client and B is the server, not to be confused with the constant
    19 Server, who is in charge of all public keys.
    20 
    21 The model assumes that no fraudulent certificates are present, but it does
    22 assume that some private keys are to the spy.
    23 
    24 REMARK.  The event "Notes A {|Agent B, Nonce PMS|}" appears in ClientCertKeyEx,
    25 CertVerify, ClientFinished to record that A knows M.  It is a note from A to
    26 herself.  Nobody else can see it.  In ClientCertKeyEx, the Spy can substitute
    27 his own certificate for A's, but he cannot replace A's note by one for himself.
    28 
    29 The Note event avoids a weakness in the public-key model.  Each
    30 agent's state is recorded as the trace of messages.  When the true client (A)
    31 invents PMS, he encrypts PMS with B's public key before sending it.  The model
    32 does not distinguish the original occurrence of such a message from a replay.
    33 In the shared-key model, the ability to encrypt implies the ability to
    34 decrypt, so the problem does not arise.
    35 
    36 Proofs would be simpler if ClientCertKeyEx included A's name within
    37 Crypt KB (Nonce PMS).  As things stand, there is much overlap between proofs
    38 about that message (which B receives) and the stronger event
    39 	Notes A {|Agent B, Nonce PMS|}.
    40 *)
    41 
    42 TLS = Public + 
    43 
    44 consts
    45   (*Pseudo-random function of Section 5*)
    46   PRF  :: "nat*nat*nat => nat"
    47 
    48   (*Client, server write keys generated uniformly by function sessionK
    49     to avoid duplicating their properties.
    50     Theyimplicitly include the MAC secrets.*)
    51   sessionK :: "(nat*nat*nat)*bool => key"
    52 
    53   certificate      :: "[agent,key] => msg"
    54 
    55 defs
    56   certificate_def
    57     "certificate A KA == Crypt (priK Server) {|Agent A, Key KA|}"
    58 
    59 syntax
    60     clientK, serverK :: "nat*nat*nat => key"
    61 
    62 translations
    63   "clientK (x)"	== "sessionK(x,True)"
    64   "serverK (x)"	== "sessionK(x,False)"
    65 
    66 rules
    67   inj_PRF       "inj PRF"	
    68 
    69   (*sessionK is collision-free and makes symmetric keys*)
    70   inj_sessionK  "inj sessionK"	
    71 
    72   isSym_sessionK "isSymKey (sessionK x)"
    73 
    74   (*serverK is similar*)
    75   inj_serverK   "inj serverK"	
    76   isSym_serverK "isSymKey (serverK x)"
    77 
    78   (*Clashes with pubK and priK are impossible, but this axiom is needed.*)
    79   clientK_range "range clientK <= Compl (range serverK)"
    80 
    81 
    82 consts    tls :: event list set
    83 inductive tls
    84   intrs 
    85     Nil  (*Initial trace is empty*)
    86          "[]: tls"
    87 
    88     Fake (*The spy, an active attacker, MAY say anything he CAN say.*)
    89          "[| evs: tls;  B ~= Spy;  
    90              X: synth (analz (spies evs)) |]
    91           ==> Says Spy B X # evs : tls"
    92 
    93     SpyKeys (*The spy may apply PRF, clientK & serverK to available nonces*)
    94          "[| evsSK: tls;
    95 	     Says Spy B {|Nonce NA, Nonce NB, Nonce M|} : set evsSK |]
    96           ==> Says Spy B {| Nonce (PRF(M,NA,NB)),
    97 			    Key (clientK(NA,NB,M)),
    98 			    Key (serverK(NA,NB,M)) |} # evsSK : tls"
    99 
   100     ClientHello
   101 	 (*(7.4.1.2)
   102 	   XA represents CLIENT_VERSION, CIPHER_SUITES and COMPRESSION_METHODS.
   103 	   It is uninterpreted but will be confirmed in the FINISHED messages.
   104 	   NA is CLIENT RANDOM, while SID is SESSION_ID.
   105            UNIX TIME is omitted because the protocol doesn't use it.
   106            May assume NA ~: range PRF because CLIENT RANDOM is 28 bytes
   107 	   while MASTER SECRET is 48 byptes*)
   108          "[| evsCH: tls;  A ~= B;  Nonce NA ~: used evsCH;  NA ~: range PRF |]
   109           ==> Says A B {|Agent A, Nonce NA, Number SID, Number XA|}
   110 	        # evsCH  :  tls"
   111 
   112     ServerHello
   113          (*7.4.1.3 of the TLS Internet-Draft
   114 	   XB represents CLIENT_VERSION, CIPHER_SUITE and COMPRESSION_METHOD.
   115            SERVER CERTIFICATE (7.4.2) is always present.
   116            CERTIFICATE_REQUEST (7.4.4) is implied.*)
   117          "[| evsSH: tls;  A ~= B;  Nonce NB ~: used evsSH;  NB ~: range PRF;
   118              Says A' B {|Agent A, Nonce NA, Number SID, Number XA|}
   119 	       : set evsSH |]
   120           ==> Says B A {|Nonce NB, Number SID, Number XB,
   121 			 certificate B (pubK B)|}
   122                 # evsSH  :  tls"
   123 
   124     ClientCertKeyEx
   125          (*CLIENT CERTIFICATE (7.4.6) and KEY EXCHANGE (7.4.7).
   126            The client, A, chooses PMS, the PREMASTER SECRET.
   127            She encrypts PMS using the supplied KB, which ought to be pubK B.
   128            We assume PMS ~: range PRF because a clash betweem the PMS
   129            and another MASTER SECRET is highly unlikely (even though
   130 	   both items have the same length, 48 bytes).
   131            The Note event records in the trace that she knows PMS
   132                (see REMARK at top). *)
   133          "[| evsCX: tls;  A ~= B;  Nonce PMS ~: used evsCX;  PMS ~: range PRF;
   134              Says B' A {|Nonce NB, Number SID, Number XB, certificate B KB|}
   135 	       : set evsCX |]
   136           ==> Says A B {|certificate A (pubK A), Crypt KB (Nonce PMS)|}
   137 	      # Notes A {|Agent B, Nonce PMS|}
   138 	      # evsCX  :  tls"
   139 
   140     CertVerify
   141 	(*The optional Certificate Verify (7.4.8) message contains the
   142           specific components listed in the security analysis, F.1.1.2.
   143           It adds the pre-master-secret, which is also essential!
   144           Checking the signature, which is the only use of A's certificate,
   145           assures B of A's presence*)
   146          "[| evsCV: tls;  A ~= B;  
   147              Says B' A {|Nonce NB, Number SID, Number XB, certificate B KB|}
   148 	       : set evsCV;
   149 	     Notes A {|Agent B, Nonce PMS|} : set evsCV |]
   150           ==> Says A B (Crypt (priK A)
   151 			(Hash{|Nonce NB, certificate B KB, Nonce PMS|}))
   152               # evsCV  :  tls"
   153 
   154 	(*Finally come the FINISHED messages (7.4.8), confirming XA and XB
   155           among other things.  The master-secret is PRF(PMS,NA,NB).
   156           Either party may sent its message first.*)
   157 
   158     ClientFinished
   159         (*The occurrence of Notes A {|Agent B, Nonce PMS|} stops the 
   160           rule's applying when the Spy has satisfied the "Says A B" by
   161           repaying messages sent by the true client; in that case, the
   162           Spy does not know PMS and could not sent ClientFinished.  One
   163           could simply put A~=Spy into the rule, but one should not
   164           expect the spy to be well-behaved.*)
   165          "[| evsCF: tls;  
   166 	     Says A  B {|Agent A, Nonce NA, Number SID, Number XA|}
   167 	       : set evsCF;
   168              Says B' A {|Nonce NB, Number SID, Number XB, certificate B KB|}
   169 	       : set evsCF;
   170              Notes A {|Agent B, Nonce PMS|} : set evsCF;
   171 	     M = PRF(PMS,NA,NB) |]
   172           ==> Says A B (Crypt (clientK(NA,NB,M))
   173 			(Hash{|Nonce M, Number SID,
   174 			       Nonce NA, Number XA, Agent A, 
   175 			       Nonce NB, Number XB, Agent B|}))
   176               # evsCF  :  tls"
   177 
   178     ServerFinished
   179 	(*Keeping A' and A'' distinct means B cannot even check that the
   180           two messages originate from the same source. *)
   181          "[| evsSF: tls;
   182 	     Says A' B  {|Agent A, Nonce NA, Number SID, Number XA|}
   183 	       : set evsSF;
   184 	     Says B  A  {|Nonce NB, Number SID, Number XB,
   185 		 	  certificate B (pubK B)|}
   186 	       : set evsSF;
   187 	     Says A'' B {|certificate A KA, Crypt (pubK B) (Nonce PMS)|}
   188 	       : set evsSF;
   189 	     M = PRF(PMS,NA,NB) |]
   190           ==> Says B A (Crypt (serverK(NA,NB,M))
   191 			(Hash{|Nonce M, Number SID,
   192 			       Nonce NA, Number XA, Agent A, 
   193 			       Nonce NB, Number XB, Agent B|}))
   194               # evsSF  :  tls"
   195 
   196     ClientAccepts
   197 	(*Having transmitted ClientFinished and received an identical
   198           message encrypted with serverK, the client stores the parameters
   199           needed to resume this session.*)
   200          "[| evsCA: tls;
   201 	     Notes A {|Agent B, Nonce PMS|} : set evsCA;
   202 	     M = PRF(PMS,NA,NB);  
   203 	     X = Hash{|Nonce M, Number SID,
   204 	               Nonce NA, Number XA, Agent A, 
   205 		       Nonce NB, Number XB, Agent B|};
   206              Says A  B (Crypt (clientK(NA,NB,M)) X) : set evsCA;
   207              Says B' A (Crypt (serverK(NA,NB,M)) X) : set evsCA |]
   208           ==> 
   209              Notes A {|Number SID, Agent A, Agent B, Nonce M|} # evsCA  :  tls"
   210 
   211     ServerAccepts
   212 	(*Having transmitted ServerFinished and received an identical
   213           message encrypted with clientK, the server stores the parameters
   214           needed to resume this session.*)
   215          "[| evsSA: tls;
   216              Says A'' B {|certificate A KA, Crypt (pubK B) (Nonce PMS)|}
   217 	       : set evsSA;
   218 	     M = PRF(PMS,NA,NB);  
   219 	     X = Hash{|Nonce M, Number SID,
   220 	               Nonce NA, Number XA, Agent A, 
   221 		       Nonce NB, Number XB, Agent B|};
   222              Says B  A (Crypt (serverK(NA,NB,M)) X) : set evsSA;
   223              Says A' B (Crypt (clientK(NA,NB,M)) X) : set evsSA |]
   224           ==> 
   225              Notes B {|Number SID, Agent A, Agent B, Nonce M|} # evsSA  :  tls"
   226 
   227     ServerResume
   228          (*Resumption is described in 7.3.  If B finds the SESSION_ID
   229            then he sends HELLO and FINISHED messages, using the
   230            previously stored MASTER SECRET*)
   231          "[| evsSR: tls;  A ~= B;  Nonce NB ~: used evsSR;  NB ~: range PRF;
   232              Notes B {|Number SID, Agent A, Agent B, Nonce M|} : set evsSR;
   233 	     Says A' B {|Agent A, Nonce NA, Number SID, Number XA|}
   234 	       : set evsSR |]
   235           ==> Says B A (Crypt (serverK(NA,NB,M))
   236 			(Hash{|Nonce M, Number SID,
   237 			       Nonce NA, Number XA, Agent A, 
   238 			       Nonce NB, Number XB, Agent B|}))
   239               # Says B A {|Nonce NB, Number SID, Number XB|} # evsSR  :  tls"
   240 
   241     ClientResume
   242          (*If the response to ClientHello is ServerResume then send
   243            a FINISHED message using the new nonces and stored MASTER SECRET.*)
   244          "[| evsCR: tls;  
   245 	     Says A  B {|Agent A, Nonce NA, Number SID, Number XA|}
   246 	       : set evsCR;
   247              Says B' A {|Nonce NB, Number SID, Number XB|} : set evsCR;
   248              Notes A {|Number SID, Agent A, Agent B, Nonce M|} : set evsCR |]
   249           ==> Says A B (Crypt (clientK(NA,NB,M))
   250 			(Hash{|Nonce M, Number SID,
   251 			       Nonce NA, Number XA, Agent A, 
   252 			       Nonce NB, Number XB, Agent B|}))
   253               # evsCR  :  tls"
   254 
   255     Oops 
   256          (*The most plausible compromise is of an old session key.  Losing
   257            the MASTER SECRET or PREMASTER SECRET is more serious but
   258            rather unlikely.*)
   259          "[| evso: tls;  A ~= Spy;  
   260 	     Says A B (Crypt (sessionK((NA,NB,M),b)) X) : set evso |]
   261           ==> Says A Spy (Key (sessionK((NA,NB,M),b))) # evso  :  tls"
   262 
   263 end