src/HOL/Auth/OtwayRees.thy
author paulson
Thu, 08 Jan 1998 18:10:34 +0100
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Expressed most Oops rules using Notes instead of Says, and other tidying
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(*  Title:      HOL/Auth/OtwayRees
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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 "otway" for the Otway-Rees protocol.
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Version that encrypts Nonce NB
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From page 244 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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OtwayRees = Shared + 
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consts  otway   :: event list set
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inductive "otway"
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  intrs 
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         (*Initial trace is empty*)
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    Nil  "[]: otway"
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         (*The spy MAY say anything he CAN say.  We do not expect him to
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           invent new nonces here, but he can also use NS1.  Common to
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           all similar protocols.*)
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    Fake "[| evs: otway;  B ~= Spy;  
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             X: synth (analz (spies evs)) |]
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          ==> Says Spy B X  # evs : otway"
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         (*Alice initiates a protocol run*)
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    OR1  "[| evs1: otway;  A ~= B;  B ~= Server;  Nonce NA ~: used evs1 |]
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          ==> Says A B {|Nonce NA, Agent A, Agent B, 
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                         Crypt (shrK A) {|Nonce NA, Agent A, Agent B|} |} 
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                 # evs1 : otway"
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         (*Bob's response to Alice's message.  Bob doesn't know who 
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	   the sender is, hence the A' in the sender field.
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           Note that NB is encrypted.*)
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    OR2  "[| evs2: otway;  B ~= Server;  Nonce NB ~: used evs2;
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             Says A' B {|Nonce NA, Agent A, Agent B, X|} : set evs2 |]
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          ==> Says B Server 
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                  {|Nonce NA, Agent A, Agent B, X, 
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                    Crypt (shrK B)
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                      {|Nonce NA, Nonce NB, Agent A, Agent B|}|}
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                 # evs2 : otway"
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         (*The Server receives Bob's message and checks that the three NAs
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           match.  Then he sends a new session key to Bob with a packet for
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           forwarding to Alice.*)
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    OR3  "[| evs3: otway;  B ~= Server;  Key KAB ~: used evs3;
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             Says B' Server 
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                  {|Nonce NA, Agent A, Agent B, 
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                    Crypt (shrK A) {|Nonce NA, Agent A, Agent B|}, 
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                    Crypt (shrK B) {|Nonce NA, Nonce NB, Agent A, Agent B|}|}
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               : set evs3 |]
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          ==> Says Server B 
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                  {|Nonce NA, 
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                    Crypt (shrK A) {|Nonce NA, Key KAB|},
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                    Crypt (shrK B) {|Nonce NB, Key KAB|}|}
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                 # evs3 : otway"
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         (*Bob receives the Server's (?) message and compares the Nonces with
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	   those in the message he previously sent the Server.*)
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    OR4  "[| evs4: otway;  A ~= B;  
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             Says B Server {|Nonce NA, Agent A, Agent B, X', 
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                             Crypt (shrK B)
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                                   {|Nonce NA, Nonce NB, Agent A, Agent B|}|}
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               : set evs4;
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             Says S' B {|Nonce NA, X, Crypt (shrK B) {|Nonce NB, Key K|}|}
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               : set evs4 |]
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          ==> Says B A {|Nonce NA, X|} # evs4 : otway"
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         (*This message models possible leaks of session keys.  The nonces
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           identify the protocol run.*)
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    Oops "[| evso: otway;  B ~= Spy;
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             Says Server B {|Nonce NA, X, Crypt (shrK B) {|Nonce NB, Key K|}|}
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               : set evso |]
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          ==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso : otway"
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end