src/HOL/Auth/NS_Shared.thy
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(*  Title:      HOL/Auth/NS_Shared
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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_shared" for Needham-Schroeder Shared-Key protocol.
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From page 247 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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NS_Shared = Shared + 
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consts  ns_shared   :: event list set
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inductive "ns_shared"
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  intrs 
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         (*Initial trace is empty*)
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    Nil  "[]: ns_shared"
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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: ns_shared;  X: synth (analz (spies evs)) |]
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          ==> Says Spy B X # evs : ns_shared"
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         (*Alice initiates a protocol run, requesting to talk to any B*)
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    NS1  "[| evs1: ns_shared;  Nonce NA ~: used evs1 |]
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          ==> Says A Server {|Agent A, Agent B, Nonce NA|} # evs1
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                :  ns_shared"
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         (*Server's response to Alice's message.
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           !! It may respond more than once to A's request !!
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	   Server doesn't know who the true sender is, hence the A' in
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               the sender field.*)
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    NS2  "[| evs2: ns_shared;  Key KAB ~: used evs2;
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             Says A' Server {|Agent A, Agent B, Nonce NA|} : set evs2 |]
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          ==> Says Server A 
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                (Crypt (shrK A)
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                   {|Nonce NA, Agent B, Key KAB,
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                     (Crypt (shrK B) {|Key KAB, Agent A|})|}) 
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                # evs2 : ns_shared"
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          (*We can't assume S=Server.  Agent A "remembers" her nonce.
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            Need A ~= Server because we allow messages to self.*)
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    NS3  "[| evs3: ns_shared;  A ~= Server;
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             Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|}) 
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               : set evs3;
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             Says A Server {|Agent A, Agent B, Nonce NA|} : set evs3 |]
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          ==> Says A B X # evs3 : ns_shared"
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         (*Bob's nonce exchange.  He does not know who the message came
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           from, but responds to A because she is mentioned inside.*)
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    NS4  "[| evs4: ns_shared;  Nonce NB ~: used evs4;
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             Says A' B (Crypt (shrK B) {|Key K, Agent A|}) : set evs4 |]
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          ==> Says B A (Crypt K (Nonce NB)) # evs4
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                : ns_shared"
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         (*Alice responds with Nonce NB if she has seen the key before.
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           Maybe should somehow check Nonce NA again.
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           We do NOT send NB-1 or similar as the Spy cannot spoof such things.
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           Letting the Spy add or subtract 1 lets him send ALL nonces.
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           Instead we distinguish the messages by sending the nonce twice.*)
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    NS5  "[| evs5: ns_shared;  
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             Says B' A (Crypt K (Nonce NB)) : set evs5;
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             Says S  A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})
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               : set evs5 |]
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          ==> Says A B (Crypt K {|Nonce NB, Nonce NB|}) # evs5 : ns_shared"
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         (*This message models possible leaks of session keys.
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           The two Nonces identify the protocol run: the rule insists upon
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           the true senders in order to make them accurate.*)
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    Oops "[| evso: ns_shared;  Says B A (Crypt K (Nonce NB)) : set evso;
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             Says Server A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})
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               : set evso |]
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          ==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso : ns_shared"
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end