src/HOL/Auth/Yahalom.thy
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(*  Title:      HOL/Auth/Yahalom
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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 "yahalom" for the Yahalom protocol.
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From page 257 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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Yahalom = Shared + 
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consts  yahalom   :: agent set => event list set
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inductive "yahalom lost"
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  intrs 
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         (*Initial trace is empty*)
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    Nil  "[]: yahalom lost"
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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: yahalom lost;  B ~= Spy;  
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             X: synth (analz (sees lost Spy evs)) |]
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          ==> Says Spy B X  # evs : yahalom lost"
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         (*Alice initiates a protocol run*)
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    YM1  "[| evs: yahalom lost;  A ~= B;  Nonce NA ~: used evs |]
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          ==> Says A B {|Agent A, Nonce NA|} # evs : yahalom lost"
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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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    YM2  "[| evs: yahalom lost;  B ~= Server;  Nonce NB ~: used evs;
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             Says A' B {|Agent A, Nonce NA|} : set evs |]
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          ==> Says B Server 
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                  {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
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                # evs : yahalom lost"
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         (*The Server receives Bob's message.  He responds by sending a
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            new session key to Alice, with a packet for forwarding to Bob.*)
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    YM3  "[| evs: yahalom lost;  A ~= Server;  Key KAB ~: used evs;
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             Says B' Server 
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                  {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
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               : set evs |]
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          ==> Says Server A
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                   {|Crypt (shrK A) {|Agent B, Key KAB, Nonce NA, Nonce NB|},
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                     Crypt (shrK B) {|Agent A, Key KAB|}|}
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                # evs : yahalom lost"
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         (*Alice receives the Server's (?) message, checks her Nonce, and
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           uses the new session key to send Bob his Nonce.*)
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    YM4  "[| evs: yahalom lost;  A ~= Server;  A ~= B;  
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             Says S A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, Nonce NB|},
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                        X|}  : set evs;
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             Says A B {|Agent A, Nonce NA|} : set evs |]
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          ==> Says A B {|X, Crypt K (Nonce NB)|} # evs : yahalom lost"
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         (*This message models possible leaks of session keys.  The Nonces
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           identify the protocol run.  Quoting Server here ensures they are
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           correct.*)
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    Oops "[| evs: yahalom lost;  A ~= Spy;
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             Says Server A {|Crypt (shrK A)
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                                   {|Agent B, Key K, Nonce NA, Nonce NB|},
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                             X|}  : set evs |]
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          ==> Says A Spy {|Nonce NA, Nonce NB, Key K|} # evs : yahalom lost"
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constdefs 
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  KeyWithNonce :: [key, nat, event list] => bool
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  "KeyWithNonce K NB evs ==
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     EX A B na X. 
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       Says Server A {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|} 
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         : set evs"
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end