src/HOL/Auth/Yahalom2.thy
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(*  Title:      HOL/Auth/Yahalom2
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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, Variant 2.
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This version trades encryption of NB for additional explicitness in YM3.
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Also in YM3, care is taken to make the two certificates distinct.
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From page 259 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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Yahalom2 = Shared + 
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consts  yahalom   :: event list set
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inductive "yahalom"
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  intrs 
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         (*Initial trace is empty*)
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    Nil  "[]: yahalom"
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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;  B ~= Spy;  
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             X: synth (analz (spies evs)) |]
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          ==> Says Spy B X  # evs : yahalom"
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         (*Alice initiates a protocol run*)
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    YM1  "[| evs1: yahalom;  A ~= B;  Nonce NA ~: used evs1 |]
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          ==> Says A B {|Agent A, Nonce NA|} # evs1 : yahalom"
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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  "[| evs2: yahalom;  B ~= Server;  Nonce NB ~: used evs2;
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             Says A' B {|Agent A, Nonce NA|} : set evs2 |]
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          ==> Says B Server 
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                  {|Agent B, Nonce NB, Crypt (shrK B) {|Agent A, Nonce NA|}|}
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                # evs2 : yahalom"
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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 certificate for forwarding to Bob.
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           Fields are reversed in the 2nd certificate to prevent attacks!! *)
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    YM3  "[| evs3: yahalom;  A ~= B;  A ~= Server;  Key KAB ~: used evs3;
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             Says B' Server {|Agent B, Nonce NB,
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			      Crypt (shrK B) {|Agent A, Nonce NA|}|}
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               : set evs3 |]
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          ==> Says Server A
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               {|Nonce NB, 
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                 Crypt (shrK A) {|Agent B, Key KAB, Nonce NA|},
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                 Crypt (shrK B) {|Nonce NB, Key KAB, Agent A|}|}
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                 # evs3 : yahalom"
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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  "[| evs4: yahalom;  A ~= Server;  
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             Says S A {|Nonce NB, Crypt (shrK A) {|Agent B, Key K, Nonce NA|},
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                        X|}  : set evs4;
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             Says A B {|Agent A, Nonce NA|} : set evs4 |]
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          ==> Says A B {|X, Crypt K (Nonce NB)|} # evs4 : yahalom"
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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 "[| evso: yahalom;  A ~= Spy;
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             Says Server A {|Nonce NB, 
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                             Crypt (shrK A) {|Agent B, Key K, Nonce NA|},
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                             X|}  : set evso |]
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          ==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso : yahalom"
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end