src/HOL/Auth/Yahalom2.thy

set_of_list -> set

(*  Title:      HOL/Auth/Yahalom2
    ID:         $Id$
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1996  University of Cambridge

Inductive relation "yahalom" for the Yahalom protocol, Variant 2.

This version trades encryption of NB for additional explicitness in YM3.
Also in YM3, care is taken to make the two certificates distinct.

From page 259 of
  Burrows, Abadi and Needham.  A Logic of Authentication.
  Proc. Royal Soc. 426 (1989)
*)

Yahalom2 = Shared + 

consts  yahalom   :: agent set => event list set
inductive "yahalom lost"
  intrs 
         (*Initial trace is empty*)
    Nil  "[]: yahalom lost"

         (*The spy MAY say anything he CAN say.  We do not expect him to
           invent new nonces here, but he can also use NS1.  Common to
           all similar protocols.*)
    Fake "[| evs: yahalom lost;  B ~= Spy;  
             X: synth (analz (sees lost Spy evs)) |]
          ==> Says Spy B X  # evs : yahalom lost"

         (*Alice initiates a protocol run*)
    YM1  "[| evs: yahalom lost;  A ~= B;  Nonce NA ~: used evs |]
          ==> Says A B {|Agent A, Nonce NA|} # evs : yahalom lost"

         (*Bob's response to Alice's message.  Bob doesn't know who 
	   the sender is, hence the A' in the sender field.*)
    YM2  "[| evs: yahalom lost;  B ~= Server;  Nonce NB ~: used evs;
             Says A' B {|Agent A, Nonce NA|} : set evs |]
          ==> Says B Server 
                  {|Agent B, Nonce NB, Crypt (shrK B) {|Agent A, Nonce NA|}|}
                # evs : yahalom lost"

         (*The Server receives Bob's message.  He responds by sending a
           new session key to Alice, with a packet for forwarding to Bob.
           !! Fields are reversed in the 2nd packet to prevent attacks!! *)
    YM3  "[| evs: yahalom lost;  A ~= B;  A ~= Server;  Key KAB ~: used evs;
             Says B' Server {|Agent B, Nonce NB,
			      Crypt (shrK B) {|Agent A, Nonce NA|}|}
               : set evs |]
          ==> Says Server A
               {|Nonce NB, 
                 Crypt (shrK A) {|Agent B, Key KAB, Nonce NA|},
                 Crypt (shrK B) {|Nonce NB, Key KAB, Agent A|}|}
                 # evs : yahalom lost"

         (*Alice receives the Server's (?) message, checks her Nonce, and
           uses the new session key to send Bob his Nonce.*)
    YM4  "[| evs: yahalom lost;  A ~= Server;  A ~= B;  
             Says S A {|Nonce NB, Crypt (shrK A) {|Agent B, Key K, Nonce NA|},
                        X|}
               : set evs;
             Says A B {|Agent A, Nonce NA|} : set evs |]
          ==> Says A B {|X, Crypt K (Nonce NB)|} # evs : yahalom lost"

         (*This message models possible leaks of session keys.  The nonces
           identify the protocol run.  Quoting Server here ensures they are
           correct. *)
    Oops "[| evs: yahalom lost;  A ~= Spy;
             Says Server A {|Nonce NB, 
                             Crypt (shrK A) {|Agent B, Key K, Nonce NA|},
                             X|}  : set evs |]
          ==> Says A Spy {|Nonce NA, Nonce NB, Key K|} # evs : yahalom lost"

end