src/HOL/Auth/OtwayRees_AN.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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Simplified version with minimal encryption but explicit messages
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Note that the formalization does not even assume that nonces are fresh.
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This is because the protocol does not rely on uniqueness of nonces for
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security, only for freshness, and the proof script does not prove freshness
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properties.
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From page 11 of
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  Abadi and Needham.  Prudent Engineering Practice for Cryptographic Protocols.
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  IEEE Trans. SE 22 (1), 1996
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*)
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OtwayRees_AN = 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 |]
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          ==> Says A B {|Agent A, Agent B, Nonce NA|} # 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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    OR2  "[| evs2: otway;  B ~= Server;
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             Says A' B {|Agent A, Agent B, Nonce NA|} : set evs2 |]
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          ==> Says B Server {|Agent A, Agent B, Nonce NA, Nonce NB|}
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                 # evs2 : otway"
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         (*The Server receives Bob's message.  Then he sends a new
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           session key to Bob with a packet for forwarding to Alice.*)
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    OR3  "[| evs3: otway;  B ~= Server;  A ~= B;  Key KAB ~: used evs3;
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             Says B' Server {|Agent A, Agent B, Nonce NA, Nonce NB|}
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               : set evs3 |]
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          ==> Says Server B 
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               {|Crypt (shrK A) {|Nonce NA, Agent A, Agent B, Key KAB|},
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                 Crypt (shrK B) {|Nonce NB, Agent A, Agent B, 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 {|Agent A, Agent B, Nonce NA, Nonce NB|} : set evs4;
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             Says S' B {|X, Crypt(shrK B){|Nonce NB,Agent A,Agent B,Key K|}|}
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               : set evs4 |]
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          ==> Says B A 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.  B is not assumed to know shrK A.*)
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    Oops "[| evso: otway;  B ~= Spy;
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             Says Server B 
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                      {|Crypt (shrK A) {|Nonce NA, Agent A, Agent B, Key K|}, 
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                        Crypt (shrK B) {|Nonce NB, Agent A, Agent B, 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