--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/TutorialI/document/Message.tex Thu Jul 26 17:16:02 2012 +0200
@@ -0,0 +1,1638 @@
+%
+\begin{isabellebody}%
+\def\isabellecontext{Message}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isatagtheory
+%
+\endisatagtheory
+{\isafoldtheory}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isadelimML
+%
+\endisadelimML
+%
+\isatagML
+%
+\endisatagML
+{\isafoldML}%
+%
+\isadelimML
+%
+\endisadelimML
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isamarkupsection{Agents and Messages%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+All protocol specifications refer to a syntactic theory of messages.
+Datatype
+\isa{agent} introduces the constant \isa{Server} (a trusted central
+machine, needed for some protocols), an infinite population of
+friendly agents, and the~\isa{Spy}:%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{datatype}\isamarkupfalse%
+\ agent\ {\isaliteral{3D}{\isacharequal}}\ Server\ {\isaliteral{7C}{\isacharbar}}\ Friend\ nat\ {\isaliteral{7C}{\isacharbar}}\ Spy%
+\begin{isamarkuptext}%
+Keys are just natural numbers. Function \isa{invKey} maps a public key to
+the matching private key, and vice versa:%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{type{\isaliteral{5F}{\isacharunderscore}}synonym}\isamarkupfalse%
+\ key\ {\isaliteral{3D}{\isacharequal}}\ nat\isanewline
+\isacommand{consts}\isamarkupfalse%
+\ invKey\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}key\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ key{\isaliteral{22}{\isachardoublequoteclose}}%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\begin{isamarkuptext}%
+Datatype
+\isa{msg} introduces the message forms, which include agent names, nonces,
+keys, compound messages, and encryptions.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{datatype}\isamarkupfalse%
+\isanewline
+\ \ \ \ \ msg\ {\isaliteral{3D}{\isacharequal}}\ Agent\ \ agent\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Nonce\ \ nat\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Key\ \ \ \ key\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ MPair\ \ msg\ msg\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Crypt\ \ key\ msg%
+\begin{isamarkuptext}%
+\noindent
+The notation $\comp{X\sb 1,\ldots X\sb{n-1},X\sb n}$
+abbreviates
+$\isa{MPair}\,X\sb 1\,\ldots\allowbreak(\isa{MPair}\,X\sb{n-1}\,X\sb n)$.
+
+Since datatype constructors are injective, we have the theorem
+\begin{isabelle}%
+Crypt\ K\ X\ {\isaliteral{3D}{\isacharequal}}\ Crypt\ K{\isaliteral{27}{\isacharprime}}\ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ K\ {\isaliteral{3D}{\isacharequal}}\ K{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ X\ {\isaliteral{3D}{\isacharequal}}\ X{\isaliteral{27}{\isacharprime}}%
+\end{isabelle}
+A ciphertext can be decrypted using only one key and
+can yield only one plaintext. In the real world, decryption with the
+wrong key succeeds but yields garbage. Our model of encryption is
+realistic if encryption adds some redundancy to the plaintext, such as a
+checksum, so that garbage can be detected.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isamarkupsection{Modelling the Adversary%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+The spy is part of the system and must be built into the model. He is
+a malicious user who does not have to follow the protocol. He
+watches the network and uses any keys he knows to decrypt messages.
+Thus he accumulates additional keys and nonces. These he can use to
+compose new messages, which he may send to anybody.
+
+Two functions enable us to formalize this behaviour: \isa{analz} and
+\isa{synth}. Each function maps a sets of messages to another set of
+messages. The set \isa{analz\ H} formalizes what the adversary can learn
+from the set of messages~$H$. The closure properties of this set are
+defined inductively.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
+\isanewline
+\ \ analz\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}msg\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ msg\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ H\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}msg\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{where}\isanewline
+\ \ \ \ Inj\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{2C}{\isacharcomma}}simp{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Fst{\isaliteral{3A}{\isacharcolon}}\ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}X{\isaliteral{2C}{\isacharcomma}}Y{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Snd{\isaliteral{3A}{\isacharcolon}}\ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}X{\isaliteral{2C}{\isacharcomma}}Y{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Decrypt\ {\isaliteral{5B}{\isacharbrackleft}}dest{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ \isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Crypt\ K\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{3B}{\isacharsemicolon}}\ Key{\isaliteral{28}{\isacharparenleft}}invKey\ K{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{22}{\isachardoublequoteclose}}%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\begin{isamarkuptext}%
+Note the \isa{Decrypt} rule: the spy can decrypt a
+message encrypted with key~$K$ if he has the matching key,~$K^{-1}$.
+Properties proved by rule induction include the following:
+\begin{isabelle}%
+G\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ analz\ G\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ analz\ H\rulename{analz{\isaliteral{5F}{\isacharunderscore}}mono}\par\smallskip%
+analz\ {\isaliteral{28}{\isacharparenleft}}analz\ H{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ analz\ H\rulename{analz{\isaliteral{5F}{\isacharunderscore}}idem}%
+\end{isabelle}
+
+The set of fake messages that an intruder could invent
+starting from~\isa{H} is \isa{synth{\isaliteral{28}{\isacharparenleft}}analz\ H{\isaliteral{29}{\isacharparenright}}}, where \isa{synth\ H}
+formalizes what the adversary can build from the set of messages~$H$.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
+\isanewline
+\ \ synth\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}msg\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ msg\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ H\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}msg\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{where}\isanewline
+\ \ \ \ Inj\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Agent\ \ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Agent\ agt\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ MPair\ \ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{3B}{\isacharsemicolon}}\ \ Y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}X{\isaliteral{2C}{\isacharcomma}}Y{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Crypt\ \ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{3B}{\isacharsemicolon}}\ \ Key\ K\ {\isaliteral{5C3C696E3E}{\isasymin}}\ H{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Crypt\ K\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\begin{isamarkuptext}%
+The set includes all agent names. Nonces and keys are assumed to be
+unguessable, so none are included beyond those already in~$H$. Two
+elements of \isa{synth\ H} can be combined, and an element can be encrypted
+using a key present in~$H$.
+
+Like \isa{analz}, this set operator is monotone and idempotent. It also
+satisfies an interesting equation involving \isa{analz}:
+\begin{isabelle}%
+analz\ {\isaliteral{28}{\isacharparenleft}}synth\ H{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ analz\ H\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ synth\ H\rulename{analz{\isaliteral{5F}{\isacharunderscore}}synth}%
+\end{isabelle}
+Rule inversion plays a major role in reasoning about \isa{synth}, through
+declarations such as this one:%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}\isamarkupfalse%
+\ Nonce{\isaliteral{5F}{\isacharunderscore}}synth\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Nonce\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}%
+\begin{isamarkuptext}%
+\noindent
+The resulting elimination rule replaces every assumption of the form
+\isa{Nonce\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H} by \isa{Nonce\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ H},
+expressing that a nonce cannot be guessed.
+
+A third operator, \isa{parts}, is useful for stating correctness
+properties. The set
+\isa{parts\ H} consists of the components of elements of~$H$. This set
+includes~\isa{H} and is closed under the projections from a compound
+message to its immediate parts.
+Its definition resembles that of \isa{analz} except in the rule
+corresponding to the constructor \isa{Crypt}:
+\begin{isabelle}%
+\ \ \ \ \ Crypt\ K\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ H%
+\end{isabelle}
+The body of an encrypted message is always regarded as part of it. We can
+use \isa{parts} to express general well-formedness properties of a protocol,
+for example, that an uncompromised agent's private key will never be
+included as a component of any message.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimML
+%
+\endisadelimML
+%
+\isatagML
+%
+\endisatagML
+{\isafoldML}%
+%
+\isadelimML
+%
+\endisadelimML
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimML
+%
+\endisadelimML
+%
+\isatagML
+%
+\endisatagML
+{\isafoldML}%
+%
+\isadelimML
+%
+\endisadelimML
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isatagtheory
+%
+\endisatagtheory
+{\isafoldtheory}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+\end{isabellebody}%
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "root"
+%%% End: