doc-src/TutorialI/Protocol/document/Event.tex

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\begin{isabellebody}%
\def\isabellecontext{Event}%
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\isamarkupsection{Event Traces \label{sec:events}%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
The system's behaviour is formalized as a set of traces of
\emph{events}.  The most important event, \isa{Says\ A\ B\ X}, expresses
$A\to B : X$, which is the attempt by~$A$ to send~$B$ the message~$X$.
A trace is simply a list, constructed in reverse
using~\isa{{\isacharhash}}.  Other event types include reception of messages (when
we want to make it explicit) and an agent's storing a fact.

Sometimes the protocol requires an agent to generate a new nonce. The
probability that a 20-byte random number has appeared before is effectively
zero.  To formalize this important property, the set \isa{used\ evs}
denotes the set of all items mentioned in the trace~\isa{evs}.
The function \isa{used} has a straightforward
recursive definition.  Here is the case for \isa{Says} event:
\begin{isabelle}%
\ \ \ \ \ used\ {\isacharparenleft}Says\ A\ B\ X\ {\isacharhash}\ evs{\isacharparenright}\ {\isacharequal}\ parts\ {\isacharbraceleft}X{\isacharbraceright}\ {\isasymunion}\ used\ evs%
\end{isabelle}

The function \isa{knows} formalizes an agent's knowledge.  Mostly we only
care about the spy's knowledge, and \isa{knows\ Spy\ evs} is the set of items
available to the spy in the trace~\isa{evs}.  Already in the empty trace,
the spy starts with some secrets at his disposal, such as the private keys
of compromised users.  After each \isa{Says} event, the spy learns the
message that was sent:
\begin{isabelle}%
\ \ \ \ \ knows\ Spy\ {\isacharparenleft}Says\ A\ B\ X\ {\isacharhash}\ evs{\isacharparenright}\ {\isacharequal}\ insert\ X\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}%
\end{isabelle}
Combinations of functions express other important
sets of messages derived from~\isa{evs}:
\begin{itemize}
\item \isa{analz\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}} is everything that the spy could
learn by decryption
\item \isa{synth\ {\isacharparenleft}analz\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isacharparenright}} is everything that the spy
could generate
\end{itemize}%
\end{isamarkuptext}%
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