preliminaries.tex 8.38 KB
 Paul Fiterau Brostean committed Jan 20, 2017 1 2 3 4 5 \section{Model learning background}\label{sec:prelims} \subsection{Mealy machines} \label{ssec:mealy} We use \textit{Mealy machines} to represent the state machine of SSH implementations. A Mealy machine is a a 5-tuple $\mathcal{M} = (Q, q_0, I, O, \rightarrow \rangle)$, where $I$, $O$ and $Q$ are finite sets of \emph{inputs}, \emph{outputs} and \emph{states}, $q_0 \in Q$ is the initial state, and $\rightarrow \subseteq Q \times I \times O \times Q$ is the \emph{transition relation}. We say $q \xrightarrow{i/o} q'$ if $(q, i, o, q') \in \rightarrow$.  Paul Fiterau Brostean committed Jan 18, 2017 6   Paul Fiterau Brostean committed Jan 20, 2017 7 8 9 A Mealy machine $\mathcal{M}$ is \emph{input enabled} if for each state $q$ and input $i$, there is a transition $q \xrightarrow{i/o} q'$, for some $o$ and $q'$. Additionally, a Mealy machine is said to be \emph{deterministic} if there is at most one such transition defined. In our setting, we restrict our representations of systems to Mealy machines that are both input enabled and deterministic.  Paul Fiterau Brostean committed Jan 18, 2017 10   Paul Fiterau Brostean committed Jan 20, 2017 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 %\begin{figure}[h] %\centering %\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=2.8cm] % \node[initial,state] (q0) {$q_0$}; % \node[state] (q1) [right of=q0] {$q_1$}; % \node[state] (q2) [right of=q1] {$q_2$}; % % \path[->] (q0) edge node [below] {X/A} (q1); % \path[->] (q1) edge node [below] {Y/B} (q2); % \path[->] (q0) edge [bend left] node {Y/A} (q2); % \path[->] (q2) edge [loop right] node [text centered, text width = 1cm] {X/A \\ Y/B} (q2); % \path[->] (q1) edge [loop below] node {X/B} (q1); %\end{tikzpicture} %\caption{Example Mealy machine} %\label{mealy example} %\end{figure}  Paul Fiterau Brostean committed Jan 18, 2017 27   Paul Fiterau Brostean committed Jan 20, 2017 28 29 \subsection{MAT Framework} \label{ssec:mat} The most efficient algorithms for model learning all follow  Paul Fiterau Brostean committed Jan 29, 2017 30 the pattern of a \emph{minimally adequate teacher (MAT)} as proposed by Angluin~\cite{Angluin1987Learning}.  Paul Fiterau Brostean committed Jan 20, 2017 31 32 33 34 35 36 37 38 39 40 41 42 43 In the MAT framework, learning is viewed as a game in which a learner has to infer an unknown automaton by asking queries to a teacher. The teacher knows the automaton, which in our setting is a deterministic Mealy machine $\M$. Initially, the learner only knows the inputs $I$ and outputs $O$ of $\M$. The task of the learner is to learn $\M$ through two types of queries: \begin{itemize} \item With a \emph{membership query}, the learner asks what the response is to an input sequence $\sigma \in I^{\ast}$. The teacher answers with the output sequence in $A_{\M}(\sigma)$. \item With an \emph{equivalence query}, the learner asks whether a hypothesized Mealy machine $\CH$ is correct, that is, whether $\CH \approx \M$. The teacher answers \emph{yes} if this is the case. Otherwise it answers \emph{no} and supplies a \emph{counterexample}, which is a sequence $\sigma \in I^{\ast}$ that triggers a different output sequence for both Mealy machines, that is, $A_{\CH}(\sigma) \neq A_{\M}(\sigma)$. \end{itemize}  Paul Fiterau Brostean committed Jan 18, 2017 44   Paul Fiterau Brostean committed Jan 20, 2017 45 46 Model learning algorithms have been developed developed for learning deterministic Mealy machines using a finite number of queries. We point to \cite{Isberner2015} for a recent overview. These algorithms are leveraged  Paul Fiterau Brostean committed Jan 24, 2017 47 48 in applications where one wants to learn a model of a black-box reactive system, or System Under Learning ({\dsut}). The teacher typically consists of the {\dsut}, which answers membership queries, and a conformance  Paul Fiterau Brostean committed Jan 20, 2017 49 testing tool \cite{LeeY96} that approximates the equivalence queries using a set  Paul Fiterau Brostean committed Jan 24, 2017 50 of \emph{test queries}. A test query consists of asking to the {\dsut} for the response to an input sequence  Paul Fiterau Brostean committed Jan 20, 2017 51 $\sigma \in I^{\ast}$, similar to a membership query.  Paul Fiterau Brostean committed Jan 18, 2017 52   Paul Fiterau Brostean committed Jan 20, 2017 53 54 55 \subsection{Abstraction} \label{ssec:mappers} Most current learning algorithms are only applicable to Mealy machines with small alphabets comprising abstract messages. Practical systems typically have parameterized input/output alphabets, whose application triggers updates on the system's state variables. To learn  Paul Fiterau Brostean committed Jan 24, 2017 56 these systems we place a \emph{mapper} between the {\dlearner} and the {\dsut}. The mapper is a transducer which translates  Paul Fiterau Brostean committed Jan 20, 2017 57 concrete inputs to abstract inputs and concrete outputs to abstract outputs. For a thorough definition of mappers, we refer to \cite{AJUV15}.  Paul Fiterau Brostean committed Jan 18, 2017 58   Paul Fiterau Brostean committed Jan 20, 2017 59 %Perhaps some explanation  Paul Fiterau Brostean committed Jan 18, 2017 60   Paul Fiterau Brostean committed Jan 20, 2017 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 % % %concrete inputs in $I$ to abstract inputs in $X$, %concrete outputs in $O$ to abstract outputs in $Y$, and vice versa. %alphabets % % %Starting from Angluin's seminal $L^{\ast}$ algorithm \cite{Ang87}, many %algorithms have been proposed for learning finite, deterministic Mealy machines %via a finite number of queries. We refer to \cite{Isberner2015} for recent overview. %In applications in which one wants to learn a model of a black-box reactive system, the teacher typically %consists of a System Under Learning (\dsut) that answers the membership queries, and a conformance %testing tool \cite{LeeY96} that approximates the equivalence queries using a set %of \emph{test queries}. A test query consists of asking to the \dsut for the response to an input sequence %$\sigma \in I^{\ast}$, similar to a membership query. % % % % % % %In protocol state fuzzing, a state machine of the implementation is learned by actively sending and receiving messages to and from the System Under Learning (SUL). A single message is called a \textit{query}, and a sequence of messages a \textit{trace}. The state machine is formed by sending consecutive traces to the SUL and analyzing the output. The trace to be sent is, in our case, determined by the L*-algorithm. When a trace is completed the SUL has to be reset to its initial state. % %After sending a sufficient amount of traces, a hypothesis is formed. The hypothesis is checked for by a testing oracle. Said oracle sends traces to the SUL, predicts an output through the hypothesis, and compares this output to the actual output received by the SUL. % %In our case, sending messages to the SUL means sending packets that contain, for example, the length of the packet, a sequence number or a list of supported encryptions. This information is unnecessary for the learning process, and is not supported by the Learnlib implementation of L* that we use. We abstract all this information away, leaving us with an abstract representation of messages. To convert these abstract messages to correct packets and back, a mapper is used. This mapper has to keep track of state variables, and has to be able to perform actions such as encryption and compression. This means that the mapper itself contains a state machine, which is based on existing knowledge about the protocol used in the SUL. % %\begin{figure}[h] %\centering %\includegraphics[scale=0.8]{Naamloos.png} %\caption{A learning setup} %\label{learning setup} %\end{figure} % %The setup shown in figure \ref{learning setup} is the setup Verleg used, and serves as an example for a typical learning setup, here Learner'' is the program that uses the L*-algorithm to generate traces to send to the SUL, these traces are in the form of abstract messages. The learner sends these messages to the mapper, which translates them to concrete packages which are sent to the SUL. A response of the SUL is then converted by the mapper to an abstract message and sent to the learner. % %\subsection{Secure Shell} \label{secure shell} % %The SSH-protocol uses a client-server structure consisting of three components. These components will be referred to as layers, however note that outer layers do not wrap inner layers, instead messages of different layers are distinguished through their message number. The three components are as follows: %\begin{itemize} %\item The transport layer protocol. This creates the basis for communication between server and client, providing a key exchange protocol and server authentication. The key exchange protocol is performed through three roundtrips. During the first, both client and server send a KEXINIT message. Then, the client sends a KEX30 message, the server responds with a KEX31 message. Finally, both parties send a NEWKEYS message, which indicates that the keys sent in the second step can be used. %\item The user authentication protocol. This component is used to authenticate a client to the server, for example, through a username and password combination, or through SSH-keys. %\item The connection protocol. This is used to provide different services to the connected client, it can thus multiplex the encrypted channel into different channels. The provided services can be services like file transfer or a remote terminal. Typical messages are requests for opening or closing channels, or requests for earlier named services.  Paul Fiterau Brostean committed Feb 07, 2017 104 %\end{itemize}