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sections/design.tex
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%!TEX root = ../main.tex
In this section we discuss the details behind the design, formal guarantees, implementation, and usage of \korg.
\subsection{High-level design}%
\label{sub:High-level design}
\cnr{need introductory paragraph about program synthesis, the main idea}
At the highest level, \korg sits on user-specified communication channels in a program written in \promela, the modeling language of the \spin model checker. The user selects an attacker model of choice and correctness properties of choice. \korg then invokes \spin, which exhaustively searches for attacks with respect to the chosen attacker model, \promela model, and correctness property.
A high-level overview of the \korg pipeline is given in the Figure \ref{fig:korg_workflow}.
@@ -16,48 +19,48 @@ A high-level overview of the \korg pipeline is given in the Figure \ref{fig:korg
\subsection{Supported Attacker Models}%
\label{sub:Supported Attacker Models}
\korg supports the automatic synthesis of attacks with respect to four general pre-defined attacker models applicable to any communication channel:
%\korg supports the automatic synthesis of attacks with respect to four general pre-defined attacker models applicable to any communication channel:
\begin{itemize}
\item \textbf{Drop Attacker Model}. Drop attackers are capable of dropping a finite number of messages off a channel.
\item \textbf{Replay Attacker Model}. Replay attackers are capable of replaying previously seen messages back onto a channel.
\item \textbf{Reorder Attacker Model}. Reorder attackers are capable of reordering messages on a channel.
\item \textbf{Insert Attacker Model}. Insert attackers are capable of inserting arbitrary messages (as specifiable by the user) onto a channel.
\end{itemize}
%\begin{itemize}
%\item \textbf{Drop Attacker Model}. Drop attackers are capable of dropping a finite number of messages off a channel.
%\item \textbf{Replay Attacker Model}. Replay attackers are capable of replaying previously seen messages back onto a channel.
%\item \textbf{Reorder Attacker Model}. Reorder attackers are capable of reordering messages on a channel.
%\item \textbf{Insert Attacker Model}. Insert attackers are capable of inserting arbitrary messages (as specifiable by the user) onto a channel.
%\end{itemize}
\korg supports four general attacker model gadgets: an attacker that can drop, replay, reorder, or insert messages on a channel. In this section we discuss the various details that went into the implementation of the gadgets that encapsulate the behavior of the respective attacker models.
% Additionally, \korg supports user-defined attacker that insert arbitrary messages onto a channel. In this section we discuss the various details that go into each attacker model.
\textbf{Drop Attacker Model Gadget}
The most simple attacker model \korg supports is an attacker that can \textit{drop} messages from a channel. The user specifies a "drop limit" value that limits the number of packets the attacker can drop from the channel. Note, a higher drop limit will increase the search space of possible attacks, thereby increasing execution time.
The dropper attacker model gadget \korg synthesizes works as follows. The gadget will nondeterministically choose to observe a message on a channel. Then, if the drop limit variable is not zero, it will consume the message. An example is shown in Figure \ref{lst:korg_drop}.
\textbf{Replay Attacker Model Gadget}
The next attacker model \korg supports is an attacker that can observe and \textit{replay} messages back onto a channel. Similarly to the drop limit for the dropping attacker model, the user can specify a "replay limit" that caps the number of observed messages the attacker can replay back onto the specified channel.
The replay attacker model gadget \korg employs works as follows. The gadget has two states, \textsc{Consume} and \textsc{Replay}. The gadget starts in the \textsc{Consume} state and nondeterministically reads (but not consumes) messages on the target channel, sending them into a local storage buffer. Once the gadget read the number of messages on the channel equivalent to the defined replay limit, its state changes to \textsc{Replay}. In the \textsc{Replay} state, the gadget nondeterministically selects messages from its storage buffer to replay onto the channel until out of messages. An example is shown in Figure \ref{lst:korg_replay}.
\textbf{Reorder Attacker Model Gadget}
\korg supports synthesizing attackers that can \textit{reorder} messages on a channel. Like the drop and replay attacker model gadgets, the user can specify a "reordering limit" that caps the number of messages that can be reordered by the attacker on the specified channel.
The reordering attacker model gadget \korg synthesizes works as follows. The gadget has three states, \textsc{Init}, \textsc{Consume}, and \textsc{Replay}. The gadget begins in the \textsc{Init} state, where it arbitrarily chooses a message to start consuming by transitioning to the \textsc{Consume} state. When in the \textsc{Consume} state, the gadget consumes all messages that appear on the channel, filling up a local buffer, until hitting the defined reordering limit. Once this limit is hit, the gadget transitions into the \textsc{Replay} state. In the \textsc{Replay} state, the gadget nondeterministically selects messages from its storage buffer to replay onto the channel until out of messages. An example is shown in Figure \ref{lst:korg_reordering}.
\textbf{Insert Attacker Models}
\korg supports the synthesis of attackers that can simply insert messages onto a channel. While the drop, replay, and reordering attacker model gadgets as previously described have complex gadgets that \korg synthesizes with respect to a user-specified channel, the insert attacker model gadget is synthesized with respect to a user-defined \textit{IO-file}. This file denotes the specific outputs and channels the attacker is capable of sending, and \korg generates a gadget capable of synthesizing attacks using the given inputs. An example I/O file is given in Figure \ref{lst:io-file}, and the generated gadget is given in Figure \ref{lst:io-file-synth}.
These attacker models can be mixed and matched as desired by the \korg user. For example, a user can specify a drop attacker and replay attacker to target channel 1, a reordering attacker to target channel 2, and an insert attacker to target channel 3. If multiple attacker models are declared, \korg will synthesize attacks where the attackers on different channel \textit{coordinate} to construct a unifying attack.
\subsection{Soundness And Completeness of Korg}%
\label{sub:Soundness And Completeness}
\input{sections/examples}
\newcommand{\comp}{\mid\mid}
\newcommand{\ioint}{\mathcal{C}}
% \korg also supports the synthesis of gadgets with respect to user-defined inputs and outputs. The user defines an \textit{IO-file} denoting the specific input and output messages the attacker is capable of sending, and \korg generates a gadget capable of synthesizing attacks with respect to the user's specification.
Fundamentally, the theoretical framework that \korg implements proposed by Hippel et al. reasons about \textit{communicating processes}; similarly, \korg is best understood as a synthesizer for attackers that sit \textit{between} communicating processes.
The theoretical attack synthesis framework and \korg use slightly different formalisms. Both employ derivations the general \textit{Input/Output (I/O) automata}, state machines whose transitions indicate sending or receiving a message.\footnote{
A fundamental assumption both \korg and the theoretical attack synthesis framework rely upon is unicast transition relations of I/O automata within this context. That is, if one sending automata has an output transition matching an input transition of two receiving automata, only one input/output transition pair can be composed upon. Model checkers for I/O automata such as \spin will explore both possibilities.
}
In particular, the theoretical attack synthesis framework defines their own notion of a \textit{process} and argues their attack synthesis algorithm maintains soundness and completeness guarantees with respect to it, while \korg relies upon \spin's preferred model checking formalism, the B\"uchi Automata. Both utilize linear temporal logic as their specification language of choice.
We ultimately seek to conclude \korg maintains the guarantees of the theoretical framework it implements, therefore it is necessary to demonstrate the equivalence of \textit{processes} from the theoretical attack synthesis framework with the B\"uchi Automata. For ease of reading and clarity, we only provide shortened narrations of the arguments here. The detailed, definitions, theorems, and proofs are provided in Appendix Section \ref{sub:korg_proofs}.
%\korg is an implementation of the theoretical attack synthesis framework proposed by Hippel et al. This framework enjoys soundness and completeness guarantees for attacks discovered; that is, if there exists an attack, it is discovered, and if an attack is discovered, it is valid. However, the attack synthesis framework proposed by Hippel et al. reasons about an abstracted, theoretical process construct. Therefore, in order to correctly claim \korg is also sound and complete, it is necessary to demonstrate discovering an attack within the theoretical framework reduces to the semantics of \spin, the model checker \korg is built on top of.
%There exists a semantic gap between the theoretical attack synthesis framework proposed by Hippel et al., and the semantics of \korg. Therefore, in order to correctly claim \korg maintains the soundness and completeness of the theoretical framework it implements, it suffices to demonstrate finding an attack within the theoretical attack synthesis framework precisely reduces to the semantics of \spin.
%the model checker \korg is implemented on top of.
\begin{theorem}
A process, as defined in Hippel et al., always directly corresponds to a B\"uchi Automata.
\end{theorem}
In short, a process in the theoretical attack synthesis framework is a Kripke Structure equipped with input and output transitions. That is, when composing two processes, an output transition must be matched to a respective input transition. Processes also include atomic propositions, which the given linear temporal logic specifications are defined over. We invoke and build on the well-known correspondence between Kripke Structures and \ba to show our desired correspondence.
\begin{theorem}
Checking whether there exists an attacker under a given threat model, the R-$\exists$ASP problem as proposed in Hippel et al., is equivalent to B\"uchi Automata language inclusion (which is in turn solved by the \spin model checker).
\end{theorem}
Via the previous theorem, we can translate the threat model processes and the victim processes to \ba and intersect them. B\"uchi Automata intersection corresponds with \ba language inclusion, which is in turn solved by \spin. From this result, we naturally get a complexity-theoretic result for finding an attacker from a given threat model.
%\begin{proof}
%Recalling the definitions from Hippel et al., a \textit{process} is Kripke structure whose transitions are equipped additional input and output operations in the same flavor as a standard I/O automata.\footnote{Modeling processes in this way allows for the simultaneous modeling of message passing while also maintaining the ability to leverage Linear Temporal Logic for specification}
@@ -75,20 +78,12 @@ Via the previous theorem, we can translate the threat model processes and the vi
%\end{proof}
\begin{theorem}
Checking whether there exists an attacker for a given threat model, the R-$\exists$ASP problem as proposed in Hippel et al., is PSPACE-complete.
\end{theorem}
By the previous argument the attack synthesis problem reduces to intersecting multiple \ba (or alternatively \ba language inclusion), which is well-known to be PSPACE-complete \cite{Kozen_1977}.
Although this result implies \korg has a rough upper bound complexity, in practice due the various implementation-level optimizations of \spin finding attacks on some property is generally fast, but proving their absence via a state-space search can expensive \cite{Clarke_Wang}.
Since \korg uses \spin as its underlying model checker, we can effectively conclude \korg is sound and complete.
%By the previous argument, the R-$\exists$ASP problem reduces to intersecting multiple \ba, which is well-known to be PSPACE-complete \cite{Kozen_1977}.
\subsection{The Korg Implementation}%
\label{sub:The Korg Implementation}
\subsection{\korg Implementation}%
\label{sub:impl}
We implemented \korg on top of the \spin, a popular and robust model checker for reasoning about distributed and concurrent systems. Intuitively, models written in \promela, the modeling language of \spin, are communicating state machines whose messages are passed over defined \textit{channels}. Channels in \promela can either be unbuffered \textit{synchronous} channels, or buffered \textit{asynchronous} channels. \korg generates attacks \textit{with respect} to these defined channels.
@@ -106,7 +101,7 @@ active proctype Peer2() {
}
\end{lstlisting}
\korg is designed to parse user-chosen channels and generate gadgets for sending, receiving, and manipulating messages on them. \korg has built-in gadgets that are designed to emulate various real-world attacker models, as further described in Section \ref{sec:usage_attacker_models}.
\korg is designed to parse user-chosen channels and generate gadgets for sending, receiving, and manipulating messages on them. \korg has built-in gadgets that are designed to emulate various real-world attacker models.
%Additionally, users can explicitly define which messages a generated gadget can send and receive.
Once one or multiple gadgets are generated, \korg invokes \spin to check if a given property of interest remains satisfied in the presence of the attacker gadgets.
@@ -114,8 +109,7 @@ Once one or multiple gadgets are generated, \korg invokes \spin to check if a gi
\label{sub:Usage}
To demonstrate the usage of \korg, we'll walk through an example of proving the alternate bit protocol (ABP) is secure with respect to attackers that can replay messages. ABP is a simple communication protocol that provides reliable communication between two peers over an unreliable communication by continually agreeing on a bit value.
To demonstrate the usage of \korg, we provide a step-by-step example of proving the alternate bit protocol (ABP) is secure with respect to attackers that can replay messages. ABP is a simple communication protocol that provides reliable communication between two peers over an unreliable communication by continually agreeing on a bit value.
To use \korg, the user first authors a \promela model and a correctness property in LTL. For example, take the \promela model as shown in Listing \ref{lst:abp}. The sender repeatedly sends its stored bit, \texttt{A\_curr}, to the receiver. The receiver changes its internal bit, \texttt{B\_curr}, and sends an acknowledgement to the sender. When the sender receives the acknowledgement, it will bitflip \texttt{A\_curr} and repeatedly send the updated bit. A natural specification for this protocol, formalized into the LTL property \texttt{eventually\_agrees}, states that if the sender and receiver do not currently agree on a bit, they eventually will be able to reach an agreement.
@@ -152,7 +146,7 @@ ltl eventually_agrees {
Next, the user selects a \textit{channel} to generate an attacker on, and an attacker model of choice. For example, we select \texttt{StoR} and \texttt{RtoS} as our channels of choice, \texttt{replay} as our attacker model of choice, and assume the ABP model is in the file \texttt{abp.pml}. Then, we run \korg via command line.
\begin{lstlisting}[label={lst:korg-shell}]
$ ./korg --model=abp.pml --attacker=replay --channel=StoR,RtoS --eval
$ ./panda --model=abp.pml --attacker=replay --channel=StoR,RtoS --eval
\end{lstlisting}
\korg will then modify the \texttt{abp.pml} file to include the \texttt{replay} attacker gadgets attacking channels \texttt{StoR} and \texttt{RtoS}, and model-check it with \spin. \korg outputs the following text, cut down for readability, indicating an exhaustive search for attacks:
@@ -162,7 +156,7 @@ Full statespace search for:
ltl eventually_agree ((A_curr!=B_curr))) implies (eventually ((A_curr==B_curr))
Korg's exhaustive search is complete, no attacks found!
PANDA's exhaustive search is complete, no attacks found!
\end{lstlisting}
If desired, \texttt{--output} can also be specified so the \korg-modified \texttt{abp.pml} can be more closely examined and modified. A full shell-script replicating this example is available in the artifact.