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sections/abstract.tex
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Distributed protocols underpin the modern internet, making their correctness and security critical. Formal methods provide rigorous tools for analyzing protocol correctness and cryptographic security, yet existing tools fall short for denial of service (DoS) analysis. We introduce \korg, a tool that synthesizes attacks on distributed protocols by targeting communication channels to violate linear temporal logic (LTL) specifications. \korg provides sound, complete analysis, synthesizing attacks or proving their absence through exhaustive state-space search. With support for pre-defined and custom attacker models, \korg enables targeted DoS analysis and broader LTL-based verification, demonstrated through various case studies.
Distributed protocols are the lynchpin of the modern internet,
underpinning every internet service.
This has in turn motivated a massive amount of research ensuring the security,
reliability, and performance of distributed protocols.
A wide-ranging assumption in these works is assuming distributed
protocols operate over \textit{faulty} or
\textit{attacker-controlled} channels, where messages can be arbitrarily
inserted, dropped, replayed, or reordered.
Formal methods work formally verifying distributed protocols
typically defines their own notion of imperfect or malicious channels,
then constructively proves their protocol is correct with respect to it.
In this work we take a fundamentally different approach:
we develop a rigorous methodology for
automatically discovering \textit{attack traces}
on distributed protocols with respect to imperfect channels,
and we introduce \korg, a highly generalizable tool for synthesizing
attacks on distributed protocols that implements our methodology.
\korg provides sound, complete analysis, synthesizing attacks on arbitrary
linear temporal logic (LTL) protocol specifications
or proving the absence of such through an exhaustive state-space search.
We demonstrate the applicability of \korg by employing to study TCP, SCTP, and Raft.
% ===== OLD ABSTRACT ======
%Distributed protocols underpin the modern internet, making their correctness and security critical. Formal methods provide rigorous tools for analyzing protocol correctness and cryptographic security, yet existing tools fall short for denial of service (DoS) analysis. We introduce \korg, a tool that synthesizes attacks on distributed protocols by targeting communication channels to violate linear temporal logic (LTL) specifications. \korg provides sound, complete analysis, synthesizing attacks or proving their absence through exhaustive state-space search. With support for pre-defined and custom attacker models, \korg enables targeted DoS analysis and broader LTL-based verification, demonstrated through various case studies.

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sections/case_studies.tex
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@@ -109,6 +109,10 @@ Dropping AppendEntryResponse messages & no \\
\end{figure}
In our experiments, we found just one attack on our \texttt{raft-bug.pml} \promela model, violating election safety in particular. In this scenario, peer A and peer B are candidates for election. Peer A receives three votes, one from itself and two from other peers, and Peer B receives two votes, one from itself and one from another peer. The replay attacker simply replays the vote sent to peer B. Then, both Peer A and Peer B are convinced they won the election and change their state to leader. Following this, leader completeness is also naturally violated. In this scenario, \korg demonstrates its ability to discover subtle bugs in protocol logic, exploiting the buggy Raft implementation.
\subsection{SCTP}%
\label{sub:SCTP}
SCTP is a transport-layer protocol proposed as an alternative to TCP, featuring a four-way handshake, multi-homing, and multi-streaming. Among other use cases, SCTP is the data transfer protocol for various telecoms signaling protocols as well as WebRTC. For our analysis, we borrow the ten LTL properties and \promela models derived from the SCTP RFCs as described in \cite{Ginesin2024}. We evaluated the SCTP \promela model against \korg's drop, replay, and reordering attacker models on a single uni-directional communication channel. SCTP is designed to resist these attacker models, and we employ \korg to exhaustively demonstrate this is the case.
%our Raft model satisfies $\phi_1$-$\phi_5$ assuming perfect channels, and \korg allowed us to reason precisely about the effect of imperfect, vulnerable channels.

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sections/conclusion.tex
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In conclusion, \korg addresses a critical gap in the formal verification of distributed protocols by enabling the synthesis of communication channel-based attacks against arbitrary linear temporal logic specifications. By leveraging \spin, \korg ensures soundness and completeness in attack synthesis. Its modular support for pre-defined attacker models enhances its versatility, enabling thorough protocol analysis across diverse and interesting scenarios. We demonstrate the effectiveness of \korg by employing it to study TCP and Raft, marking it as an invaluable tool for ensuring the validity and security of distributed protocols.
In conclusion, \korg addresses a critical gap in the formal verification of distributed protocols by enabling the synthesis of communication channel-based attacks against arbitrary linear temporal logic specifications. By leveraging \spin, \korg ensures soundness and completeness in attack synthesis. Its modular support for pre-defined attacker models enhances its versatility, enabling thorough protocol analysis across diverse and interesting scenarios. We demonstrate the effectiveness of \korg by employing it to study TCP, Raft, and SCTP, marking it as an invaluable tool for ensuring the validity and security of distributed protocols.

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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{Mathematical Preliminaries}%
\label{sub:Mathematical Preliminaries}
Linear Temporal Logic (LTL) is a model logic for reasoning about program executions. In LTL, we say a program $P$ \textit{models} a property $\phi$ (notationally, $P \models \phi$). That is, $\phi$ holds over every execution of $P$. If $\phi$ does not hold over every execution of $P$, we say $P \not\models \phi$. The LTL language is given by predicates over a first-order logic with additional temporal operators: \textit{next}, \textit{always}, \textit{eventually}, and \textit{until}.
An LTL model checker is a tool that, given $P$ and $\phi$, can automatically check whether or not $P \models \phi$; in general, LTL is a \textit{decidable} logic, and LTL model checkers will always be able to decide whether $P \models \phi$ given enough time and resources.
We use $\mid \mid$ to denote rendezvous composition. That is, if $S = P \mid \mid Q$, processes $P$ and $Q$ are composed together into a singular state machine by matching their equivalent transitions.
\textit{LTL program synthesis} is the problem of, given an LTL specification $\phi$, automatically deriving a program $P$ that satisfies $\phi$ (that is, $P \models \phi$). \textit{LTL attack synthesis} is logically dual to LTL program synthesis. In attack synthesis, the problem is flipped: given a program $P$ and a property $\phi$ such that $P \models \phi$, we ask whether there exists some "attack" $A$ such that $(P \mid \mid A) \not\models \phi$. Fundamentally, \korg is a synthesizer for such an $A$.
\subsection{High-level design}%
\label{sub:High-level design}
As aforementioned, \korg is based on \textit{LTL attack synthesis}; in particular, \korg synthesizes attacks with respect to \textit{imperfect} channels. That is, \korg is designed to synthesize attacks that involve replaying, dropping, reordering, or inserting messages on one or more communication channels.
%As aforementioned, \korg is based on \textit{LTL attack synthesis};
\korg is designed to synthesize attacks with respect to \textit{imperfect} channels. That is, \korg is designed to synthesize attacks that involve replaying, dropping or reordering messages on one or more communication channels relied upon by the victim protocol.
%The methodology behind the construction of \korg is based on \textit{LTL attack synthesis}.
@@ -36,180 +26,11 @@ A high-level visual overview of the \korg pipeline is given in Figure \ref{fig:k
\end{figure}
\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:
%\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 models: 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}.
\begin{figure}[h]
\begin{lstlisting}[caption={Example dropping attacker model gadget with drop limit of 3, targetting channel "cn"}, label={lst:korg_drop}]
chan cn = [8] of { int, int, int };
active proctype attacker_drop() {
int b_0, b_1, b_2;
byte lim = 3; // drop limit
MAIN:
do
:: cn ? [b_0, b_1, b_2] -> atomic {
if
:: lim == 0 -> goto BREAK;
:: else ->
cn ? b_0, b_1, b_2; // consume message on the channel
lim = lim - 1;
goto MAIN;
fi
}
od
BREAK:
}
\end{lstlisting}
\end{figure}
\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}.
\begin{figure}[h]
\begin{lstlisting}[caption={Example replay attacker model gadget with the selected replay limit as 3, targetting channel "cn"}, label={lst:korg_replay}]
chan cn = [8] of { int, int, int };
// local memory for the gadget
chan gadget_mem = [3] of { int, int, int };
active proctype attacker_replay() {
int b_0, b_1, b_2; int i = 3;
CONSUME:
do
// read messages until the limit is passed
:: cn ? [b_0, b_1, b_2] -> atomic {
cn ? <b_0, b_1, b_2> -> gadget_mem ! b_0, b_1, b_2;
i--;
if
:: i == 0 -> goto REPLAY;
:: i != 0 -> goto CONSUME;
fi }
od
REPLAY:
do
:: atomic {
// nondeterministically select a random value from the storage buffer
int am;
select(am : 0 .. len(gadget_mem)-1);
do
:: am != 0 ->
am = am-1;
gadget_mem ? b_0, b_1, b_2 -> gadget_mem ! b_0, b_1, b_2;
:: am == 0 ->
gadget_mem ? b_0, b_1, b_2 -> cn ! b_0, b_1, b_2;
break;
od }
// doesn't need to use all messages on the channel
:: atomic {gadget_mem ? b_0, b_1, b_2; }
// once mem has no more messages, we're done
:: empty(gadget_mem) -> goto BREAK;
od
BREAK:
}
\end{lstlisting}
\end{figure}
% \subsection{Supported Attacker Models}%
% \label{sub:Supported Attacker Models}
\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}.
\begin{figure}[h]
\begin{lstlisting}[caption={Example reordering attacker model gadget with the selected replay limit as 3, targetting channel "cn"}, label={lst:korg_reordering}]
chan cn = [8] of { int, int, int };
chan gadget_mem = [3] of { int, int, int };
active proctype attacker_reordering() priority 255 {
byte b_0, b_1, b_2, blocker; int i = 3;
INIT:
do
:: { // arbitrarily choose a message to start consuming on
blocker = len(cn);
do :: b != len(c) -> goto INIT; od
}
:: goto CONSUME;
od
CONSUME:
do
// consume messages with high priority
:: c ? [b_0] -> atomic {
c ? b_0 -> gadget_mem ! b_0; i--;
if
:: i == 0 -> goto REPLAY;
:: i != 0 -> goto CONSUME;
fi }
od
REPLAY:
do
// replay messages back onto the channel, also with priority
:: atomic {
int am;
select(am : 0 .. len(gadget_mem)-1);
do
:: am != 0 ->
am = am-1;
gadget_mem ? b_0 -> attacker_mem_0 ! b_0;
:: am == 0 ->
gadget_mem ? b_0 -> c ! b_0;
break;
od }
:: atomic { empty(gadget_mem) -> goto BREAK; }
od
BREAK:
}
\end{lstlisting}
\end{figure}
\begin{figure}[h]
\begin{lstlisting}[caption={Example I/O file targetting channel "cn"}, label={lst:io-file}]
cn:
I:
O:1-1-1, 1-2-3, 3-4-5
\end{lstlisting}
\begin{lstlisting}[caption={Example gadget synthesized from an I/O file targetting the channel "cn"}, label={lst:io-file-synth}]
chan cn = [8] of { int, int, int };
active proctype daisy() {
INIT:
do
:: cn ! 1,1,1;
:: cn ! 1,2,3;
:: cn ! 3,4,5;
:: goto RECOVERY;
od
RECOVERY:
}
\end{lstlisting}
\end{figure}
\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.
\input{sections/examples}
% \input{sections/examples}
@@ -247,7 +68,10 @@ These attacker models can be mixed and matched as desired by the \korg user. For
\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. \spin has existed for over 40 years, and has been applied to dozens of real systems including the Mars Rover \cite{Holzmann_2014}, Path-Star Access server \cite{Holzmann_Smith_2000}, and an avionics operating system \cite{mcp}. Additionally, \spin has spawned a dedicated formal methods symposium, currently in its 32nd year\footnote{\url{https://spin-web.github.io/SPIN2025/}}, and earned the 2002 ACM Software System award.
\textbf{The SPIN Model Checker}.
We choose to implement \korg on top of the \spin, a popular and robust model checker for reasoning about distributed and concurrent systems. \spin has existed for over 40 years, and has been applied to dozens of real systems including the Mars Rover \cite{Holzmann_2014}, Path-Star Access server \cite{Holzmann_Smith_2000}, and an avionics operating system \cite{mcp}. Additionally, \spin has spawned a dedicated formal methods symposium, currently in its 32nd year\footnote{\url{https://spin-web.github.io/SPIN2025/}}, and earned the 2002 ACM Software System award. Alternatively, the \korg could easily be built on top of other automated reasoning tools besides \spin, including TLA+ using the methodology described in \cite{message_queues_TLA}, Dafny using the formulation of I/O automata described in \cite{Hsieh_Mitra_2019}, and mCRL2 using its process algebra-based modeling framework \cite{mCRL2}. We choose \spin over these options due to its historical popularity and robustness.
%TLSMIN \cite{TLSMIN}, and mCRL2 \cite{mCRL2}
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.
@@ -268,22 +92,34 @@ active proctype Peer2() {
\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.
\textbf{Preventing \korg Livelocks}
In general, there are two types of LTL properties: safety, and liveness. Informally, safety properties state "a bad thing never happens," and liveness properties state "a good thing always happens."
Therefore, safety properties can be violated by finite traces, while liveness properties require infinite traces to be violated.
When evaluating a \korg attacker model gadget against a \promela model and a liveness property, it is crucial to ensure the gadget has no cyclic behavior. If a \korg gadget has cyclic behavior in any way, it will trivially violate the liveness
property and produce a garbage attack trace. To prevent this, we make the following considerations.
First, we design our \korg gadgets such that they never arbitrarily send and consume messages to a single channel. Second, we allow \korg gadgets,
which are always processing messages on channels, to arbitrarily "skip" messages on a channel if need be. To demonstrate the latter, consider the extension of the drop attacker model gadget in Figure \ref{lst:drop_passer}. We implement message skipping by arbitrarily stopping and waiting after observing a message on a channel; once the channel is observed changing lengths, the message is considered skipped and future messages can be consumed.
%\korg supports the automatic synthesis of attacks with respect to four general pre-defined attacker models applicable to any communication channel:
\textbf{Attacker Gadget Implementations}.
\korg supports synthesizing three general attackers, implementing the gadgets as described in section \ref{sec:Attacker Gadgets}: attackers that can drop, replay, or reorder messages on a channel. We now discuss the various details that went into the implementations of the various attacker gadgets within \spin.
% an attacker that can drop, replay, reorder, or insert messages on a channel. As aforementioned, they
% 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 Gadget Implementation}.
The most simple model \korg implements is an attacker that can \textit{drop} messages from a channel. The gadget works as follows. A pre-defined limit value \texttt{lim} is set, and the attacker begins in the \texttt{MAIN} state. Whenever a message is observed on a channel, if \texttt{lim == 0} the gadget progresses to the \texttt{BREAK} state. Otherwise, the observed message is consumed, \texttt{lim} is decremented, and the gadget returns to the \texttt{MAIN} state. An example \textit{drop} gadget automatically synthesized with \korg against the channel \texttt{cn} is shown in figure \ref{lst:korg_drop}.
% An example of a gadget attacking a channel transmitting three integers is shown in Figure \ref{lst:korg_drop}.
% 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}.
\begin{figure}[h]
\begin{lstlisting}[caption={Example dropping attacker model gadget with message skipping}, label={lst:drop_passer}]
\label{lst:korg_drop}
\begin{lstlisting}[]
chan cn = [8] of { int, int, int };
active proctype attacker_drop() {
int b_0, b_1, b_2, blocker;
int b_0, b_1, b_2;
byte lim = 3; // drop limit
MAIN:
do
@@ -292,25 +128,213 @@ MAIN:
:: lim == 0 -> goto BREAK;
:: else ->
cn ? b_0, b_1, b_2; // consume message on the channel
lim = lim - 1;
goto MAIN;
fi
}
// pass over a message on a channel as needed
lim = lim - 1; goto MAIN;
fi }
od
BREAK: }
\end{lstlisting}
\caption{Example dropping attacker model gadget with drop limit of 3, targetting channel "cn"}
\label{lst:korg_drop}
\end{figure}
\textbf{Replay Attacker Gadget Implementation}.
The next model \korg implements is an attacker that can \textit{replay} messages on a channel. The gadget works as follows. The attacker model gadget comes with a pre-defined message limit value \texttt{lim}, which defines the length of the gadget storage FIFO buffer \texttt{gadget\_mem}. Then, the gadget enters the \texttt{CONSUME} state and nondeterministically chooses messages on the channel \texttt{cn} to copy into \texttt{gadget\_mem}. Once \texttt{lim=0}, the gadget transitions into the state \texttt{REPLAY}, where items are randomly selected from \texttt{gadget\_mem} to be replayed back onto the channel. Note, because \texttt{gadget\_mem} is a FIFO buffer, we must rotate messages within the channel in order to randomly select a value from it. Additionally, messages can also be nondeterministically removed from \texttt{gadget\_mem}, as all messages do not necessarily need to be replayed. Once \texttt{gadget\_mem} is empty, the gadget transitions to the \texttt{BREAK} state. An example gadget automatically synthesized with \korg against the channel \texttt{cn} is shown in figure \ref{lst:korg_replay}.
% 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}.
\begin{figure}[h]
\begin{lstlisting}[]
chan cn = [8] of { int, int, int };
// local memory for the gadget
chan gadget_mem = [3] of { int, int, int };
active proctype attacker_replay() {
int b_0, b_1, b_2; int lim = 3;
CONSUME:
do
// read messages until the limit is passed
:: cn ? [b_0, b_1, b_2] -> atomic {
// wait for the channel to change lengths
// then, once it does, go to MAIN
cn ? <b_0, b_1, b_2> -> gadget_mem ! b_0, b_1, b_2;
lim--;
if
:: lim == 0 -> goto REPLAY;
:: lim != 0 -> goto CONSUME;
fi }
od
REPLAY:
do
:: atomic {
// nondeterministically select a random value from the storage buffer
int am;
select(am : 0 .. len(gadget_mem)-1);
do
:: am != 0 ->
am = am-1;
gadget_mem ? b_0, b_1, b_2 -> gadget_mem ! b_0, b_1, b_2;
:: am == 0 ->
gadget_mem ? b_0, b_1, b_2 -> cn ! b_0, b_1, b_2;
break;
od }
// doesn't need to replay all stored msgs
:: atomic {gadget_mem ? b_0, b_1, b_2; }
// once mem has no more messages, we're done
:: empty(gadget_mem) -> goto BREAK;
od
BREAK: }
\end{lstlisting}
\caption{Example replay attacker model gadget with the selected replay limit as 3, targetting channel "cn"}
\label{lst:korg_replay}
\end{figure}
\textbf{Reorder Attacker Gadget Implementation}.
The final and most complex gadget \korg implements is an attacker that can \textit{reorder} messages on a channel. The gadget works as follows. The attacker model gadget comes with a pre-defined message limit value \texttt{lim}, which defines the length of the gadget storage FIFO buffer \texttt{gadget\_mem}. The gadget also has the highest \textit{execution priority} in the system, which ensures the gadget can always reorder messages on the victim channel without other processes interfering. The gadget first enters the \texttt{INIT} state --- in this state, the gadget non-deterministically chooses to pass messages on the victim channel, or transition to the \texttt{CONSUME} state. In the \texttt{CONSUME} state, the gadget consumes each message it sees and stores them in \texttt{gadget\_mem}, a FIFO buffer. Upon consuming each message from the victim channel, \texttt{lim} is decremented. Once \texttt{lim=0}, the gadget transitions to \texttt{REPLAY}. Then, messages are randomly selected from \texttt{gadget\_mem} to be replayed back onto the channel. Note, because \texttt{gadget\_mem} is a FIFO buffer, we must rotate messages within the channel in order to randomly select a value from it. Additionally, messages can also be nondeterministically removed from \texttt{gadget\_mem}, as all messages do not necessarily need to be replayed. Once \texttt{gadget\_mem} is empty, the gadget transitions to the \texttt{BREAK} state. An example gadget automatically synthesized with \korg against the channel \texttt{cn} is shown in figure \ref{lst:korg_reordering}.
% The attacker model gadget comes with a pre-defined message limit value \texttt{lim}, which defines the length of the gadget storage FIFO buffer \texttt{gadget\_mem}. Then, the gadget enters the \texttt{CONSUME} state and nondeterministically chooses messages on the channel \texttt{cn} to copy into \texttt{gadget\_mem}. Once \texttt{lim=0}, the gadget transitions into the state \texttt{REPLAY}, where items are randomly selected from \texttt{gadget\_mem} to be replayed back onto the channel. Note, because \texttt{gadget\_mem} is a FIFO buffer, we must rotate messages within the channel in order to randomly select a value from it. Additionally, messages can also be nondeterministically removed from \texttt{gadget\_mem}, as all messages do not necessarily need to be replayed. Once \texttt{gadget\_mem} is empty, the gadget transitions to the \texttt{BREAK} state.
% \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}.
\begin{figure}[h]
\begin{lstlisting}[]
chan cn = [8] of { int, int, int };
// local memory for the gadget
chan gadget_mem = [3] of { int, int, int };
active proctype attacker_reordering() priority 255 {
byte b_0, b_1, b_2, blocker; int lim = 3;
INIT:
do
:: wait_until_pass(ch);
:: goto CONSUME;
od
CONSUME:
do
// consume messages with high priority
:: c ? [b_0] -> atomic {
c ? b_0 -> gadget_mem ! b_0; lim--;
if
:: lim == 0 -> goto REPLAY;
:: lim != 0 -> goto CONSUME;
fi }
od
REPLAY:
do
// replay messages back onto the channel, also with priority
:: atomic {
int am;
select(am : 0 .. len(gadget_mem)-1);
do
:: am != 0 ->
am = am-1;
gadget_mem ? b_0 -> attacker_mem_0 ! b_0;
:: am == 0 ->
gadget_mem ? b_0 -> c ! b_0;
break;
od }
:: atomic { empty(gadget_mem) -> goto BREAK; }
od
BREAK: }
\end{lstlisting}
\caption{Example reordering attacker model gadget with the selected replay limit as 3, targetting channel "cn"}
\label{lst:korg_reordering}
\end{figure}
% \begin{figure}[h]
% \begin{lstlisting}[caption={Example I/O file targetting channel "cn"}, label={lst:io-file}]
% cn:
% I:
% O:1-1-1, 1-2-3, 3-4-5
% \end{lstlisting}
% \begin{lstlisting}[caption={Example gadget synthesized from an I/O file targetting the channel "cn"}, label={lst:io-file-synth}]
% chan cn = [8] of { int, int, int };
% active proctype daisy() {
% INIT:
% do
% :: cn ! 1,1,1;
% :: cn ! 1,2,3;
% :: cn ! 3,4,5;
% :: goto RECOVERY;
% od
% RECOVERY:
% }
% \end{lstlisting}
% \end{figure}
% \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.
\textbf{Preventing \korg Livelocks}.
In general, there are two types of LTL properties: safety, and liveness. Informally, safety properties state "a bad thing never happens," and liveness properties state "a good thing always happens."
Therefore, safety properties can be violated by finite traces, while liveness properties require infinite traces to be violated.
When evaluating a \korg attacker model gadget against a \promela model and a liveness property, it is crucial to ensure the gadget has no cyclic behavior. If a \korg gadget has cyclic behavior in any way, it will trivially violate the liveness
property and produce a garbage attack trace. To prevent this, we make the following considerations.
First, we design our \korg gadgets such that they never arbitrarily send and consume messages to a single channel. Second, we allow \korg gadgets,
which are always processing messages on channels, to arbitrarily "skip" messages on a channel if need be. To demonstrate the latter, consider the extension of the drop attacker model gadget in Figure \ref{lst:drop_passer}. We implement message skipping by arbitrarily stopping and waiting after observing a message on a channel; once the channel is observed changing lengths, the message is considered skipped and future messages can be consumed.
\textbf{Passing Messages On Channels}.
In order to arbitrarily pass messages on channels in \spin, required functionality for all three gadgets we present, we exploit the finite channel length assumption. Our \spin gadget is shown below.
\begin{quote}
\begin{lstlisting}
inline wait_until_pass(chan ch){
cn ? [b_0, b_1, b_2] -> {
// wait for chan to change lengths. then, exit the loop
blocker = len(cn);
do
:: blocker != len(cn) -> goto MAIN;
od
}
:: goto BREAK;
od
BREAK:
:: blocker != len(cn) -> break;
od }
}
\end{lstlisting}
\end{figure}
\end{lstlisting}
\end{quote}
That is, when we enter \texttt{wait\_until\_pass}, we track the length of the channel \texttt{cn} and wait until \texttt{len(cn)} changes. This allows us to arbitrarily pass messages on a given channel \texttt{cn} without reasoning directly about the message.
% \begin{figure}[h]
% \begin{lstlisting}[caption={Example dropping attacker model gadget with message skipping}, label={lst:drop_passer}]
% chan cn = [8] of { int, int, int };
% active proctype attacker_drop() {
% int b_0, b_1, b_2, blocker;
% byte lim = 3; // drop limit
% MAIN:
% do
% :: cn ? [b_0, b_1, b_2] -> atomic {
% if
% :: lim == 0 -> goto BREAK;
% :: else ->
% cn ? b_0, b_1, b_2; // consume message on the channel
% lim = lim - 1;
% goto MAIN;
% fi
% }
% // pass over a message on a channel as needed
% :: cn ? [b_0, b_1, b_2] -> atomic {
% // wait for the channel to change lengths
% // then, once it does, go to MAIN
% blocker = len(cn);
% do
% :: blocker != len(cn) -> goto MAIN;
% od
% }
% :: goto BREAK;
% od
% BREAK:
% }
% \end{lstlisting}
% \end{figure}
\subsection{Usage}%

44
sections/introduction.tex
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@@ -1,4 +1,46 @@
%!TEX root = ../main.tex
Distributed protocols are the lynchpin of the modern internet,
representing the fundamental communication and coordination backbone
of all modern services over the internet.
The vast importance of distributed protocols has motivated ample
research in ensuring their security, reliability, and
performance. One popular approach in prior literature
has been the employment of
\textit{formal methods}, the use of mathematically rigorous techniques,
to analyze and verify distributed protocols.
Formal methods has been applied to verify Raft \cite{Wilcox_Woos_Panchekha_Tatlock_Wang_Ernst_Anderson, Woos_Wilcox_Anton_Tatlock_Ernst_Anderson_2016, Ongaro_Ousterhout},
Paxos \cite{Delzanno_Tatarek_Traverso_2014, ironfleet, Rahli_Vukotic_Völp_Esteves-Verissimo_2018}, PBFT \cite{Sergey_Wilcox_Tatlock_2018, ironfleet}, and countless other distributed protocols \cite{Smith_1997, Narayana_Chen_Zhao_Chen_Fu_Zhou_2006, Arun_Arashloo_Saeed_Alizadeh_Balakrishnan_2021, Beurdouche}.
A common assumption among all the prior formal methods work is assuming
distributed protocols operate over \textit{imperfect} or
\textit{attacker-controlled} communication channels, where
messages can be arbitrarily dropped, replayed, or reordered, then proving
the targeted protocol maintains properties of interest with respect to them.
In this work, we take a fundamentally different approach to studying distributed protocols under imperfect channels. While previous work generally assumes one specific channel configuration and primarily seeks to manually construct proofs with respect to it, we study protocols under various channel configurations and seek to automatically discover interesting attack traces, counterexamples, and guarantees.
We introduce a general methodology for automatically discovering dropping, replay, reordering attacks traces on distributed protocols, and we introduce \korg, a highly generalizable tool for synthesizing attacks on distributed protocols that implements our methodology and the drop, replay, and reordering attacker models. \korg targets the communication channels between the protocol endpoints, and synthesizes attacks to violate general linear temporal logic (LTL) specifications. \korg is designed to either synthesize an attack, or prove the absence of such via an exhaustive state-space search. \korg is sound and complete, meaning if there exists an attack \korg will find it, and \korg will never have false positives. \korg is also designed to be easy to use once the protocol model is constructed: all a user must do is select the victim channels, select the desired attacker models, and invoke \korg.
In this work we take an approach rooted in \textit{formal methods} and \textit{automated reasoning} to construct \korg. In particular, we employ \textit{model checking}, a sub-discipline of formal methods, to decidably and automatically find attacks in protocols or prove the absence of such.
We summarize our contributions:
\begin{itemize}
\item We present generalizable gadgets representing attackers capable of dropping, replaying, and reordering messages on communication channels of distributed protocols.
\item We present \korg, a tool for synthesizing attacks against distributed communication protocols. \korg supports four general attacker models: an attacker that can drop, replay, reorder, or insert messages on a channel.
\item We provide an overview of \korg and demonstrate its usage by walking through applying it to the ABP protocol
\item We present three case studies for three well-known protocols, TCP, Raft, and SCTP, illustrating the usefulness of \korg.
\end{itemize}
We release our code and our models as open source at \url{https://anonymous.4open.science/r/attacksynth-artifact-1B5D}.
%Formal methods work typically assumes the communication channe
%One common assumption among all the prior work is assuming or explicitly defining some notion of an \textit{imperfect} or \textit{malicious} communication channel, then proving the target protocol maintains certain properties with respect to them.
% ======= OLD INTRODUCTION ========
\begin{comment}
Distributed protocols are the foundation for the modern internet, and therefore ensuring their correctness and security is paramount. To this end, formal methods, the use of mathematically rigorous techniques for reasoning about software, has been increasingly employed to analyze and study distributed protocols. Historically, formal methods has been employed for reasoning about concurrency and distributed algorithms \cite{Lamport_1994, Holzmann_1997, Clarke_Wang}, and in recent years formal methods have been employed at scale to reason about the security of cryptographic protocols and primitives \cite{Basin_Cremers_Dreier_Sasse_2022, Kobeissi_Nicolas_Tiwari, Blanchet_Jacomme, Basin_Linker_Sasse}.
%, Blanchet_Smyth_Cheval_Sylvestre
@@ -17,3 +59,5 @@ We summarize our contributions:
We release our code and our models as open source at \url{https://anonymous.4open.science/r/attacksynth-artifact-1B5D}.
\end{comment}

24
sections/proofs.tex
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@@ -1,4 +1,20 @@
\korg is an implementation of the theoretical attack synthesis framework proposed by \cite{Hippel2022_anonym}. 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 \cite{Hippel2022_anonym} 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.
In this section we describe the theoretical foundations of \korg, arguments of its soundness, completeness, and complexity.
\subsection{Mathematical Preliminaries}%
\label{sub:Mathematical Preliminaries}
Linear Temporal Logic (LTL) is a model logic for reasoning about program executions. In LTL, we say a program $P$ \textit{models} a property $\phi$ (notationally, $P \models \phi$). That is, $\phi$ holds over every execution of $P$. If $\phi$ does not hold over every execution of $P$, we say $P \not\models \phi$. The LTL language is given by predicates over a first-order logic with additional temporal operators: \textit{next}, \textit{always}, \textit{eventually}, and \textit{until}.
An LTL model checker is a tool that, given $P$ and $\phi$, can automatically check whether or not $P \models \phi$; in general, LTL is a \textit{decidable} logic, and LTL model checkers will always be able to decide whether $P \models \phi$ given enough time and resources.
We use $\mid \mid$ to denote rendezvous composition. That is, if $S = P \mid \mid Q$, processes $P$ and $Q$ are composed together into a singular state machine by matching their equivalent transitions.
\textit{LTL program synthesis} is the problem of, given an LTL specification $\phi$, automatically deriving a program $P$ that satisfies $\phi$ (that is, $P \models \phi$). \textit{LTL attack synthesis} is logically dual to LTL program synthesis. In attack synthesis, the problem is flipped: given a program $P$ and a property $\phi$ such that $P \models \phi$, we ask whether there exists some "attack" $A$ such that $(P \mid \mid A) \not\models \phi$. Fundamentally, \korg is a synthesizer for such an $A$, based upon the distributed systems attacker framework as described in \cite{Hippel2022}.
\subsection{Proofs of Soundness and Completeness}%
\label{sub:Proofs of Soundness and Completeness}
As aforementioned, \korg is an extended implementation of the theoretical attack synthesis framework proposed by \cite{Hippel2022}. 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 \cite{Hippel2022} 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 \cite{Hippel2022_anonym}, 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.
@@ -31,7 +47,7 @@ A transition \( (s, x, s') \in T \) is called an \emph{input transition} if \( x
\setcounter{theorem}{0}
\begin{theorem}
A process, as defined in \cite{Hippel2022_anonym}, always directly corresponds to a \ba.
A process, as defined in \cite{Hippel2022}, always directly corresponds to a \ba.
\end{theorem}
\begin{proof}
@@ -87,7 +103,7 @@ A threat model is a tuple \( (P, (Q_i)_{i=0}^m, \phi) \) where:
\end{definition}
\begin{theorem}
Checking whether there exists an attacker under a given threat model, the R-$\exists$ASP problem as proposed in \cite{Hippel2022_anonym}, is equivalent to B\"uchi Automata language inclusion (which is in turn solved by the \spin model checker).
Checking whether there exists an attacker under a given threat model, the R-$\exists$ASP problem as proposed in \cite{Hippel2022}, is equivalent to B\"uchi Automata language inclusion (which is in turn solved by the \spin model checker).
\end{theorem}
\begin{proof}
@@ -107,7 +123,7 @@ Where rendezvous composition for I/O \ba is precise the same as for I/O Kripke A
\end{proof}
\begin{theorem}
Checking whether there exists an attacker for a given threat model, the R-$\exists$ASP problem as proposed in \cite{Hippel2022_anonym}, is in PSPACE.
Checking whether there exists an attacker for a given threat model, the R-$\exists$ASP problem as proposed in \cite{Hippel2022}, is in PSPACE.
\end{theorem}
\begin{proof}

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sections/related_work.tex
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@@ -1,3 +1,3 @@
\textbf{Similar Tools}. Several formal methods tools reason about attackers on secure protocols, primarily in the cryptographic context: ProVerif, VerifPal, Tamarin, and Scyther are \textit{Symbolic} and abstract away cryptographic primitives as terms \cite{Kobeissi_Nicolas_Tiwari, Proverif, Tamarin, Cremers}, while CryptoVerif and EasyCrypt are \textit{computational} and reason about game-based cryptographic security proofs \cite{Blanchet_Jacomme, Pereira}. For a general overview, see \cite{ParnoSOK, Basin_Cremers_Meadows_2018}. Before \korg, model checker-based approaches for reasoning about secure protocols have typically employed \spin or TLA+ and only reasoned about correctness \cite{Khan_Mukund_Suresh_2005, Clarke_Wang, wayne_adversaries, Narayana_Chen_Zhao_Chen_Fu_Zhou_2006, Delzanno_Tatarek_Traverso_2014}.
\hspace{1em} \textbf{Similar Tools}. Several formal methods tools reason about attackers on secure protocols, primarily in the cryptographic context: ProVerif, VerifPal, Tamarin, and Scyther are \textit{Symbolic} and abstract away cryptographic primitives as terms \cite{Kobeissi_Nicolas_Tiwari, Proverif, Tamarin, Cremers}, while CryptoVerif and EasyCrypt are \textit{computational} and reason about game-based cryptographic security proofs \cite{Blanchet_Jacomme, Pereira}. For a general overview, see \cite{ParnoSOK, Basin_Cremers_Meadows_2018}. Before \korg, model checker-based approaches for reasoning about secure protocols have typically employed \spin or TLA+ and only reasoned about correctness \cite{Khan_Mukund_Suresh_2005, Clarke_Wang, wayne_adversaries, Narayana_Chen_Zhao_Chen_Fu_Zhou_2006, Delzanno_Tatarek_Traverso_2014}.
\textbf{Reasoning About Channels}. There is a long history of using formal methods tools ad-hoc to reason about on-channel attackers, particularly in the context of Byzantine protocols \cite{Wilcox_Woos_Panchekha_Tatlock_Wang_Ernst_Anderson, Castro_Liskov_2002, Delzanno_Tatarek_Traverso_2014}. Formal methods tools have also been applied to reason about message tampering \cite{Henda}, delays \cite{Ginesin}, and congestion control \cite{TCPwn}.
\textbf{Reasoning About Channels}. There is a long history of using formal methods tools ad-hoc to reason about on-channel attackers, particularly in the context of Byzantine protocols \cite{Wilcox_Woos_Panchekha_Tatlock_Wang_Ernst_Anderson, Castro_Liskov_2002, Delzanno_Tatarek_Traverso_2014}. Formal methods tools have also been applied to reason about message tampering \cite{Henda}, delays \cite{Ginesin}, and congestion control \cite{TCPwn}. In fact, the mathematical attacker synthesis described in \cite{Hippel2022} comes with a simple implementation in \spin, \textsc{Korg}, which allows a user to manually specify messages to be \textit{inserted} onto a victim channel. Our tool nicely extends \textsc{Korg}, while relieving the user of any specific manual specification.

0
sections/usage.tex
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