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\begin{document}
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\chapter{Multiparty Computation in Scalable Hardware Security Modules}
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\section{Fast MPC and Slow HSMs}

Multiparty Computation (MPC) is a cryptographic construct that allows several networked parties to jointly perform a
computation in such a way that the inputs to the computation remain private to the parties providing them, and no single
party must be trusted for the computation to produce the correct result. Conceptually, MPC is similar to a secret
sharing scheme that shares computation instead of data between untrusted parties. The computation primitive MPC offers
is a cryptographic answer to the issue of bootstrapping trust in a computing system. 

%The most challenging scenarios in computing arise when multiple 
%parties such as manufacturers and operators, servers and clients, or sellers and buyers need to interact through
%computation. In many practical situations, it is impossible to create a single computer that can be trusted by every
%participant. MPC is a generic solution to a multitude of such scenarios reducing the problem of creating a single,
%shared computer everyone can trust simultaneously to everyone creating their own computer that they only can trust.

We can deconstruct the problem of trust in computing into two largely disjunct parts: Establishing trust in a computing
system during its creation is one, and maintaining this trust throughout its life is the other. For the second part of
this problem, maintaining trust in a system once trusted, we have an ample supply of good methods such as encryption,
authentication, and formally proven protocols. In contrast, establishing trust in a computing system is largely
intractable and despite a large corpus of academic research on approaches such as hardware trojan detection and
physicaly unclonable functions, only two approaches find practical adoption: In one, we build the system ourselves from
the ground up, making sure to leave no part vulnerable to third-party compromise. In the other, we arbitrarily buy a
computer from a randomly chosen physical store, assuming that while an attacker can target any particular system, they
cannot target all systems simultaneously and we give them too little time to target the system we buy.

A limitation of both approaches is that in either case, while the party creating or acquiring the system can trust it,
they cannot prove its trustworthiness to other parties. MPC solves this issue by allowing every party to contribute
their trusted system to the protocol, cryptographically bootstrapping common trust in the computation and its
output\footnote{
    In fact, MPC does more than just bootstrapping from each participant trusting their own system to a trusted shared
    computation. In an MPC protocol providing semi-honest or better security, MPC even \emph{relaxes} each party's trust
    requirement from trusting their own system to trusting that any $n$-of-$k$ out of all systems contributing to the
    protocol.
}.

MPC is a uniquely powerful cryptographic primitive, yet it has still not found widespread practical adoption. This is
because MPC is extremely resource-intensive to run. MPC protocols exist on a continuum trading off between extreme
memory and bandwidth requirements on one end and intense computational requirements on the other end. At a first glance,
MPC and Hardware Security Modules look like they would complement each other well, but HSMs cannot keep up with the
intense computational requirements posed by MPC.

Commercially available HSMs are quoted to perform between X and Y\todo{Look up number range} individual cryptographic
operations per second. Meanwhile, an MPC protocol doing something as simple as a single AES encryption, corresponding to
X\todo{look up numbers} logic gates or Y\todo{look up numbers} x86-64 instructions, requires
\emph{millions}\todo{Validate and add citation} of cryptographic operations when performed in MPC. As a result, applying
conventional HSMs to MPC at any practical scale is infeasible by multiple orders of magnitude.

HSMs are slow compared to contemporary computers because they are limited in their power dissipation, and power
dissipation is largely proportional to processing speed. In the limited fields where HSMs have found commercial
application, this limitation was never considered important and market forces pushing towards faster HSMs remain
light\todo{Can we find a citation here?}. Fundamentally, conventional HSMs must envelope the entire payload in a tamper
sensing mesh to detect drilling attacks, but a tamper sensing mesh that is impermeable to a drill is also impermeable to
air. As a result, any heat conducted from the HSMs processor to the outside world must pass through the mesh. At the
same time, the mesh cannot be thinned either because thinning it would enable micro-drilling attacks. The result of
these constraints is a high thermal resistance between the HSM's processor and an external heat sink, which limits
maximum power dissipation to a fraction of what is achieved in modern CPUs or even GPUs.

Inertial HSMs solve this issue since they allow their payload to be air cooled without compromising security, and they
expand the feasible security boundary size from the several hundred milliliters offered by conventional HSMs to several
liters and more, enabling the integration of standard, off-the-shelf server components such as mainboards, CPUs, CPU
coolers, and power supplies. In this chapter, we will first provide a short overview of the theory of MPC before
elaborating a design of an IHSM tailored to MPC tasks including performance calculations and unique design aspects. We
will conclude with an outlook of applications unlocked by our design as well as promising areas for future improvements
of our design. 

\section{The Fundamentals of Multiparty Computation}

\subsection{Fundamental Primitives}
\subsubsection{Secret Sharing}
\subsubsection{Oblivious Transfer}

\subsection{Boolean MPC}
% Yao's Garbled Circuits

\subsection{Arithmetic MPC}
% BGW

\subsection{Practical Application}
\subsubsection{Preprocessing and Online Phases}
\subsubsection{OT extensions}
\subsubsection{Constant-Round MPC}

\subsection{Security Models in MPC}

\subsection{Performance}

\subsection{Practical Deployments}

\subsection{MPC in HSMs}

\subsection{HSM Construction}

\subsection{Solutions}

\section{A High-Performance IHSM for MPC Applications}

\subsection{A Practical Performance Target}

\subsection{Hardware Requirements}

\subsection{A Joint Cooling and IHSM Envelope Powertrain}

\subsection{Rotation-Invariant Envelope Power Supply}
% Twisted Inductor paper

\subsection{Software Considerations}

\subsection{Fast Zeroization of Non-Customizable Memories}
% Thermite experiements and paper

\section{Outlook}

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\appendix

\end{document}