\chaptertitle{Multiparty Computation in Scalable Hardware Security Modules}

\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

A central engineering challenge in inertial HSMs is transferring power and data between the payload and the rotating
mesh cage. Industrially, power and data transfer through rotating joints is usually done using slip ring assemblies. A
slip ring consists of one or more contacts that wipe on a rotating circular surface. Industrially, metal spring contacts
plated with hard gold or other common surface coatings are used for transferring small currents and data signals, and
carbon brushes are used for higher currents. Slip rings are widely used in motors and other rotating machinery.

For use in IHSMs, slip rings have several limitations. First, they are complex precision-machined components and thus
are rather expensive. Beyond cost, they also have performance limitations. Generally, slip rings are most well-suited to
slow rotation, as high rotation increases the wear of the contacts. The design target of \qty{1000}{rpm} we use in IHSMs
are at the upper end of what commercial slip rings usually support. A third disadvantage is that they are sensitive, and
any misalignment or contamination by dust can increase wear and cause intermittant contact.

An IHSM's data link can easily be realized using optical communication. Although power transfer using light is also
possible---and we have in fact demonstrated it in our first prototype IHSM---it comes at the disadvantage of a heavy
rotating assembly since large solar cells are needed, and it has poor end-to-end efficiency. For the large-scale meshes
needed in a high-performance IHSM tailored to SMPC applications, we engineered a better solution: A rotation-invariant
inductive Wireless Power Transfer link.

While Wireless Power Transfer (WPT) can be implemented in many different ways, the vast majority are variants of
Inductive WPT, where the primary and secondary side are linked primarily through the magnetic component of the
electromagnetic field, and coils are used as the transmitting and receiving antenna. Inductive WPT uses low frequency,
which reduces circuit complexity, and it is well-suited for transferring high power across short distances. The
electronic realization of a WPT link is usually similar to that of a DC/DC converter, except that in place of the
inductor or flyback transformer, the pair of transceiver coils is used. Compared to a flyback transformer, the WPT
link's transceiver coil pair has a lower coupling coefficient that varies with distance.

A challenge in WPT links is the strong dependency between link inductor coupling coefficient and distance. In a naïve
implementation that uses the link coils as a simple transformer, link efficiency would drop sharply with distance. To
decrease the impact of this distance dependency, almost all WPT implementations combine the transceiver coils with
capacitors to form a pair of tuned tank circuits that are driven like they would be in a resonant converter. Like in
resonant converters, a variety of topologies such as series, parallel, or series-parallel LC are used for these tuning
circuits.



\subsection{Software Considerations}

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

\section{Outlook}

