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@ -60,9 +60,9 @@
that convert QKD signals to (insecure) classical signals and back.
In this paper, we outline an application of the IHSM approach first proposed by \textcite{gotteCantTouchThis2022} to
QKD that bootstraps a physically secure repeater node. At the core of our proposal is an optical passthrough
connecting multiple optical fibers from the payload through the mesh to the outside world. Our design is low-cost,
scales to dozens of optical fibers and allows the joint pass-through of electrical connections.
QKD that bootstraps a physically secure repeater node. At the core of our proposal is a work-in-progress optical
passthrough connecting multiple optical fibers from the payload through the mesh to the outside world. Our design is
low-cost, scales to dozens of optical fibers and allows the joint pass-through of electrical connections.
\end{abstract}
\section{Introduction}
@ -297,16 +297,14 @@ approximately \qty{11}{\milli\meter} when using minimal overlap between tab heig
\begin{figure}
\centering
\subcaptionbox[Helical transition of single fiber]{Single fiber}{\includegraphics[width=.45\textwidth]{helix_transition.png}}
\hfill
\subcaptionbox[Helical transition of fiber bundle]{Fiber bundle}{\includegraphics[width=.45\textwidth]{helix_bundle.png}}
\subcaptionbox[Helical transition of single fiber]{Single fiber}{\includegraphics[width=.25\textwidth]{helix_transition.png}}
\subcaptionbox[Helical transition of fiber bundle]{Fiber bundle}{\includegraphics[width=.25\textwidth]{helix_bundle.png}}
\caption[Helically coiling fibers inside the axis tube]{
The necessary mesh spacing can be reduced by coiling the fibers inside of the axis tube. The coiled fibers enter
the inter-mesh space at an angle equal to the helix lead angle, which reduces the amount of space necessary to
complete the transition to horizontal along a circular arc. In this example, a \qty{6}{\milli\meter} outer
diameter tube with a \qty{0.5}{\milli\meter} wall thickness is shown with 6 fibers with \qty{0.9}{\milli\meter}
outer diameter coiled to a constant bend radius of \qty{9}{\milli\meter}. The lead angle of the resulting helix
is \qty{61.5}{\degree}, and past the tube exit, only \qty{5.16}{\milli\meter} of inter-mesh space are necessary.
Minimum mesh spacing can be reduced by coiling the fibers inside of the shaft tube. The coiled fibers enter the
inter-mesh space at an angle equal to the helix lead angle. Shown here is a \qty{6}{\milli\meter} outer diameter
tube with a \qty{0.5}{\milli\meter} wall thickness and 6 fibers with \qty{0.9}{\milli\meter} outer diameter
coiled to a constant bend radius of \qty{9}{\milli\meter}. The lead angle of the helix is \qty{61.5}{\degree}.
The resulting inter-mesh spacing is \qty{5.16}{\milli\meter}.
}
\label{qkd_fig_fiber_helix}
\end{figure}
@ -364,42 +362,19 @@ Concentric labyrinth meshes allow for a wide range of different configurations.
next is the sum of the required width of the inter-mesh space and the safety margin needed betwween any cables or the
inter-mesh bracket and the tabs. When the mesh is constructed using rigid PCB tabs that are inserted as-is, without
bending them, and when all tabs have the same width and thickness, the radial width of the swept area decreases from tab
to tab going outwards as shown in Figure\ \ref{qkd_fig_mesh_ring_reduction}. A consequence of this is that when the
design target are constant width inter-mesh spaces, the tabs' pitch decreases going outwards.
to tab going outwards. A consequence of this is that when the design target are constant width inter-mesh spaces, the
tabs' pitch decreases going outwards.
\begin{figure}
\centering
\includegraphics[width=\textwidth]{mesh_ring_reduction.pdf}
\caption[Coaxial labyrinth mesh tab swept area]{Top-down view of a coaxial labyrinth mesh with three tabs, with the
area swept by each tab highlighted. When rigid, planar tabs of a single width $w$ are used, the radial width of the
swept areas decreases and approaches the tabs' thickness $t$ as their radius $r$ increases.
}
\label{qkd_fig_mesh_ring_reduction}
\end{figure}
The safety margin required to avoid collisions between the meshes and the stator\todo{stator is a nice word for the
entire non-rotating part of the assembly. stator/star bracket?} can be kept low for the primary mesh because this mesh
has high-quality bearings on both ends, leading to good axis alignment. In contrast, for the secondary mesh considerable
margins have to be included if the mesh is driven by a cooling fan motor, as the bearings in such fans are not very
precise. With loose bearings, angular axis misalignment can lead to several millimeters of deflection in both the radial
and axial dimensions as illustrated in Figure\ \ref{qkd_fig_mesh_ring_bearing_tolerance}.
\begin{figure}
\centering
\includegraphics[width=\textwidth]{mesh_ring_bearing_tolerance.pdf}
\caption[Coaxial labyrinth mesh axis alignment tolerance illustration]{Illustration of the effect of angular
misalignment of the axis of rotation caused by tolerances in motor bearings in a coaxial labyrinth mesh with two
tabs. The area swept by each tab, and its increase due to misalignment are highlighted. The left illustration shows
the ideal and misaligned meshes, and the right illustration superimposes the area increase from the left
illustration on the ideally aligned mesh. This illustration is not to scale.}
\label{qkd_fig_mesh_ring_bearing_tolerance}
\end{figure}
The safety margin required to avoid collisions between the meshes and the stator can be kept low for the primary mesh
because this mesh has high-quality bearings on both ends, leading to good axis alignment. In contrast, for the secondary
mesh, margins have to be included if the mesh is driven by a cooling fan motor, as the bearings in such fans
are not very precise, resulting in misalignment increasing with radius.
\subsection{Offset labyrinth meshes}
\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth,page=2]{shaft_countermeasures_b.pdf}
\includegraphics[width=0.5\textwidth,page=2]{shaft_countermeasures_b.pdf}
\caption[Offset labyrinth mesh schema]{Offset labyrinth mesh schema, cross-section and top-down views. The two
dashed lines indicate the two meshes' offset axes of rotation, shifted in $x$ direction in both views.}
\label{qkd_fig_offset_lab_schema}
@ -425,7 +400,7 @@ feedthrough that improves on the simple helical feedthrough we introduced above.
\begin{figure}
\centering
\includegraphics[width=\textwidth]{schema_wire.pdf}
\includegraphics[width=0.5\textwidth]{schema_wire.pdf}
\caption[Offset labyrinth mesh schema with fiber layout]{}
\label{qkd_fig_offset_lab_fiber}
\end{figure}
@ -448,23 +423,16 @@ perspectives.
\begin{figure}
\centering
\includegraphics[width=\textwidth]{render_exp_1.png}
\includegraphics[width=0.5\textwidth]{render_exp_1.png}
\caption[Offset labyrinth mesh assmbly exploded render]{}
\label{qkd_fig_lab_mesh_exp_1}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\textwidth]{render_exp_2.png}
\caption[Offset labyrinth mesh assmbly exploded render]{}
\label{qkd_fig_lab_mesh_exp_2}
\end{figure}
\subsection{Interlocking gear meshes}
\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth,page=3]{shaft_countermeasures_b.pdf}
\includegraphics[width=0.5\textwidth,page=3]{shaft_countermeasures_b.pdf}
\caption[Offset gear labyrinth mesh schema]{Offset gear labyrinth mesh schema, cross-section and top-down views. In
this example, the axis is shifted by about twice the offset from the previous offset labyrinth mesh schema in
Figure\ \ref{qkd_fig_offset_lab_schema}.}
@ -490,28 +458,6 @@ In this setup, the mesh tabs act like gear teeth. Depending on the ratio between
meshes do not have to rotate at the same rate of rotation and harmonic ratios are possible. Additionally, unlike actual
gears which need to constantly maintain an area of contact, both co-rotating and counter-rotating setups are possible.
\begin{figure}
\centering
\subcaptionbox[Offset gear labyrinth mesh assembly render]{}{\includegraphics[width=\textwidth]{render_side_1.png}}
\subcaptionbox[Offset gear labyrinth mesh assembly render]{}{\includegraphics[width=\textwidth]{render_side_2.png}}
\caption{
Renderings of the complete offset labyrinth gear mesh assembly.
}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\textwidth]{gear_plan_1.pdf}
\caption[Offset gear mesh assmbly schema]{}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\textwidth]{gear_plan_2.pdf}
\caption[Offset gear mesh schedule]{}
\end{figure}
\section{Physical attacks and countermeasures}
In this section we will consider possible ways to attack an IHSM-secured QKD relay, as well as potential
countermeasures.