# High cooperativity coupling of rare earth spins with planar superconducting
resonator

Sihao Wang  Department of Electrical Engineering, Yale University, New Haven,
CT 06511, USA  Likai Yang  Department of Electrical Engineering, Yale
University, New Haven, CT 06511, USA  Rufus L. Cone  Department of Physics,
Montana State University, Bozeman, MT 59717, USA  Charles W. Thiel  Department
of Physics, Montana State University, Bozeman, MT 59717, USA  Hong X. Tang
<EMAIL_ADDRESS>Department of Electrical Engineering, Yale University, New
Haven, CT 06511, USA

###### Abstract

Interfacing superconducting microwave resonator with rare earth doped crystals
presents a promising hybrid quantum system for applications including spin-
assisted transducers and memories. The coupling strength between spins of rare
earth ions and the microwave photons is characterized by the cooperativity.
Here we report an ultra-high cooperativity $C\sim$ 650 between rare earth
spins and a planar superconducting microwave resonator that features a highly
uniform magnetic field for harnessing the strong anisotropic coupling strength
of erbium doped yttrium orthosilicate. This cooperativity rivals that from a
bulk dielectric resonator and paves a path for efficiently coupling of spins
with microwave photons on an integrated platform.

Rare earth ions (REI) have been an attractive candidate for quantum
information processing thanks to their favorable optical and spin properties.
Stable optical transition and high fluorescence quantum efficiency allow spin
control and detection through optical photons [1, 2]. Extremely long coherence
time from electronic and nuclear spins makes REIs an ideal choice for quantum
information storage [3, 4]. Their narrow homogeneous linewidth further
presents opportunities for spectral multiplexing in a broader inhomogeneous
linewidth of the spin ensemble [5]. Among rare earth elements, erbium (Er)
emerges as a popular choice because of its optical transitions in the
telecommunication band. This avoids the need for frequency conversion and
facilitates integration with existing fiber optic technology.

Common choices of host crystals for REIs include yttrium orthosilicate
(Y2SiO5), yttrium orthovanadate (YVO4), and lithium niobate (LiNbO3). Yttrium
orthosilicate (YSO) gains its popularity thanks to its weak environmental
nuclear magnetic moments. Efficient long-lived multimode photonic memories [6,
7, 8] have been demonstrated using REI doped YSO, which enables entanglement
storage [9], quantum teleportation [10], and quantum state transfer from
atomic vapor [11].

Strong microwave coupling with spins is essential in enabling efficient
quantum state manipulation [12], isolating a spin ensemble from the
environmental spin bath [13], and relaxing the optical coupling requirement
for a high efficiency microwave-to-optical transducer [14]. Due to the large
mode size mismatch, and hence the poor mode overlap between resonant spins and
the microwave photon field, microwave resonators are often employed to enhance
their coupling strengths. These include both bulk three-dimensional (3D)
cavities [15, 16, 17, 18, 19] and planar superconducting resonators [20, 21,
22, 23, 24, 25]. By providing a homogeneous magnetic field (B field) and high
spatial mode overlap with the embedded REI-doped crystal, 3D dielectric
cavities benefit from spin-number enhancement from the REI ensemble and enable
an ultra-high cooperativity of $C\sim 600$ [19]. On the other hand, planar
superconducting resonators offer a small device footprint and mode volume, and
thus enhanced single spin coupling rates. However, the magnetic field
distribution tends to become less uniform with microscale patterned
structures, thus reducing the effective modal overlap between spins and the RF
magnetic field. Experiments on coupling to rare earth ions have so far yielded
a cooperativity of $C\sim 30$ [23, 25]. Further improvement is required to
improve the mode overlap while maintaining a high Q factor.

In this work, we present an ultra-high cooperativity of $C\sim 650$ between
Er3+ ions and a niobium nitride (NbN) superconducting microwave resonator
through designing the parallel nanowire strips for homoegenous B field and
utilizing the anisotropic coupling strength in an erbium doped yttrium
orthosilicate (Er:YSO) crystal. We use flip chip bonding techniques to
integrate the Er:YSO crystal on a NbN superconducting resonator with a Q
factor $Q>10^{5}$. Electron spin resonance (ESR) spectra are measured at
different orientations to demonstrate strong coupling and high cooperativity.

A commercial bulk 10 ppm natural abundance Er:YSO crystal (Scientific
Materials) was cut into a cuboid (5 mm $\times$ 4 mm $\times$ 3 mm) along the
three dielectric axes ($D_{1}$, $D_{2}$, $b$) and flip chip bonded on a NbN
superconducting microwave resonator with the $b$ axis perpendicular to the
bonding interface. The thin film of 50 nm NbN is grown on a high resistivity
silicon substrate using atomic layer deposition (ALD), with a sheet resistance
$R_{\mathrm{sq}}\sim 45\,\Omega/\mathrm{sq}$. We fabricate microwave
resonators by patterning hydrogen silsequioxane (HSQ) on NbN thin film with
electron beam lithography (EBL) and etching in reactive ion etching (RIE) with
chlorine. The resonator has a shape of a racetrack for strong coupling with
the hoop antenna. The width, radius, and straight section length of the
racetrack resonator are $100\,\mu$m, $800\,\mu$m and $1500\,\mu$m,
respectively. Three parallel $1\,\mu$m-wide strips act as inductors that
replace one straight section of the racetrack resonator. These inductor strips
are connected to the racetrack resonator through interdigitated (IDT)
capacitors. This design allows the generated vortices inside the racetrack
resonator to traverse out, hence stabilizing the cavity frequency under a
strong external B field. The final flip chip bonded device is housed in a
copper cavity box to reduce radiation loss to the environment. Fig. 1a) shows
a photo of the device inside the copper box. The external static B field
$B_{0}$ is applied parallel to the inductor strips. The oscillating B field
$B_{1}$ from the inductor strips is therefore perpendicular to $B_{0}$. The
use of flip chip bonding permits free orientation of the Er:YSO crystal on the
microwave resonator. Fig. 1b) is an optical micrograph of the NbN microwave
resonator. The narrow inductor strips are magnified in the inset. The
corresponding circuit model is shown in Fig. 1c), where the microwave
resonator is modeled as an LC resonator and the hoop antenna as an inductor.
Fig. 1d) is the cross-sectional plot of the oscillating B field $B_{1}$ from
the inductor strips. As opposed to the commonly used meander inductors where
the current in the adjacent straight sections flows in opposite directions,
the current in the three parallel inductor strips flows in the same direction,
resulting in a more uniform B field $B_{1}$ inside the bonded Er:YSO crystal.
Fig. 1e) is the oscillating B field $B_{1}$ strength at 35 $\mu$m above the
NbN microwave resonator, indicated by the dashed line in Fig. 1d). A
homogeneous B field distribution above the inductor strips plays an important
role in reducing the spin linewidth.

Figure 1:  (a) A photograph of the packaged device. The NbN microwave
resonator was fabricated on a high resistivity silicon substrate that sits on
a bigger piece of high resistivity silicon carrier in a copper cavity. A hoop
antenna was used to couple to the device. The crystal axes are indicated and
the applied static magnetic field $B_{0}$ is oriented parallel to the
resonator inductor strips. (b) The optical micrograph of the NbN resonator. A
zoom-in image of the narrow inductor strips is shown in the inset. (c) The
corresponding circuit model of the device. (d) The cross-sectional arrow plot
of the oscillating magnetic field $B_{1}$ around the inductor strips. The thin
strips are exaggerated for viewing purposes. (e) The oscillating magnetic
field profile at 35 $\mu$m above the microwave resonator, indicated by the
dashed line in (d). The uniform magnetic field facilitates a narrow spin
linewidth. The narrow inductor strips are exaggerated for illustration
purpose.

The packaged device is loaded in the mixing chamber of a dilution fridge with
a base temperature of 10 mK. The actual device temperature is 30 mK due to a
thermal gradient. A vector network analyzer (VNA) is used to measure the
$S_{21}$ response. The microwave resonator has a resonance frequency at 5.7
GHz at zero applied B field $B_{0}=0$. The Q factor of the cavity is fitted
with a Fano resonance to take into account the background response. Q $\sim
130000$ is obtained at the input power of -70 dBm, at which the loss from two
level systems is minimized.

The Hamiltonian of the coupled system is given as

$\displaystyle
H=\mu_{B}\mathbf{B}\cdot\mathbf{g}\cdot\mathbf{S}-\mu_{n}g_{n}\mathbf{B}\cdot\mathbf{I}+\mathbf{I}\cdot\mathbf{Q}\cdot\mathbf{I}+\mathbf{S}\cdot\mathbf{A}\cdot\mathbf{I},$
(1)

where $\mu_{B}$ ($\mu_{n}$) is the electron (nuclear) Bohr magnetron,
$g_{n}=-0.1618$ is the nuclear $g$-factor, $\mathbf{g}$ is the anisotropic
electron $g$-factor tensor, $\mathbf{Q}$ is the nuclear quadruple tensor and
$\mathbf{A}$ is the hyperfine interaction tensor. The first two terms of the
spin Hamiltonian are electron and nuclear Zeeman splittings, which are
proportional to the applied B field $B_{0}$. The third and the fourth term are
the nuclear quadruple interaction and the hyperfine interaction, independent
of $B_{0}$. Based on the published tensor values [26, 27], we can calculate
the eigen-energy spectra of the Er:YSO crystal at different orientations [28].

The crystal structure of Er:YSO is described by space group $C_{2h}^{6}$,
where Er3+ ions substitute Y3+ ions at two distinct crystallographic sites,
both characterized by $C_{1}$ symmetry. For each crystallographic site, the
crystal’s $C_{2}$ rotation symmetry and inversion symmetry give rise to four
subclass sites in the crystal with different local orientations. Based on
their response to the applied B field, these subclass sites can be further
divided into two groups. The group related to the inversion symmetry is
magnetically equivalent as it responds to a B field of arbitrary direction
identically. The other group related to the $C_{2}$ symmetry is magnetically
inequivalent. These two subclass sites interact with an applied B field
differently, except for two special cases, when the B field is either applied
along the $b$ axis or in the $D_{1}$-$D_{2}$ plane. During the measurement, a
static B field $B_{0}$ is applied parallel to the inductor strips in the
$D_{1}$-$D_{2}$ plane to minimize the vortex-induced loss. The oscillating B
field $B_{1}$ from the inductors is perpendicular to $B_{0}$. Fig. 2a) and
Fig. 2b) are the Breit-Rabi diagrams of Er3+ ions at site 1 and site 2 when
the oscillating B field $B_{1}$ is $\sim 20^{\circ}$ from the $D_{1}$ axis.
The strong electron spin transitions due to the electron Zeeman term at both
sites under the selection rule $\Delta m_{s}=\pm 1$ are marked by the red
arrows. The odd number isotope 167Er has a nuclear spin of $I=7/2$, resulting
in the satellite hyperfine spin state transitions (black arrows) with $\Delta
m_{i}=0$ and the nuclear quadruple transitions (blue arrows) with $\Delta
m_{i}=\pm 1$.

The length of the arrows are selected to match the microwave resonance
frequency to demonstrate the positions of level anti-crossing. This level
anti-crossing is manifested as the coupling of the microwave field to the
spins and hence an additional loss channel of the resonator, resulting in a
drop of Q factor of the microwave resonance. In the case of perfect alignment,
only one level anti-crossing for Er3+ ions, and therefore one dip of the Q
factor at each site, should be observed when sweeping the B field strength.
However, two dips are observed (see Supplementary Information for details),
indicating a small misalignment between the applied B field and the
$D_{1}$-$D_{2}$ plane. By utilizing an additional balance coil with applied B
field in the perpendicular direction, we are able to cancel the out-of-plane
component of $B_{0}$. The deviation angle is estimated to be $\sim
1.05^{\circ}$, which is comparable to the expected uncertainty in the crystal
orientation. Fig. 2c) shows the variation of Q factor with the sweeping B
field. Solid (dashed) markers represent the assignment of each level anti-
crossing to the spin state transition at each site in Fig. 2a) and b). The
prominent dips correspond to the strong Zeeman electron spin state transitions
and the satellite dips correspond to the transitions with nuclear hyperfine
states. Fig. 2d) is the corresponding frequency shift of the microwave
resonance at level anti-crossing fields. The background quadratic dependence
of the microwave resonance frequency on $B_{0}$ due to the nonlinearity from
the kinetic inductance in the narrow inductor strips is normalized to
highlight the frequency shift.

Figure 2:  (a) The simulated Breit-Rabi diagram of Er:YSO for spins residing
at site 1 subject to an oscillating magnetic field $B_{1}$ oriented 20∘ from
D1 axis in the D1-D2 plane. The allowed and forbidden transitions at 5.7 GHz
are shown in solid arrows with different colors. (b) The corresponding Breit-
Rabi diagram for spins at site 2. The allowed transitions are shown by dashed
arrows with different colors. The inset shows a schematic of the orientation
of the YSO crystal with respect to the magnetic fields. (c) The spectrum of
the loaded Q factor of the superconducting microwave resonator with the static
magnetic field $B_{0}$. Each dip in the spectrum indicates a level anti-
crossing between the spin and microwave modes. Transitions from site 1(2) are
indicated with solid(dashed) markers. (d) The frequency shift of the ESR
spectrum with the static magnetic field $B_{0}$. The quadratic dependence of
the superconducting microwave resonance with the static magnetic field $B_{0}$
has been normalized.

The collective coupling $\nu$ between the spin ensemble and the microwave
resonator is proportional to the effective $g$-factor $g$ by
$\nu=g\mu_{B}\sqrt{n\xi\omega_{0}\mu_{0}/(4\hbar)}$, where $\mu_{B}$ is the
Bohr magneton, $n\sim 10^{17}$ cm-3 is the concentration of Er3+ ions,
$\xi\sim 0.25$ is the geometry factor accounted for the mode overlap with
spins and the spin coupling with the oscillating field, and $\omega_{0}$ is
the microwave resonance frequency. For an oscillating B field $B_{1}$ in the
$D_{1}$-$D_{2}$ plane, the collective coupling strength is maximized when the
angle between $B_{1}$ and the $D_{1}$ axis is close to $120^{\circ}$ and
minimized when the angle is near $30^{\circ}$. Fig. 3a) shows the evolution of
the microwave resonance with the sweeping B field $B_{0}$ when $B_{1}$ is at
the angle of $20^{\circ}$ to the crystal axis $D_{1}$ for Er3+ ions at site 1.
The level anti-crossing near $B_{0}=48$ mT can be extracted. The modified
resonator frequency $\omega$ and decay rate $\kappa$ is fitted with a
simplified phenomenological model [21, 25]

$\displaystyle\omega$ $\displaystyle=$
$\displaystyle\omega_{0}-\frac{\nu^{2}\Delta}{\Delta^{2}+\gamma_{s}^{2}/4},$
(2) $\displaystyle\kappa$ $\displaystyle=$
$\displaystyle\kappa_{c}+\frac{\nu^{2}\gamma_{s}}{\Delta^{2}+\gamma_{s}^{2}/4},$
(3)

where $\Delta=\omega-\omega_{0}$ is the detuning, $\gamma_{s}$ is the spin
inhomogeneous linewidth, and $\kappa_{c}$ is the initial microwave cavity
decay rate. Fig. 3b) and c) show fitting of the frequency shift and linewidth,
yielding the collective coupling strength $\nu=(2\pi)2.5$ MHz, the spin
ensemble inhomogeneous linewidth $\gamma_{s}=(2\pi)26.6$ MHz, and the cavity
linewidth $\kappa_{c}=(2\pi)41$ kHz. The cooperativity is thus
$C=4\nu^{2}/(\kappa_{c}\gamma_{s})=22$.

For a large cooperativity, we rotate the Er:YSO crystal so that the angle
between $B_{1}$ and the $D_{1}$ axis is 112∘, near 120∘ for maximum $g$. Fig.
3d) is a similar plot of the resonance evolution with sweeping $B_{0}$ when
$B_{1}$ is at 112∘ to the crystal axis $D_{1}$ for Er3+ ions at site 1. At
this orientation, the coupling of the spins to the oscillating B field $B_{1}$
is maximized, but the interaction with the static B field $B_{0}$ is
minimized. The out-of-plane component of $B_{0}$ is beyond the compensation
range of the balance coil. Therefore, no balance coil is applied at 112∘ and
the applied $B_{0}$ is $\sim 1.05^{\circ}$ deviated from the $D_{1}$-$D_{2}$
plane. This deviation results in the lifting of the degeneracy of the subclass
sites related to the $C_{2}$ rotation of the crystal lattice.

The resonator frequency and decay rate are fitted with a modified model to
account for the double level anti-crossings from the subclass levels.

$\displaystyle\omega$ $\displaystyle=$
$\displaystyle\omega_{0}-\frac{\nu_{1}^{2}\Delta}{\Delta^{2}+\gamma_{1}^{2}/4}-\frac{\nu_{2}^{2}\Delta}{\Delta^{2}+\gamma_{2}^{2}/4},$
(4) $\displaystyle\kappa$ $\displaystyle=$
$\displaystyle\kappa_{c}+\frac{\nu_{1}^{2}\gamma_{1}}{\Delta^{2}+\gamma_{1}^{2}/4}+\frac{\nu_{2}^{2}\gamma_{2}}{\Delta^{2}+\gamma_{2}^{2}/4},$
(5)

where $\nu_{1(2)}$ and $\gamma_{1(2)}$ are the collective coupling strength
and the linewidth for ions at subclass level 1 (2) respectively. Fig. 3e) and
f) show the fitting of the frequency shift and linewidth, yielding
$\nu_{1}=(2\pi)12.5$ MHz, $\nu_{2}=(2\pi)12.2$ MHz, $\gamma_{1}=(2\pi)18.5$
MHz, $\gamma_{2}=(2\pi)18.1$ MHz and $\kappa_{c}=(2\pi)51$ kHz. The
corresponding cooperativities for each subclass are
$C_{1}=4\nu_{1}^{2}/(\kappa_{c}\gamma_{1})=650$ and
$C_{2}=4\nu_{2}^{2}/(\kappa_{c}\gamma_{2})=634$.

Figure 3:  (a-c) The electron spin level anti-crossing for the oscillating
magnetic field $B_{1}$ oriented 20∘ from the D1 axis in the D1-D2 plane. (a)
The S21 spectra of the microwave resonance when sweeping the static magnetic
field $B_{0}$ across the level anti-crossing point. (b) The frequency shift as
a function of the applied static magnetic field $B_{0}$ and the fitting. (c)
The resonator linewidth as a function of the applied static magnetic field
$B_{0}$ and the fitting. (d-f) The electron spin level anti-crossing for the
oscillating magnetic field $B_{1}$ oriented 112∘ from the D1 axis. The two
subclass modes indicate that the magnetic field is slightly off from the D1-D2
plane. (d) The S21 spectra of the microwave resonance when sweeping the static
magnetic field $B_{0}$ across the level anti-crossing point. (e) The frequency
shift as a function the applied static magnetic field $B_{0}$ and the fitting.
(f) The resonator linewidth as a function of the applied static magnetic field
$B_{0}$ and the fitting.

The cooperativity of $C\sim 650$ is one order of magnitude larger than the
literature values from cases with planar superconducting microwave resonators,
rivaling that from the 3D cavity with high spin number enhancement. Yet, this
cooperativity can be further optimized. Our current manual alignment during
the flip chip bonding process is not perfect, causing the crystal orientation
to deviate from the optimal angle for the $g$-factor. The lifting of
degeneracy due to the out-of-plane B field can be suppressed with a larger
balance coil, bringing about a two-fold improvement as spins from both
subclasses contribute. Further improvement could come from the reduction of
vortex-induced microwave loss, hence a smaller $\kappa_{c}$. These
improvements are evidenced by the fitting results from the double level anti-
crossings without a balance coil at $20^{\circ}$ (see Supplementary
Information for details). Fitting with Eq. 4 and 5 yields
$\nu_{1}(20^{\circ})=(2\pi)1.5$ MHz, $\nu_{2}(20^{\circ})=(2\pi)1.6$ MHz,
$\gamma_{1}(20^{\circ})=(2\pi)18.7$ MHz, $\gamma_{2}(20^{\circ})=(2\pi)18.8$
MHz and $\kappa_{c}(20^{\circ})=(2\pi)51$ kHz. The corresponding
cooperativities are $C_{1}(20^{\circ})=9$ and $C_{2}(20^{\circ})=11$. Notice
that the spin linewidth $\gamma_{s}$ is higher when the balance coil is
applied. This is likely due to the imperfect cancellation of the out-of-plane
B field so that the two level anti-crossings do not overlap completely. The
flip chip bonding process may still leave a small gap between the crystal and
the superconducting resonator, reducing the geometry overlapping factor $\xi$.
The theoretical estimation of the coupling strength with zero gap and $g=12$
at $\xi\sim 0.25$ is $\nu_{\mathrm{theo}}\sim(2\pi)28.7$ MHz, which is more
than two times higher than the current extracted value, resulting in a
cooperativity of thousands. Direct deposition and fabrication of
superconducting resonators on the Er:YSO crystal [25] is a potential solution
for minimizing the gap, but at the expense of the flexibility to orientate the
crystal at an arbitrary angle.

In conclusion, we realize high cooperativity coupling between an Er3+ spin
ensemble and the microwave resonator by producing a more homogeneous B field
and exploiting the anisotropic $g$-factor tensor. An ultra-high cooperativity
of $C=650$ is achievable, which is comparable to that from large 3D resonators
with high spin number enhancement. This result marks an important step towards
a high efficiency microwave-to-optical transducer, an essential component in
building a coherent link between a superconducting quantum circuit and optical
quantum network. The strong coupling also paves the way for spin manipulation
and detection such as cooling of spin ensembles and high sensitivity spin
detection. An efficient state transfer and mapping in and out of the spin
states with strong coupling is highly desired in a quantum memory device.

## I. Acknowledgement

This work is supported by Department of Energy, Office of Basic Energy
Sciences, Division of Materials Sciences and Engineering under Grant DE-
SC0019406. The authors would like to thank Dr. Yong Sun, Sean Rinehart, Kelly
Woods, and Dr. Michael Rooks for their assistance provided in the device
fabrication. The fabrication of the devices was done at the Yale School of
Engineering & Applied Science (SEAS) Cleanroom and the Yale Institute for
Nanoscience and Quantum Engineering (YINQE).

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# Diversifying Multi-aspect Search Results Using Simpson’s Diversity Index

Jianghong Zhou  Emory University201 Dowman DriveAtlantaUnited StatesGa. 30322
<EMAIL_ADDRESS>,  Eugene Agichtein  Emory UniversityAtlantaUnited
States<EMAIL_ADDRESS>and  Surya Kallumadi  The Home
DepotAtlantaUnited States<EMAIL_ADDRESS>
(2020)

###### Abstract.

In search and recommendation, diversifying the multi-aspect search results
could help with reducing redundancy, and promoting results that might not be
shown otherwise. Many previous methods have been proposed for this task.
However, previous methods do not explicitly consider the uniformity of the
number of the items’ classes, or evenness, which could degrade the search and
recommendation quality. To address this problem, we introduce a novel method
by adapting the Simpson’s Diversity Index from biology, which enables a more
effective and efficient quadratic search result diversification algorithm. We
also extend the method to balance the diversity between multiple aspects
through weighted factors and further improve computational complexity by
developing a fast approximation algorithm. We demonstrate the feasibility of
the proposed method using the openly available Kaggle shoes competition
dataset. Our experimental results show that our approach outperforms previous
state of the art diversification methods, while reducing computational
complexity.

search result diversification, Simpson’s diversity index for search, efficient
search diversification computation

††journalyear: 2020††copyright: acmcopyright††conference: Proceedings of the
29th ACM International Conference on Information and Knowledge Management;
October 19–23, 2020; Virtual Event, Ireland††booktitle: Proceedings of the
29th ACM International Conference on Information and Knowledge Management
(CIKM ’20), October 19–23, 2020, Virtual Event, Ireland††price: 15.00††doi:
10.1145/3340531.3412163††isbn: 978-1-4503-6859-9/20/10

##  1\. Introduction

Diversifying search results is of vital importance in many search systems due
to the ambiguity of search queries and the complexity of users’ intents. In
multi-aspect search, a diverse set of search results are more likely to
satisfy the users’ needs and improve the online shopping experience.
Therefore, many approaches for diversifying results in information retrieval
and recommender systems have been proposed (Zhou and Agichtein, 2020), among
which the algorithms based on DPPs (Determinantal Point Processes) are
considered to be state of the art methods. DPPs aim to balance diversity and
relevance, and are based on the geometric properties of vectors associated
with a set of items (Kulesza et al., 2012). DPPs define the diversity of a set
by the volume of a parallelepiped spanned by the vectors of this set. The
volume is determined by the vectors’ length and their cosine similarity, which
can represent the relevance and similarity respectively. Specifically, DPPs
compute the determinant of the product of the selected items’ matrix and its
transpose to identify a diverse subset of results.

Diversity is characterised by two aspects 1) richness and 2) evenness
(Simpson, 1949). Richness quantifies the number of different classes elements
in a set, while evenness considers the uniformity of the distribution of these
classes. However, DPPs only consider the richness aspect (Xie et al., 2017).
It narrows the definition of diversity, which may degrade actual diverse
search results. Besides, evenness can affect richness, especially the item has
multiple aspects (Stirling and Wilsey, 2001).

In addition to not considering “evenness”, DPPs also suffer from high
computation complexity, which is NP hard. In its greedy formulation, the
computation complexity is $O(N^{4})$, in which $N$ is the scale of search
space. Therefore, many variations are developed to improve its computational
efficiency (Chen et al., 2017)(Chen et al., 2018)(Kulesza and Taskar, 2011).

Due to the aforementioned difficulties, we consider another model to measure
diversity, which is Simpson’s diversity index (Simpson, 1949). It measures the
probability that two items are chosen at random and independently from a set
is the same. Both Shannon entropy and Simpson’s diversity index measure
richness and evenness. Notwithstanding, Simpson’s diversity index is a
pairwise approach. Through some transformations and improvements, we develop
it to a binary quadratic program, with predicable approximation bounds.

We evaluate our approach on a standard benchmark dataset from Kaggle shoes’
price competition (https://www.kaggle.com/datafiniti/womens-shoes-prices,
https://www.kaggle.com/datafiniti/mens-shoe-prices). The experimental results
show that the proposed method outperforms state of the art DPP algorithms and
extensions. In summary, our contributions are threefold:

1. Introducing Simpson’s diversity index (SDI) to search result diversification domain.

2. We operationalize SDI computation as a quadratic program, which can be solved efficiently.

3. We show that the proposed method outperforms state of the art methods on a standard e-commerce search benchmark.

Next, we motivate our method and place it in the context of related prior
work.

##  2\.  Related Work

In this part, we emphasize the importance of evenness, brief the major
baseline method $--$ DPPs, and introduce SDI as a diversity model in multi-
aspect search problems.

###  2.1.  Richness and Evenness

Prior research on search diversification focused on the richness of the
results (Simpson, 1949). Richness quantifies the number of different types the
dataset of interest contains, while evenness considers the uniformity of the
distribution of these types. However, evenness is also important for search
diversification. Importantly for the e-commerce setting, it can affect users’
online shopping experience. For example, consider a product catalog with 1000
A items, 500 B items, and 500 C items. Suppose, we attempt to retrieve 12
results as diverse as possible to fit on the first page of the results.
Without considering evenness, the expected search results might be 6 A items,
3 B items, and 3 C items. While considering evenness, the expected results are
all 4. The richness of the two versions of the results is identical. However,
the information entropy of the second set of results is higher, meaning that
higher evenness could increase the information that the users receive in a
limited space. In multi-aspect search, evenness is even more important. In
multi-aspect search, the search results are the combination of many
independent single-aspect searches. In prior research, (Simpson, 1949) shows
that the combinations of the even results are the most diverse. Therefore,
evenness affects the richness of multi-aspect search as well.

The above discussion shows that evenness is significant for diversity
analysis. However, vast majority of the diversity models for search do not
consider results’ evenness. Therefore, we propose to use a model considering
evenness to enrich the diversity model for search. We propose to adopt the
Simpson’s diversity index (SDI) method from biology for this task (Simpson,
1949). But first, we formally introduce the DPP-based algorithms for result
diversification and then introduce our new SDI method.

###  2.2. Determinantal Point Processes for Search Diversification

Determinantal Point Processes (DPPs) are useful in domains where repulsive
effects or diversity are important aspects to model. In recommender systems
and information retrieval domains, where the discovery of documents and items
are significant, DPPs can be used to diversify results. In search problems,
DPPs are a subset selection problem. We define the search space as a set $S$,
whose size is $N$, and the search results are a subset $S^{\prime}$, whose
size is $k$. $B_{S^{\prime}}$ represents the selected items in $S^{\prime}$.
DPPs can be formulated as:

$X=\underset{S^{\prime}\subseteq S}{\operatorname{argmax}}$
det$({B^{T}_{S^{\prime}}B_{S^{\prime}}}))$

$X$ is the volume of a parallelepiped spanned by the vectors of $B$. It is
determined by the vectors’ length (relevance) and their cosine similarity
(similarity). By maximizing $X$, we can obtain the best subset of $S$,
considering both diversity and relevance.

However, DPPs are a richness-greedy diversification method, because $X$ does
not change when we apply linear transformations to revise the evenness of $B$.
Therefore, the evenness of the obtained subset of each aspect is not promised.
In multi-aspect search, the results are the combination of every aspect. As we
mentioned in Section 2.1, this can lead to weaker diversity of the
combination.

###  2.3. Simpson’s diversity index

Simpson’s Diversity Index (SDI) was originally introduced in biology to
measure both the evenness and richness of a habitat (Simpson, 1949), and aims
to estimate the probability that two randomly selected individuals from a
sample will be the same. Apparently, if the habitat has more species
(Diversity), this probability is smaller. Based on Jensen’s inequality, if the
total number of the animals in the habitat is a constant, this probability is
also smaller when the numbers of each species are the same (Evenness).

More formally, SDI is defined as the probability that two items are chosen at
random and independently from a set is the same:

$D=\frac{\sum_{i=1}^{R}{(n_{i}(n_{i}-1))}}{N(N-1)}$

Where $R$ is the number of classes. $n_{i}$ is the number of items of the
$i$th class. $N$ is the total number of all items. Smaller $D$ means higher
diversity. SDI considers both richness and evenness, according to Section 2.1,
it is more suitable to diversify search results over multi-aspect items.

##  3\. Diversifying Multi-aspect Search Results Using SDI

In this section, we present a method that diversifies multi-aspect search
results using Simpson’s diversity index. We first present an important
variation of Simpson’s diversity index and then explain how we apply it to
search. We conclude by constructing a quadratic program to compute SDI more
efficiently.

###  3.1. Diversifying Multi-aspect Search Results using Simpson’s diversity
index

In multi-aspect search, items are labeled by many aspects. We first consider
the SDI of an aspect. In addition to the equation in Section 2.2, we have
another way to calculate SDI.

In a set, we denote the number of items in this set as $N$. $R$ is the number
of items’ classes. $n_{i}$ is the number of items of the $i$th class.

When we randomly select two items as a pair, there are $\frac{1}{2}N(N-1)$
pairs. For each pair, they belong to the same class or not. The total number
of pairs belonging to the same class is $\sum_{i<j\leq N}{(a_{i}\&a_{j})}$.
Where $a_{i}$ is the Item $i$. If two items are the same $(a_{i}\&a_{j})=1$,
else $(a_{i}\&a_{j})=0$. If we also count the item itself, we have:

(1) $D(p,S^{\prime})=\frac{2\sum_{i,j\in S^{\prime},i\leq
j}{(a_{p,i}\&a_{p,j})}}{|S^{\prime}|(|S^{\prime}|+1)}$

Where $p$ is the aspect, $P$ is the aspect set, $S^{\prime}$ is the selected
set, $S$ is the whole set, $|S|$ is the size of $S$. $a_{p,i}$ is the Aspect
$p$ of Item $i$.

If we consider all the aspects at the same time, we have:

$H(S^{\prime})=\sum_{p\in P}{\omega_{p}\frac{D(p,S^{\prime})}{D(p,S)}}$

In this equation, we first normalize each aspect’s SDI, because different
aspects’ SDI may have different scales. Then, we weigh every aspect with
$\omega_{p}$. If we only consider diversification, $\omega_{p}=1$. However, in
the search problem, relevance is also very important. When the item is highly
relevant to some aspects. For example, when users search ’blue shoe’, it is
not necessary to present other colors’ shoes anymore. Therefore, the ’color’
aspect should be penalized. In this paper,
$\omega_{p}=1-\frac{k_{p}-1}{|S^{\prime}|-1}$, Where $k_{p}$ is the number of
the most common aspect of Aspect $p$ in top $|S^{\prime}|$ relevant results.
For convenience, we let $\phi_{p}=\frac{\omega_{p}}{D(p,S)}$.

This transformation of SDI helps us organize it to a more efficient form to be
optimized $--$ the binary quadratic program (BQP).

###  3.2. The Binary Quadratic Program

In this section, we transfer the SDI optimization to a BQP problem, which has
thorough previous research to systematically be approximated and optimized
(Ma, 2010)(Clarkson, 2010)(Springer, 2002). Since $H(S^{\prime})$ is pairwise,
it can be computed in an easy way. Let’s expand $H(S^{\prime})$.

$H(S^{\prime})=\sum_{i,j\in S^{\prime},i\leq
j}{\frac{2}{|S^{\prime}|(|S^{\prime}|+1)}\sum_{p\in
P}{\phi_{p}(a_{p,i}\&a_{p,j})}}$

Let $Q_{i,j}={\frac{2}{|S^{\prime}|(|S^{\prime}|+1)}\sum_{p\in
P}{\phi_{p}(a_{p,i}\&a_{p,j})}}$, we can reformulate $H(S^{\prime})$ as
$H(S^{\prime})=\frac{1}{2}x^{T}Qx$, $x$ is a vector representing $S^{\prime}$.
The length of $x$ equals to $|S|$. Each entry is an item of $S$. The entry of
the chosen item is 1, or it is 0. If we further consider the relevance, we
have:

(2)
$\min_{x}T(S^{\prime})=\min_{x}H(S^{\prime})+R(S^{\prime})=\min_{x}\frac{1}{2}x^{T}Qx+b^{T}x$

Where $b$ is the relevance vector. Consequently, it becomes a binary quadratic
program problem, whose constraints are: s.t.
$x_{i}\in\\{0,1\\},\sum_{k=1}^{|S|}{x_{k}}=|S^{\prime}|$, where $x_{i}$ is the
entry of $x$.

Equation 2 is a classical BQP problem. In this paper, we first relax it to a
convex optimization problem (Ma, 2010). Then we use the Frank–Wolfe algorithm
to optimize it (Clarkson, 2010). Finally, we use Goemans and Williamson
procedure for the approximate solutions (Springer, 2002). Such a procedure
guarantees that the solution is a close approximation that
$T\in[T_{min},\frac{\pi}{2}T_{min}]$.

##  4\. Experimental Setting and Results

We first introduce the experimental datasets, including the queries generation
and items’ collection. Then, we describe the evaluation methods, initial
relevance ranking, and the baseline methods used to report the experimental
results.

###  4.1. Datasets

We experiment with two datasets: a publicly available Kaggle benchmark for the
searching items dataset, and a complementary dataset constructed using
publicly available Amazon Web Search engine interface for the queries dataset.

Kaggle Shoes Price Competition Dataset (Kaggle): Kaggle shoe price dataset is
a list of shoes and their associated information, containing 19046 women shoes
and 19387 men shoes. However, the items of this dataset also contain clothes,
gloves, jewelry, and so on. Some items do not have features. To focus on the
diversity problem, we remove items without features, clothes items, jewelry
items, gloves items, trousers items, and toys items. At last, we have 14609
items. Besides, even though the items have many aspects, they do not have the
values of many aspects. Therefore, we only choose 21 most commonly used
features: ’Season’, ’Material’, ’Gender’, ’Shoe Size’, ’Color’, ’Brand’, ’Age
Group’, ’Heel Height’, ’Fabric Material’, ’Shoe Width’, ’Occasion’, ’Shoe
Category’, ’Casual & Dress Shoe Style’, ’Shoe Closure’, ’Assembled Product
Dimensions (L x W x H)’, ’Fabric Content’, ’Shipping Weight (in pounds)’,
’prices.offer’, ’prices.amountMin’, ’prices.amountMax’ and ’prices.isSale’.

Amazon Queries Suggestions Dataset (AQS): To complement the Kaggle queries
dataset, we created a new dataset automatically constructed for the “shoes”
category using the query suggestions provided by the Amazon Web Search engine.
Specifically, we collected the queries suggestions for the top-level category
’shoes’. This process resulted in 384 queries, such as ’fur lined winter coat
women’. The AQS dataset is available at the URL
https://docs.google.com/spreadsheets/d/17DMU5pMSiNxi05yu5pdEvrUf3b0mIAF1rYn2ypruS7A/edit?usp=sharing.

###  4.2. Baselines and Experimental Setting

####  4.2.1. Setting

In the experiments, we search for queries and every model returns the top 10
results. We used the averaged results of all queries as the data points.

All the diversification methods considered, and our proposed method, require
the relevance vectors and the similarity matrices. In this paper,
BM25(Robertson et al., 2009) score of each item with respect to the query. For
the item-item similarity matrix, the number of identical aspects between the
items is used, which could be improved in future work.

To trade off the relevance and diversity, we introduce a parameter $\theta$.
$\theta$ adjusts the relation between diversity and relevance in the following
way:$(1-\theta)H(S^{\prime})+\theta R(S^{\prime})$. For the proposed method,
the approximate rate $\epsilon$ is 0.0001.

####  4.2.2. Baselines

We use three baselines, including Greedy version DPPs and two recent and
influential variations. 1) DPPs Greedy: Greedily selecting items to maximize
the determinant (Borodin, 2009). 2) k-DPPs: It is a sample-based DPPs, which
can accelerate the Greedy DPPs. However, since it localizes the optimization,
the performance may be unstable (Kulesza and Taskar, 2011). 3) Fast MAP DPPs:
A novel approach improves the computation complexity of the maximum a
posteriori (MAP) inference DPPs, which is the state of art DPPs algorithm
(Chen et al., 2018).

###  4.3. Evaluation Metrics

We now summarize the metrics used to compare the methods.

Coverage Rate(CR): The coverage rate measures the diversity of the subset
(Castells et al., 2011). For each aspect of the item, they have at most 10
features or the number of this aspect’s features in this set. The coverage
rate is a diversity metric.

$CR(S^{\prime})=\frac{1}{|P|}\sum_{p\in
P}{\frac{|A^{\prime}_{p}|}{\min(|S^{\prime}|,|A_{p}|)}}$

Where $S^{\prime}$ is the selected set, $P$ is the set of all aspects,
$A^{\prime}_{p}$ is the features of Aspect $p$ in the selected set and $A_{p}$
is the features of Aspect $p$ .

NDCG@10: We use normalized discounted cumulative gain (NDCG) to measure
ranking results of the relevance. Since both results of DPPs and the proposed
method do not have the order, we rank the selected subset based on the items’
relevance before computing the NDCG@10 (Castells et al., 2011).

$\alpha$-NDCG: A variations of NDCG, which can measure both relevance and
diversity (Castells et al., 2011).

Variance: We use averaged variance of every aspect’s number of features to
measure the evenness (Ricotta, 2017).

###  4.4. Results

The results of diversity, evenness, and relevance are presented in Figure 1.
The result of the computing time is illustrated in Table 1. In Figure 1, the
trade-off parameter $\theta$ ranges from 0 to 1, whose step size is 0.1. For
CR(a), NDCG@10(b), and $\alpha$-NDCG(c), the larger their value, the better
the performance of the model is. For variance(d), a lower line means the model
is evener. In Table 1, less computing time means the model is faster.
Generally, the proposed method outperforms the baselines in terms of
relevance, diversity, and evenness, especially when $\theta$ ranges from 0.3
to 0.7. The improvement is up to more than 15%. In terms of computing time,
the proposed method spends less time than most of the baselines.

We use CR to measure the richness of the multi-aspect results in Figure 1 (a),
which shows the proposed method outperforms the baselines when $\theta$ ranges
from 0.2 to 0.8. In terms of relevance, the NDCG@10 scores from Figure 1 (b)
show that the proposed method has closed performances. We further use
$\alpha$-NDCG to measure the relevance and diversity at the same time in
Figure 1 (c), which demonstrates that the proposed approach has the best
performance while $\theta$ ranges from 0.4 to 0.7. Figure 1 (d) further
applies the Variance to measure the evenness of the returned results. In this
figure, we find that when the model emphasizes diversity ($\theta$ closes to
0), the variance of SDI is smaller than all the baselines. We further test the
computing time of the proposed method and summarize the results in Table 1,
revealing that the proposed method is slower than k-DPPs but faster than other
baselines.

$\begin{array}[]{cc}\includegraphics[width=238.49231pt]{cr.jpg}&\includegraphics[width=238.49231pt]{ndcg.jpg}\\\ (a)&(b)\\\ \includegraphics[width=238.49231pt]{alpha.jpg}&\includegraphics[width=238.49231pt]{v.jpg}\\\ (c)&(d)\end{array}$ Figure 1.  Comparison of trade-off performance between relevance and diversity under different choices of trade-off parameters $\theta$ on Amazon Queries Suggestions dataset (a, c) and Kaggle Shoes Price Competition Dataset (b, d). Table 1.  Comparison of average running time (in milliseconds) Model | SDI | DPPs-Greedy | k-DPPs | Fast-MAP-DPPs
---|---|---|---|---
Computing Time | 45.32 | 1093.48 | 17.86 | 98.45

##  5\. Analysis & Discussion

We now discuss the proposed method’s advantages and drawbacks based on the
experimental results above. Figure 1 (a) (b) (c) show that our SDI method
outperforms all the baselines while we consider diversity and relevance with
similar or closed weights. Simultaneously, Figure 1 (d) shows that the
evenness of SDI is substantially higher than the baselines’, supporting the
analysis in Section 2.

Table 1 reports the computation time of 4 methods, which aligns with their
computation complexity. Greedy DPPs’ is $O(N^{4})$. Fast-MAP-DPPs’ is closed
to $O(N^{3})$. k-DPPs’ is $O(Nk^{2})$. The proposed method has $O(1/\epsilon)$
iterations, and each iteration is just linear programming. Although the
proposed method is slower than k-DPPs, k-DPPs have the worst general
performance in Figure 1, which still supports the conclusion that SDI is a
competitive diversity model.

##  6\. Conclusions

In this paper, we presented a novel approach to multi-aspect search results
diversification, by adapting the Simpson’s Diversity Index (SDI) from biology
for this task. Unlike important previous SOTA family of methods for
diversification, our proposed method considers both evenness and richness.
Based on theoretical analysis and experimental evaluation, we show that the
evenness is significant for multi-aspect search, which is common in
e-commercial product search. By defining the relevance and diversity in
different ways, SDI can be further applied to other search and recommendation
methods based on learning-to-rank or neural search and recommendation
algorithms (Zoph and Le, 2016). In the future, we plan to explore
incorporating our SDI-based approach directly into learning-to-rank models, to
further improve search and recommendation performance for e-commerce search
and recommendation.

## References

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# Secure Email Transmission Protocols
— A New Architecture Design

Gabriel Chen
University of Illinois Urbana Champaign
<EMAIL_ADDRESS>Rick Wanner
SANS Institute
<EMAIL_ADDRESS>
###### Abstract

During today’s digital age, emails have become a crucial part of
communications for both personal and enterprise usage. However, email
transmission protocols were not designed with security in mind, and this has
always been a challenge while trying to make email transmission more secure.
On top of the basic layer of SMTP, POP3, and IMAP protocols to send and
retrieve emails, there are several other major security protocols used in
current days to secure email transmission such as TLS/SSL, STARTTLS, and
PGP/GPG encryption. The most general design used in email transmission
architecture is SMTP with PGP/GPG encryption sending through an TLS/SSL secure
channel. Regardless, vulnerabilities within these security protocols and
encryption methods, there is still work can be done regarding the architecture
design. In this paper, we discuss the challenges among current email
transmission security protocols and architectures. We explore some new
techniques and propose a new email transmission architecture using EEKS
structure and Schnorr Signature to eliminate the usage of PGP/GPG for
encryption while achieving Perfect Forward Secrecy.

##  1 Introduction

Email has become an integral part of commerce and personal daily life. Since
the time emails started being used to exchange important information and
treated as written evidence, email security, or digital information
transmission security in general, has always been a challenge within both
personal and enterprise usage. Without adding too much complexity onto the
transmission architecture, a secure yet simple email transmission design is
desired. Considering the original email transmission protocol without security
built in, SMTP, has been deployed over all these years towards general email
servers, redesigning from scratch with security in mind is not feasible.
Through years, researchers and engineers are building encryption and
compression blocks on top of SMTP to make email transmission more secure [1,
7, 11, 17], and some of the research has a specific system target such as
Android system [10]. Now, the transmission process is indeed much more secure
than the original one used when the first email was sent. However, there are
still many weakness and vulnerabilities in current email transmission
architecture design.

Here, we present a new architecture design using EEKS architecture with
Schnorr Signature to secure email transmission with Perfect Forward Secrecy.
In Section 2, we go over the fundamental email transmission architecture
design with an introduction to basic email transmission protocols. In Section
3, we discuss vulnerabilities in our current general email transmission
architecture designs and show how urgent it is for a better architecture. In
Section 4, we discuss some modern approaches to a better email transmission
architecture design including EEKS architecture, DMARCBox, quantum entangling
for authentication, and Schnorr Signature. Finally, we discuss our new
architecture which combines the power of EEKS and Schnorr Signature in Section
5.

##  2 Preliminary

To have a better grasping of the current email architecture design, below we
give a refresher regarding definitions of some fundamental protocols and
terminologies utilized while sending and receiving emails.

###  2.1 Fundamental Email Protocols and Terminologies

SMTP

SMTP stands for Simple Mail Transfer Protocol [19, 23]. This is the most
standard email transmission protocol used to send emails. It is transferred in
pain text without any security or encryption methods built on top. However, it
is reliable to guarantee the transmission as it will provide an error message
back to the sender if the email failed to be delivered.

POP

POP stands for Post Office Protocol, and POP3 is POP version 3 [18]. It is
utilized while downloading emails from email servers. When POP is used, emails
are automatically deleted after first retrieve. This makes POP good for one
single client accessing one single mailbox with less internet usage and more
independency from the server.

IMAP

IMAP stands for Internet Message Access Protocol [18]. It is also an email
receiving protocol. It is different from POP as IMAP does not delete messages
after retrieving. Thus, IMAP can support multiple clients accessing one single
mailbox. However, IMAP will consume more network usage and is more dependent
on the server.

SSL/TLS

TLS stands for Transport Layer Security and SSL stands for Secure Socket Layer
[23]. After a TCP channel is established, a SSL/TLS certificate will be sent
and a secure channel will be established after the SSL/TLS handshake.[13]
Today, TLS is more secure than SSL and should be a replacement of SSL [9].

STARTTLS

STARTTLS is the protocol which attempts to establish a secure SSL/TLS channel
[6]. It is used with SMTP, IMAP, and POP3. The STARTTLS process happens before
the SSL/TLS handshake and it will either establish a secure SSL/TLS tunnel or
fall back to simple SMTP depends on the design. If the design has enforced
TLS, the fallback strategy is ending the connection; otherwise if the design
is opportunistic TLS, the fallback strategy is transmitting without TLS.

PGP/GPG

PGP stands for Pretty Good Privacy and GPG stands for GNU Privacy Guard. GPG
is a free alternative to the PGP program [5]. PGP is an asymmetric key
encryption program which utilize cryptography to support data confidentiality
and authentication. PGP utilizes RSA and IDEA for encryption, and GPG utilizes
NIST and AES as its encryption algorithms.

SPF

SPF stands for Sender Policy Framework. It is an authentication protocol to
prevent sender’s address forgery [18]. Since SMTP does not validate the
sender’s address, anyone can potentially put whatever one wants in the
sender’s address. To mitigate this vulnerability, a type of DNS record
contains SPF header which has a list of domains which are authorized to send
emails. When an email send attempt is made, sender’s domain is verified using
this DNS record to detects any unauthorized activities. If any unauthorized
email sending is detected, the email is rejected.

DKIM

DKIM stands for Domain Keys Identified Mail [18]. It also mitigates the
sender’s address forgery. DKIM uses digital signature with asymmetric keys to
verify the sender is who they claim to be, and it also verifies the content of
the email is not changed. DKIM is more advanced than SPF as it solves the
issue that SPF allows same server forgery.

DMARC

DMARC stands for Domain Based Message Authentication Reporting and Conformance
[18]. It is another email authentication protocol which works with DKIM and
SPF. These three protocols are usually used together to mitigate email sender
forgery and strengthen the overall security.

S/MIME

S/MIME stands for Secure/Multipurpose Internet Mail Extensions [23]. It is a
protocol to support end-to-end email encryption and support by most email
servers. S/MIME uses digital certificates to guarantee the authentication and
confidentiality of emails, and it encrypts of the contents of emails before
sending them out to the internet to achieve end-to-end encryption. The
downside of S/MIME is that it only encrypts the contents but not the header or
metadata.

###  2.2 Fundamental Design of Email Transmission

In current general email transmission designs, emails are sent through SMTP,
and received using POP3 / IMAP [8, 22]. However, pure SMTP and POP3/IMAP are
transmitted using plaintext which do not provide any security. To add
security, these protocols are encapsulated in a secure transmission channel
such as SSL/TLS spanned through STARTTLS. In this design, the transmission
tunnel is secured but not the message itself. If the channel is compromised,
the message can be read in plaintext. Therefore, encryption algorithms such as
GPG/PGP are used to encrypt messages going through SSL/TLS tunnels to further
strength the security.

With the knowledge of above fundamental email transmission protocols, we will
discuss the basic fundamental email transmission design used in modern days.
The general design include two clients sides and two email servers sides. Let
us assume Alice and Bob are trying to send emails to each other, and Alice
initiate the first ever email. Alice’s email is constructed on Alice’s
client’s side, then transmitted to Alice’s email server which also called a
Mail Transfer Agent (MTA). Next, Alice’s email will go from Alice’s email
server to Bob’s email server, and it will be sent to Bob’s client side
eventually.

Figure 1:  Email Transfer from Alice to Bob

As we see in figure 1, after Alice clicks the “send” button on her client
side, her email can be encrypted using either PGP/GPG or S/MIME. In PGP/GPG,
either RSA or AES encryption algorithm is used. After the encryption, the
cipher text is transferred to Alice’s MTA using SMTP within a secure TLS
channel after the STARTTLS attempt. Then, a DNS look up will be performed to
find Bob’s MTA. After getting the address of Bob’s MTA, Alice’s email will be
transferred to Bob’s MTA also through SMTP. If Alice’s email server and Bob’s
email server are in different domains, different security design might
involve, and there is a fall back or connection drop choice for Alice’s MTA,
which means if Bob’s MTA does not support security requirements which are
enforced by Alice’s MTA, the connection might drop. For example, Bob’s email
server does not support TLS, then if Alice’s email server has enforced TLS,
the connection will be dropped; however, if Alice’s email server has
opportunistic TLS, the connection will fall back to a non TLS channel. When
the email successfully arrives at Bob’s MTA and been verified using SPF, DKIM
and DMARC, it will be retrieved by Bob’s client side using either IMAP or
POP3. Both IMAP and POP3 email retrieving protocols are also wrapped around
with a secure TLS channel.

##  3 Vulnerabilities in Current Designs

Although it looks like we already have a good design which is able to achieve
secure email exchange, there are still vulnerabilities and limitations within
our transmission channel, encryption methods, and the design itself.

###  3.1 Vulnerabilities in the Transmission Channel

Regardless of the overall design, there are vulnerabilities in the blocks we
are using to build the whole email transmission process. In the current
design, TLS is utilized as the protocol to establish a secure channel to
transmit emails on top of SMTP, POP, or IMAP. To start a TLS secure channel, a
TLS handshake is initiated first to agree on a cipher, a master secret, and
certificates between two sides of the communication. The TLS agreement looks
like the following:

TLS_DHE_RSA_WITH_AES_256_CBC_SHA256

Observe that the above TLS agreement uses RSA encryption with an AES 256
encryption method and CBC mode. The integrity is enforced using the SHA 256
hashing algorithm. As we know, to establish a TLS secure channel, STARTTLS
will first attempt and see whether the other side of the communication
supports TLS. Although under modern designs, TLS is enforced in most servers
and STARTTLS is not necessary in most cases, many architects still implement
STARTTLS before attempting the TLS handshake to make sure the connection can
be established. After all, we care about the availability of the email
transmission service more than other properties in CIA triad.

Figure 2:  STARTTLS and TLS handshake

However, both the STARTTLS protocol and the TLS handshake are vulnerable to
Machine in the Middle (MitM) attack the same as many other handshake
processes. When Side A attempts its first STARTTLS message, it is unencrypted.
the attacker could sit in between Side A and Side B then perform a TLS
Stripping attack. To improve availability, STARTTLS for email may use
opportunistic TLS which falls back to a non-secure channel when TLS is not
support on the other side. In TLS stripping [20], the attacker impersonates
Side B and tells Side A that TLS is not support, then Side A will send out
message in an unsecured channel. In the end, the attacker is able to read
everything being transmitted from Side A to Side B.

Besides stripping attack, TLS is also vulnerable to certificates attack as
described in [2]. Wildcard certificates are used by many system administrators
to save time and effort while creating certificates for each domain. For
example, a wildcard certificate “*.example.com” is valid through
“www.example.com”, “ftp.example.com”, “smtp.example.com”, and etc. If this
certificate is compromised which means the attacker gained the private key of
this certificate, the attacker is able to decrypt any message transferred
through TLS using this certificate. On the other hand, if the server only
utilize Certificate Authorities (CA) signed certificate, there is a still
possibility that the CA is compromised or forged by attackers.

###  3.2 Vulnerabilities in Encryption Methods

Besides the vulnerabilities that lie within the TLS secured transmission
channel, there are also vulnerabilities in encryption methods used in email
exchange. In email transmission, PGP/GPG and S/MIME are two major encryption
methods to encrypt the message itself while data is at rest.

####  3.2.1 GPG CVE-2021-3345 Overflow Vulnerability

GPG is one of the most used encryption methods among email encryption at rest.
Major email clients such as Thunderbird and Apple Mail use GPG as their
encryption method to make emails more secure within the TLS channel. This is
one of the reasons that GPG vulnerabilities are very severe based on a huge
user amount. As users tend to believe something under a massive usage has to
be flawless, it adds on to the influence of a GPG vulnerability.

In GPG Libgcrypt version 1.9.0, there is a heap-based buffer overflow in file
_gcry_md_block_write. When the digest final function sets a large count value,
this vulnerability, CVE-2021-3345 [4], is able to compromise confidentiality,
integrity, and availability of the message being encrypted using GPG. It is
recommended to update to version 1.9.1 or later, but this vulnerability is
still under investigation without knowing how much damage it has caused until
it was disclosed in year 2021.

####  3.2.2 S/MIME and CVE-2020-1774

As we have addressed in previous section, S/MIME does not encrypt the email
header nor the metadata, and there are many different S/MIME implementation
standards among many different servers which makes it hard to scale. Thus,
there comes a fall back strategy that if the recipient’s S/MIME standard does
not support the sender’s S/MIME standard, it cannot decrypt the message
encrypted under sender’s S/MIME standards.

Besides some draw back S/MIME naturally has, there are also vulnerabilities
among S/MIME practice in real life. In CVE-2020-1774 [3], when user downloads
S/MIME keys or certificates, the name for private and public keys are the same
in exported file. This gives the possibility to mix public keys and private
keys, then send the private key to the other side of communication instead of
the public key. As we can see, this vulnerability breaks the confidentiality
while transmitting emails, and it requires very few exploitation skills for
attackers to exploit it.

####  3.2.3 Vulnerabilities in the Design

Considering the lack of a scalable secure email transmission design, the most
general email transmission process needs to consider a lot of different
situation and edge cases to make the decision to either fall back or end the
connection. Unlike other internet protocols, email transmission requires much
more availability than others in the CIA triad. As the strong requirement
towards availability, many designs intend to fall back to non-secure protocols
instead of ending connections all together. This increases the impact of a
vulnerability where a client is under an old and/or insecure mail server which
does not support the most advanced security protocols in modern designs.

##  4 New Design Approaches to Achieve Security

Based on the awareness that the fundamental email transmission architecture is
not secure, there are several approaches which can be made to design a better
email exchange architecture. In general, there are two major approaches where
we can attack this problem. We can either enhance our current fundamental
design, or introduce emerging technologies which have evolved dramatically
through recent years.

###  4.1 Current Structure Enhancement

As most email exchange architectures and protocols are already implemented,
the most achievable solution to make them more secure is to add enhancements
on top of what we already have without redesigning the whole structure. In
current well developed protocols such as SMTP, PGP/GPG, and DMARC, there is
still room for security enhancement.

####  4.1.1 EEKS Architecture

Enhanced Encryption Key System, or EEKS, is a new architecture proposed to
enhancement the security of SMTP using asymmetric cryptography [16]. The goal
of EEKS is to massively improve the accessibility to email encryption for the
general public by eliminating the usability issues of PGP/GPG.

In order to eliminate PGP/GPG but retain the asymmetric cryptography, the
process of public key exchange has to be restructured. In EEKS, it
incorporates asymmetric cryptography mechanism directly into SMTP. It extends
the SMTP command set to include an ENCRYPT command that provides cryptography
and hash functions, FINGERPRINT contains the digital signature of the original
message, TIME2LIVE enables the ability of self-destruction, and SESSION serves
as a serial of random numbers which is utilized as salt. After the SMTP gains
cryptography power, EEKS also introduces a local EEKS server and a root EEKS
server to store the key pair to replace the functionality of CA in PGP/GPG.
Essentially, local EEKS residents on the user LAN and root EEKS server lives
on the Internet where local EEKS will periodically check in with root EEKS
server for public key creation and revocation.

There are several benefits of an EEKS architecture. First of all, the
elimination of GPG/PGP service reduces the development difficulty while
building an email server as the enhanced SMTP under EEKS carries encryption by
itself. Secondly, the separation of User Agent (UA), EEKS local server, and
EEKS gives additional protection against the compromise of email account.
Thirdly, the automatic asymmetric cryptography key generation process enhances
the message confidentiality, integrity, and non-repudiation.

However, like any other security architecture, EEKS has its own weakness. For
example, the connection between all EEKS servers are protected by TLS/SSL
which has its vulnerabilities as we discussed above. Also, the EEKS encryption
process can adds additional difficulty in searching emails.

Figure 3:  EEKS Architecture

####  4.1.2 DMARCBox

Besides email message encryption, email spoofing prevention has been a major
email security topic for years. As there is no spoofing prevention built into
SMTP, SPF and DKIM were developed. On top of SPF and DKIM, DMARC was built to
better prevent sender spoofing.

However, in order to have a better prevention mechanism, we have to have a
better detection method. To detect and react as early as possible, a better
analysis tool is needed to identify malicious emails. Currently, the most
popular technique is the spam filter logic. Techniques include but not limited
to Classification, Categorization, Profiling (Machine Learning), Natural
Language Processing, Parsing and Filtering when spam filter algorithms are
built. The vulnerability for a spam folder is that emails are analyzed after
they are already delivered, and it significantly increase the possibility
where a user can easily open the spam folder and phished by malicious emails.
To build a better mechanism for malicious email detection, we need to analyze
emails during transmission and react before they are in the mailbox.

Figure 4:  DMARCBox Workflowe

DMARCBox [14] is built for the purpose of analyzing malicious emails during
transmission. It utilize the DMARC protocol to retrieve the Reporting URIs for
Aggregate Date (RUA) and Reporting URIs for Failure (RUF) records, then
provides highly readable reports based on the analysis of the email. It can be
developed as either onsite or cloud based. The overall workflow of DMARCBox
can be found in Figure 4.

Since DMARC is built on top of SPF and DKIM, DMARCBox can also utilize the
protocol details of SPF and DKIM while classifying emails. DMARCBox provides
seven different categories according to RUA and RUF, and additional reaction
protocols can be built according to these classifications.

###  4.2 Introduce New Technologies

As new technologies have been evolving dramatically since the first appearance
of SMTP, many researchers start considering to incorporate them into their new
design approaches to build a secure email architectures. New technologies such
as quantum teleportation and heavy mathematical approaches, come in to play.

####  4.2.1 Quantum Teleportation

As we move further with email transmission security, new technologies are
eagerly expected to be introduced as we are getting more and more
vulnerabilities within current protocols every single day. Since the majority
of email services grant their users enough power to perform any activities
they would like once users are authenticated, the process of authentication is
crucial. To achieve faster and more secure email authentication, much research
has been conducted such as [15]. To untangle the issue of a strong user
authentication process, Quantum Teleportation [21] as a new technology is
introduced.

Instead of relying on the algorithmic complexity in Public Key Infrastructure
(PKI), quantum teleportation achieves authentication and encryption based on
non-locality of entanglement correlation space. Before the communication, both
sides’ Mail Server (MS) will be authenticated by the Authentication Center
(CA). Then, they will use a shared quantum encryption key for email encryption
through communication. The overall authentication process is shown as in
Figure 5.

Figure 5:  Quantum Authentication

In general, this process takes five steps to achieve users quantum
authentication. In step 1, quantum entangled states are prepared, and a shared
secret key is established through the quantum distribution protocol BB84. In
step 2, the communication channel established through step 1 is closely
monitored by selecting photons by both CA and MS. If both CA and MS generates
the same measurement results from these photons, the channel is secure and
safe. In step 3, MS will measure a special quantum state based on MB with a
result for step 4. In step 4, CA will verify the measurement results from MS
in step 3. If there is anything leads to a fake MS identifier, CA will deny
the result and the channel needs to be ended because of compromise. Otherwise,
step 5 will carry on. In step 5, CA will gather the demonstration information
based on quantum encoding ready for next step. In step 6, CA will encrypt the
demonstration information from step 5 and send it to MS using the shared
secret key they exchanged in step 1. In step 7, MS receives the information
from CA sent in step 6 and verifies it by comparing it with its own
demonstration information. In step 8, two parties will exchange their roles
and verify each other again. To elaborate, MS will gather its demonstration
information and encrypt it using the shared key, then send it to CA for
verification. CA will decrypt the message and verify it with its own
demonstration information. Up until now, the authentication process has
finished and both CA’s and MS’ identities are verified.

Although the quantum teleportation authentication process utilizes the quantum
space to significantly reduce some security risks we are facing right now in
our current structures such as vulnerabilities in GPG/PGP and TLS/SSL, it has
its own drawbacks. The major drawback of this design is the quantum
teleportation is not yet achievable by the general public. Besides, this
protocol will still suffer attacks against quantum space and quantum
technologies once it is massively achievable.

####  4.2.2 Schnorr Signature

One of drawbacks in current email architecture design lies within the
incorporation of encryption mechanism. Regardless the usage of either
asymmetric or symmetric encryption, once the master encryption key is
compromised, all previous emails which were encrypted using the same key are
readable. Thus, lots of research is done to design email protocols with
Perfect Forward Secrecy (PFS) against MITM (Machine in the Middle) attack.

Here, we discuss an email protocol with PFS addressed in [12]. It incorporates
Schnorr signature with a registration phase for both sending phase and
receiving phase. We assume the verification service for registration is trust
worthy. This verification process can be built into our email servers. Before
each sending and receiving action is performed, an extra registration phase is
performed to verify both sender and receiver. After the registration, a
session key is generated based on Schnorr signature for both sending and
receiving activities. Thus, even the master encryption key which encrypts
emails contents is compromised, the session key is an extra layer to provide
PFS against eavesdropping.

Below is the process of generating a Schnorr signature pair $(e,s)$ to send a
message 111h is a one way has function, and —— is the concatenation operator..

1\. Compute $r\equiv g^{\delta}modp$, where $\delta$ is a randomly chosen
integer $1\leq\delta<q$.

2\. Compute $e\equiv h(M||r)$.

3\. Solve $s\equiv xe+\delta modq$.

And the verification of Schnorr signature is the following process.

1\. Obtain the signer public key $(p,q,g,y)$.

2\. Compute $r^{\prime}\equiv g^{s}y^{-e}modp$.

3\. Compute $e^{\prime}\equiv h(M||r^{\prime})$.

4\. Accept the signature if and only if $e^{\prime}=e$.

To break the session key, the attacker has to break the Schnorr signature. The
security of Schnorr signature is guaranteed by the Discrete Logarithm
Assumption among all discrete logarithm problems ($DLPr^{\prime}\equiv
g^{s}y^{-e}modp$). In other word, we have to be able to easily find prime
factors among all numbers to break the Schnorr signature. Under the general
assumption that $P\neq NP$ in Computer Science, there does not exist such
feasible algorithm to achieve it and will never be.

Although $P\neq NP$ assumption is generally assumed as true in Computer
Science, it does not necessarily mean this assumption is absolutely true. we
hold a neutral opinion towards this issue in this paper. If it is proved that
$P=NP$, Schnorr Signature will become useless towards email transmission
security. But after all, the whole Computer Science foundation will collapse
in a sense once we prove $P=NP$, and Schnorr Signature will be one of the
least thing we would worry about at that point.

##  5 A New Design

Below we propose a new design which combines the power of EEKS architecture
and Schnorr Signature.

###  5.1 Design Workflow

In current EEKS architecture design, it gives us the opportunity to eliminate
the usage of GPG/PGP in email transmissions and build our encryption mechanism
directly into the SMTP protocol. However, one of the major issues lie within
the EEKS architecture is that it does not provide any Perfect Forward Secrecy
(PFS). If the master encryption key is compromised, all previous messages
which were encrypted using this key can be decrypted and read. To mitigate
this weakness, we can build Schnorr signature for all sessions into EEKS
structure. In this Defense in Depth set up, we utilize Schnorr signature to
generate another encryption layer for each send/receive session. Under this
design, even if our EEKS master encryption key is compromised, all previous
sessions were still encrypted using the Schnorr signature session key which
provides us the PFS.

###  5.2 Drawback

The major drawback of our design is the assumption of $P\neq NP$. As discussed
in the previous section, if it is shown that $P=NP$ at some point in the
future, the Schnorr Signature is useless to enforce the security in email
transmission. Thus, our design will not survive under the possibility of
$P=NP$.

Another drawback of our design has to do with the fallback procedures of EEKS
architecture. Since the encryption process is built into SMTP protocols under
EEKS design, there is a chance that the other side of email server does not
support enhanced SMTP which causes issues while decrypting the message. This
can only be resolved by implementing enhanced SMTP on both side of email
servers to retain the power of EEKS design.

###  5.3 Further Possibilities

Beyond our major design which utilizes both EEKS and Schnorr Signature,
DMARCBox can be our analysis tool for filtering malicious emails while in
transmission. It is also useful when we set up allow list and transmission
rules on our email servers. Additionally towards users authentication, once
the quantum field is achievable by the general public, quantum entangling can
be an authentication method for our users’ login process to the email client
side.

##  6 Conclusion

Email transmission security has been and will continue to be a major topic in
Network Security. To achieve a better security result, a good design is
crucial. The EEKS architecture is proven to be one of the ways to achieve a
better security comparing to our current general email transmission design
using GPG/PGP. On top of EEKS, Perfect Forward Secrecy can be achieved through
Schnorr Signature for session encryption. In this way, we achieve a better
designed SMTP protocol with PFS.

After building out our email servers architecture, a tool to constantly
monitor and tweak servers’ settings is important while filtering out and
blocking any malicious emails. We explored the possibility of DMARCBox which
stops malicious emails in transmission and believe it is a good tool to build
into email servers to perform useful analysis during transmission processes.

## Further Research

With our proposed new design which combines the EEKS architecture with Schnorr
Signature, we can eliminate the usage of GPG/PGP and achieve PFS. However, we
barely touched the transmission tunnel encryption which is currently utilizing
the power of TLS/SSL. There is still a lot of work that can be done in this
part.

Essentially, our design introduces some level of complexity comparing to the
general email transmission architecture design. As we all aware, complexity
can cause network delay. Although low latency is not too important in email
transmission as we care about availability more than others in the CIA triad,
more work can still be done in low latency architecture design.

As for the authentication process, we majorly discussed one possibilities
using quantum entangling. This is not yet generally achievable under current
technology limitations. As there are many other authentication techniques can
be explored and incorporate for user login on the client side, further
research can be conducted in this aspect.

## Acknowledgments

We thank WiCyS (Women in Cybersecurity) for their generous support to this
paper.

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