Homomorphic Encryption for Secure Computation on Big Data
Roger A. Hallman, Mamadou H. Diallo, Michael A. August and Christopher T. Graves
United States Department of Defense, SPAWAR Systems Center Pacific, San Diego, Ca, U.S.A.
Keywords:
Big Data, Homomorphic Encryption, Data Privacy, Secure Computation.
Abstract:
With the ubiquity of mobile devices and the emergence of Internet of Things (IoT) technologies, most of
our activities contribute to ever-growing data sets which are used for big data analytics for a variety of uses,
from targeted advertising to making medical and financial judgments and beyond. Many individuals and
organizations adopt this new big data paradigm without giving any consideration to privacy and security when
they create this data and voluntarily give it up for aggregation. Data breaches have become such a common
occurrence that it is easy to despair that concepts like privacy and security are antiquated and we should simply
accept data leakage as a new normal. Homomorphic Encryption (HE) is a method of secure computation
which allows for calculations to be made on encrypted data without decrypting it and without giving away
information about the operations being done. While HE has historically been plagued by computational
inefficiencies, the field is rapidly advancing to a point where it is efficient enough for practical use in limited
settings. In this paper, we argue that, with sufficient investment, HE will become a practical tool for secure
processing of big data sets.
1 INTRODUCTION
The integration of current and emerging technologies
into every aspect of human activity is contributing to
the generation of ever-increasing data sets about both
individuals and organizations. This data is aggregated
for big data analytics that are put to a variety of uses,
such as targeted advertising or contributing to medical
or financial decisions. “Big data analytic” refers
to the ability to ingest extremely large quantities
of data, efficiently process and analyze it, and
make conclusions and inferences from it (Boyd and
Crawford, 2012). A major challenge for organizations
that collect, transmit, store, and process on these data
sets is how to preserve the security and privacy of the
data when processing it. The problems of protecting
data in transit and at rest have been extensively
studied (). Currently, cryptographic based security
protocols exist, which securely and efficiently protect
data sets of any size when transiting on the network
and when being stored in data store. In fact, the U.S.
Federal government has supported the development
of AES (Miller et al., 2009) and selected it as
the recommended solution for protecting data. The
remaining outstanding issue is how to efficiently and
security protected data; in particular, big data, while
in processing.
Due to this lack of practical techniques for
protecting security and privacy of data when being
processed remotely (e.x, in the cloud), news of data
security breaches, sometimes strikingly severe and
at other times seemingly trivial, is a commonplace
occurrence. Examples of particularly serious data
breaches include the 2017 Equifax data breach that
affected more than 143,000,000 people, primarily in
the United States (Ng and Musil, 2017). Much of the
data that was stolen from Equifax was in plaintext
(Newman, 2017), presumably for computational
convenience. Another particularly severe event
was the 2015 breach at the United States Office
of Personnel Management, where records of more
than 21.5 million people were stolen (Zengerle and
Cassella, 2015). Other data breaches were less
impactful but still high profile.
Homomorphic encryption has been recognized
as one of the ideal approaches to securing and
processing data in remote servers including the cloud.
HE enables operations to be performed directly on
encrypted data without ever using the decryption key.
Using HE, data is encrypted on the client side, pushed
into the cloud, securely processed, and results are
sent back to the client for decryption. A sample
prototype application making use of HE technology is
CallForFire, a defense application that we developed,
which implements the “call for indirect fire” protocol
by securely outsourcing computations to the cloud
using HE (Diallo et al., 2016). Another sample
application using HE is a cloud-based secure VOIP
340
Hallman, R., Diallo, M., August, M. and Graves, C.
Homomorphic Encryption for Secure Computation on Big Data.
DOI: 10.5220/0006823203400347
In Proceedings of the 3rd International Conference on Internet of Things, Big Data and Security (IoTBDS 2018), pages 340-347
ISBN: 978-989-758-296-7
Copyright
c
 2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

application on mobile devices (Rohloff et al., 2017)
(Secure VOIP). Other potential applications are listed
in (Archer et al., 2017), including some key attributes
of the applications such as latency, data volume, and
practicality.
HE solves an important problem in data security
and privacy. While some applications with limited
scope, such as CallForFire and Secure VOIP, can
make use of HE, currently it is not mature enough to
be a general solution for secure computation in real
world applications. In particular, the performance
of HE technology is not sufficient for performing
general purpose computations on big data sets in
a practical amount of time, preventing it from
being used in applications doing big data analytics.
Most modern applications could not be run on
a HE computation platform owing to limitations
in performance, which result from the following:
the specific HE scheme used, the implementation
of the scheme within the HE software library,
and the limitations of the hardware used to run
the applications. Furthermore, while there is
much interest in enhancing the performance of HE
technology, the HE community today is still small but
is growing.
In this paper, we argue that, with sufficient
investment, HE will become a practical tool for secure
processing of big data sets. The extrapolation of
trends in the HE community since 2009 indicate
that there is a growing interest in the development
of practical HE libraries. The time it takes for the
widespread adoption of HE to occur is a function of
the degree of research and development investment
made into the technology. This investment will enable
the necessary performance enhancements to both
the software and hardware, including enhancements
to the HE schemes used, their implementation in
the form of software libraries, and the underlying
hardware on which the libraries are run, among
other things. Currently, there is a need for more
organizations, including government, academia, and
industry, to further invest in research and development
of HE technology. Active participation by various
organizations will help to accelerate the maturity and
adoption of HE.
2 BACKGROUND ON
HOMOMORPHIC
ENCRYPTION
In this section, we present Homomorphic Encryption.
We first provide a brief high-level background,
covering the development of important cryptosystems
and implementations. We then introduce the
foundational mathematical problem for the most
practical Homomorphic Encryption schemes. Finally,
we present the current state of Homomorphic
Encryption research, including standardization efforts
and major research initiatives.
2.1 A Brief History of Homomorphic
Encryption
Fully Homomorphic Encryption, or more simply
Homomorphic Encryption (HE), refers to a secure
computation technique that was first theorized by
Rivest, Adleman, and Dertouzos in 1978 (Rivest
et al., 1978), allowing computation on encrypted
data by taking advantage of certain mathematical
properties of various encryption schemes. The
computed results remain in an encrypted state
and can be further computed on or decrypted.
In fact, many cryptographic schemes theoretically
allow varying degrees of homomorphic properties
(e.g., RSA, based on exponentiation, allows for an
additive homomorphism) however these desirable
properties are lost in the process of real world
system implementations. Partially Homomorphic
Encryption, allowing for a limited class of secure
computations on encrypted data, have been in
use for several decades (ElGamal, 1985; Paillier
et al., 1999). The first working HE scheme was
introduced in 2009 by Gentry (Gentry, 2009), which
was built on NAND gates to evaluate low-degree
polynomials over encrypted data and used a
“bootstrapping” function capable of evaluating its
own decryption circuit and at least one more
function. Gentry’s scheme was revolutionary, though
terribly inefficient. This inefficiency led other
researchers to build new HE systems that would
preserve the desirable functionality of Gentry’s work
while improving the computation efficiency. The
most successful of these newer HE implementations
are based off of the Ring Learning With Errors
(RLWE) Problem (Regev, 2010) and include the
Brakerski-Gentry-Vaikuntanathan (BGV) (Brakerski
et al., 2011) and Fan-Vercauteren (FV) (Fan and
Vercauteren, 2012) cryptography schemes.
One of the earliest implementations of any
HE scheme was Shoup and Halevi’s HELib
1
,
which was an implementation of BGV. One
implementation of the FV cryptography scheme is
Microsoft Research’s Simple Encrypted Arithmetic
Library (SEAL)
2
. There have been hardware-based
1
https://github.com/shaih/HElib
2
http://sealcrypto.org/
Homomorphic Encryption for Secure Computation on Big Data
341

optimization efforts that have improved upon the
efficiency of RLWE-based HE implementations as
well. For instance, (Cousins et al., 2017a)
demonstrated the efficacy of FPGA architectures
and (Diallo et al., 2016; Diallo et al., 2017)
demonstrated GPGPU-based optimization. The
CUDA Homomorphic Encryption Library has further
pursued GPGPU-based HE optimization (Dai and
Sunar, 2015).
2.2 Mathematical Foundations of
Homomorphic Encryption
Regev (Regev, 2010) describes the Learning With
Errors Problem as follows: Choose a parameter
n ≥ 1, a modulus q ≥ 2, and an ‘error’ probability
distribution χ on Z
q
. Let A
s,q
on Z
n
q
× Z
q
be the
probability distribution obtained by choosing a vector
a ∈ Z
n
q
uniformly at random, choosing an error e ∈ Z
q
according to χ and outputting (a,ha,si + e), with
additions performed in Z
q
. An algorithm solves
the Learning With Errors Problem with modulus
q and error distribution χ if for any s ∈ Z
n
q
, and
given an arbitrary number of samples from A
s,q
,
it outputs s with high probability. The Learning
With Errors Problem is provably hard (Albrecht
et al., 2015), however large key sizes (e.g., O(n
2
))
are required for cryptographic schemes built on the
regular Learning With Errors Problem; RLWE-based
cryptographic schemes achieve linear key sizes. The
RLWE Problem is achieved by replacing Z
n
q
with
the polynomial ring Z
q
[x]/hx
n
+ 1i, where n is
a power of 2. The hardness of RLWE under
worst-case assumptions has similarly been proven
(Lyubashevsky et al., 2013).
2.3 Recent Investment and Efforts in
Homomorphic Encryption
Gentry’s initial HE scheme and the successive
cryptographic systems that followed it have spawned
multiple implementations across academia and
industry, the most successful of which are based
on BGV and FV. While they are functionally
similar, the implementations available are quite
diverse and a standardization effort has begun
to bring current and future HE implementations
under a common framework (Lauter et al., 2017).
The demand for easily available, scalable secure
computation technology will only grow as cloud
computing services become less expensive and
more powerful. This demand will likely be met
by developers who are not cryptography experts.
Standardization is imperative to simplify and
uniformize HE implementation APIs, provide a
clear and straightforward understanding of security
properties, and pinpoint appropriate use cases for HE
in the real world.
2.3.1 API Standardization for Homomorphic
Encryption
API standardization efforts revolve around two main
thrusts (Brenner et al., 2017):
1. Storage Model APIs, which mostly follow
existing design patterns.
• Cryptographic context includes information
on the state of the homomorphic
encryption/evaluation session, instructs the
compiler on circuit generation, and determines
which cryptographic library provides the
instruction set. Cryptographic context is, in
a sense, metadata for the information being
stored and processed.
• Payload Representation of the keys, plaintexts,
and ciphertexts enables parameters and data
to be serialized, transported, and deserialized
consistently across various platforms and HE
implementations.
2. HE Assembly Language
• Circuit Description information, which
includes information on the circuits being
executed may include low-level calls to library
functions, and be library-specific.
2.3.2 Homomorphic Encryption Security
HE offers a guarantee of data security to sectors
where it is adopted, and standardization will
increase its adoption and utility. A key element of
this standardization process will be a consensus
on security parameter levels across diverse
implementations and systems. An HE scheme
has three security properties (Chase et al., 2017):
1. Indistinguishability under chosen-plaintext attack
(IND-CPA).
• No adversary has an advantage in guessing
whether a given ciphertext is an encryption
of two different messages. Encryptions are
randomized to ensure that no two encryptions
of the same message appear the same.
2. Compactness.
• Homomorphic operations on the ciphertexts do
not expand the length of the ciphertexts.
3. Efficient decryption.
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342

• Decryption runtime does not depend on
the functions which were evaluated on the
ciphertexts.
Parameter generation requires four inputs:
• A security level λ (i.e., λ = 128-bit security).
• A plaintext modulus P.
• A dimension K of all vectors to be encrypted.
• An auxiliary parameter B for controlling the
complexity of circuits that can be run to process
encrypted data.
These parameters are used to generate a public key,
a secret key, and an evaluation key. The public key
can be used by anyone to encrypt a message while
the secret key is used for decryption. The generated
evaluation key is given to an entity that will compute
on the encrypted data.
2.3.3 Use Cases for Homomorphic Encryption
HE has shown potential for a diverse array of use
cases, from the medical field to financial industries
and beyond (Archer et al., 2017). It is expected that
in the next decade or two a significant fraction of the
world population will have full genome sequences,
which will prove to be a powerful tool in the study
of biology and medicine. Human DNA and RNA
sequences are unique biometric identifiers, which
may convey medically significant or socially sensitive
information and, once released, can never be retrieved
or retracted. The adoption of HE will allow genomic
data sets to be uploaded to cloud data centers where
they can be used to provide precision medicine.
Geneticists have begun to recognize the potential
impact of HE on their field to the point that the iDASH
Privacy & Security Workshop
3
routinely has a task for
machine learning on encrypted data.
3 CURRENT TRENDS IN USING
HOMOMORPHIC
ENCRYPTION TO PROCESS
BIG DATA
A number of specific applications have been
developed to evaluate the security, usability, and
performance of HE applied to big data. In particular,
a number of Machine Learning techniques have been
investigated to analyze how they can take advantage
of HE to securely process data. Below, we survey a
number of such techniques.
3
http://www.humangenomeprivacy.org/
Graepel, et al. (Graepel et al., 2012), showed
early results that machine learning (e.g., Linear
Means and Fisher’s Linear Discriminant) on smaller,
homomorphically encrypted data sets could be
practical. Gilad-Bachrach, et al. (Gilad-Bachrach
et al., 2016), showed a dramatic improvement
in the application of neural network operations
on homomorphically encrypted data. Specifically,
they used artificial feed-forward neural networks
for predictions on a data set consisting of 60,000
hand-written digits, with each image in a 28 × 28
array. Using a training data set of 50,000 images and
a test set of the remaining 10,000, they were able to
achieve nearly 59,000 predictions per hour with about
99% accuracy.
Aslett, et al. (Aslett et al., 2015), conducted
an extensive review of software tools for statistical
machine learning on homomorphically encrypted
data. They evaluated a sample of HE implementations
from the perspective of statistical analysis and
commented on the constraints of working on
homomorphically encrypted data. Constraints that are
mentioned for almost all implementations that they
look at include:
• Simple mathematical operations that have not yet
been implemented in HE libraries (i.e., square
root, division and comparison). These constraints
typically require computation to be completed in
the clear.
• The inability of HE implementations to handle
extensive computation on floating point numbers.
Because all HE implementations require fixed
points for computation, it is common for floating
point numbers to be truncated and rescaled (Diallo
et al., 2015).
Esperanca, et al. (Esperanca et al., 2017),
demonstrate that efficient and scalable statistical
analysis of homomorphically encrypted data
sets requires specially tailored and customized
computational methods that may be very different
from state-of-the-art methods for unencrypted
environments. Aono, et al. (Aono et al., 2016),
implemented logistic regressions using multiple
HE schemes and determined that this operation
was scalable over homomorphically encrypted data,
tolerating data sets with 10
8
elements.
Yonetani, et al. (Yonetani et al., 2017), used
an homomorphic cryptosystem for visual learning,
including facial recognition and detecting places
where sensitive information could be accessible.
The Paillier Cryptosystem (Paillier et al., 1999)
was used to create a doubly-permuted homomorphic
encryption, which allows high-dimensional classifiers
to be updated securely and efficiently. Sparsity
Homomorphic Encryption for Secure Computation on Big Data
343

constraints are enforced on classifier updates, and
updated weights are decomposed into a small number
of non-zero values. Only the non-zero values are
homomorphically encrypted. The facial recognition
algorithm was trained on a data set of more than
162,000 images with a test set of about 20,000
images. The facial recognition task involved
classifying 40 different attributes and achieved 84%
accuracy. Detecting sensitive places (e.g., a lavatory,
a personal computer terminal, etc.) was achieved with
a training data set of more than 131,000 images of
places and about 7,200 test images with about 72%
accuracy.
There have been notable achievements in using
HE for machine learning tasks such as the k-nearest
neighbors problem and building convolutional neural
networks. (Shaul et al., 2018) recently used HElib
to demonstrate a scalable and efficient solution to the
k-nearest neighbors problem using encrypted data in
near real time. Given a query point, q, they were
able to find the nearest 20 points in a set of over
1,000 in under an hour. They showed that efficient
and scalable statistical algorithms are achievable in
HE environments. Additionally, they implemented a
“coin toss” algorithm and an effective “comparison”
algorithm. In their experiments, they used their
algorithms to find the nearest hotels to a given query
point in Boston, Massachusetts. (Juvekar et al., 2018)
have recently developed a low latency framework
for secure neural networks that utilizes a packed
additive HE scheme in tandem with Yao’s Garbled
Circuits, a multi-party computation technique. This
framework, labeled “GAZELLE”, enables clients to
classify private images using a convolutional neural
network while not revealing their input to the server.
Within these convolutional neural networks, HE is
used for computation within the linear network layers
and garbled circuits for computation in the non-linear
network layers. They were able to attain at least 3
orders of magnitude lower latency and 2 orders of
magnitude lower bandwidth than previous HE-based
approaches to machine learning on neural networks.
As can be seen above, several researchers are
looking at how to take advantage of HE for
performing Machine Learning-based computations
on big data sets within specific domains. The trend
of using HE approaches for analyzing big data is
promising. This trend can serve as a vehicle for
motivating the research, development, and adoption
of HE for secure computation on big data.
4 CURRENT TRENDS IN
HARDWARE OPTIMIZATION
FOR HOMOMORPHIC
ENCRYPTION
There are several trends in using hardware-based
approaches to accelerate HE operations. In particular,
the use of FPGAs, ASICs, GPUs, CPU extensions,
and clustering, are all approaches that have been
investigated. These approaches can be grouped into
two categories: offloading computation to a HE
co-processor (FPGAs, ASICs, GPUs), and using CPU
vector computation extensions.
The approach of offloading computation to a HE
co-processor enhances the performance of certain HE
operations by performing them directly in hardware,
which leads to significant overall performance
improvements when performing HE computations.
One approach is the implementation of FPGA
modules for large integer multiplication and modulus
reduction for speeding up these HE operations (Cao
et al., 2014). They demonstrated a speedup of 44x
compared to a software-based approach. In (Cousins
et al., 2017b), the authors offloaded certain transforms
and ring operations to the FPGA and demonstrated
speedup in a sample problem utilizing encrypted
string comparisons. Another approach which offloads
computations makes use of an ASIC to implement
large integer multiplication and modulus reduction
modules to significantly improve performance of HE
operations while reducing circuit footprint (i.e. gate
count) (Dorz et al., 2015).
An approach for speeding up the performance of
the FPGA is to pipeline the circuits implemented
in it. This has the advantage of optimizing the
utilization of the FPGA board, which can result in
increased throughput and reduced latency. These
approaches can be extended by combining clustering
with offloading computation to an FPGA, as proposed
in (Roy et al., 2015). The approach of using GPUs
to accelerate HE operations leverages the highly
parallelized and high throughput memory architecture
of GPUs. For instance, an implementation of HE
primitives that makes use of a GPU realized speedup
of 7.68x for encryption and 7.4x for decryption
compared to a CPU implementation (Wang et al.,
2012). The approach of using accelerated CPU
vector computation makes use of CPU instruction
set extensions (e.g., AVX, SSE, NEON) to accelerate
vector computations using SIMD. Such a technique
is used by (Migliore et al., 2017). A fully
optimized solution may require combining these
different approaches into a hybrid solution.
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5 CURRENT TRENDS IN
HOMOMORPHIC
ENCRYPTION LIBRARIES
The success of homomorphic encryption in practical
use depends on how well the community can deliver
libraries that are efficient and simple to use. Today,
there exists a number of open source HE libraries
such as HElib, NFLlib, PALISADE, and SEAL.
However, these libraries provide mostly low-level
homomorphic operations including arithmetic
addition, subtraction, multiplication, and comparison.
These operations are useful in demonstrating that
the libraries work on toy problems, but that they are
less useful when building real-world systems that
need to be deployed in the cloud. Any attempt at
building a system using these libraries will require
enormous effort from the programmer to figure out
how the capabilities of the libraries can fit their
need, and to figure out what the limitations of the
libraries are. For example, HElib doesn’t support
floating point computations. If a system requires
floating point numbers, then the task of extending
the library to handle floating point numbers is left
to the programmer. Likewise, the programmer is
left with the task of finding parameter settings that
lead to optimal performance of the library. We argue
that, in order to promote the widespread adoption
of HE, these libraries and any subsequent ones,
need to be matured by providing APIs that abstract
out the complexity of the libraries. In addition, the
libraries need to provide APIs that can be used to
easily integrate the libraries into systems by both
cryptography experts and non-experts.
Considering the complexity of defining and
implementing a homomorphic encryption scheme,
the adoption of HE may well start with solutions
that are tailored to specific problems. The HE
libraries can be optimized to efficiently solve specific
problems. This observation is based on the fact that
HE libraries can perform well with some types of
operations, and not so well with other operations. For
instance, most libraries perform well with addition
and subtraction operations, but perform poorly with
multiplication. Our own experience with HElib shows
that multiplication is slower than addition.
CallForFire. Our experience with HElib shows
that it can be used in practice with certain types
of applications including interactive applications
(Diallo et al., 2016). Recall that CallForFire is a
mission-critical, cloud-based defense application that
implements the indirect call for fire protocol used
during combat operations when an infantry unit is
impractical for engagement with a target. The call
for indirect fire protocol involves essentially a few
players. A Forward Observer is deployed in advance
in the field to look for Targets to be destroyed by
Firing Units directed by a Fire Direction Center.
Note that this protocol is interactive. When the
Forward Observer detects a Target, he/she sends the
Target’s location information to the Fire Direction
Center, which then selects a Firing Unit to destroy the
Target. In this application, the number of messages
to be exchanged between the players is minimal.
Furthermore, only two computations need to be
performed by the fire direction center: the location of
the target, and the distance between the firing unit and
the target. More importantly, these computations deal
only with addition and multiplication on integers in
the Military Grid Reference System (MGRS). MGRS
represents a location with a five-digit integer on a
fixed grid. Due to all these characteristics of the
call for fire protocol, we were able to successfully
implement CallForFire using HElib and deploy it in
the cloud to securely process the operations of the
protocol.
Secure VoIP. Prior to the development of
CallForFire, a practical VoIP teleconferencing
mobile application using end-to-end homomorphic
encryption based on NTRU had been developed. In
this application, the voice data is sampled, encoded
and encrypted on the mobile device clients that are
communicating with each other, then sent over a
generic network such as the open Internet to the
encryption-enabled cloud-based server, and mixed
at the server without decrypting the VoIP data. The
encrypted results of the mixing are then sent back to
the client mobile devices for decryption, decoding
and playback to the end-users (Rohloff et al., 2017).
Note that the only homomorphic operation used in
this application is addition. In addition, the number
of operations to be performed for any call is low. The
above characteristics of the VoIP application make it
an ideal candidate for practical implementation using
homomorphic encryption.
6 CONCLUSION AND FUTURE
WORK
In this paper, we explore the trends underlying
advances in HE development, focusing particularly
on big data. We argue that, with sufficient
investment, HE will become a practical tool for
secure processing of big data sets. The current
trends in the use of homomorphic encryption to
secure big data analysis highlights the growing
interest in the adoption of HE. This trend is
Homomorphic Encryption for Secure Computation on Big Data
345

also complemented by research in enhancing the
performance of HE through novel hardware-based
approaches. The various hardware-based approaches
shows the growing research activity in this area.
In addition, the trends in the development of HE
libraries demonstrate that libraries can be tailored to
address specific big data analytics. In the future, we
will perform a comprehensive survey of HE libraries
and hardware-based optimizations to evaluate their
performance.
REFERENCES
Albrecht, M. R., Player, R., and Scott, S. (2015). On the
concrete hardness of learning with errors. Journal of
Mathematical Cryptology, 9(3):169–203.
Aono, Y., Hayashi, T., Trieu Phong, L., and Wang, L.
(2016). Scalable and secure logistic regression via
homomorphic encryption. In Proceedings of the Sixth
ACM Conference on Data and Application Security
and Privacy, pages 142–144. ACM.
Archer, D., Chen, L., Cheon, J. H., Gilad-Bachrach, R.,
Hallman, R. A., Huang, Z., Jiang, X., Kumaresan, R.,
Malin, B. A., Sofia, H., Song, Y., and Wang, S. (2017).
Applications of homomorphic encryption. Technical
report, HomomorphicEncryption.org, Redmond WA.
Aslett, L. J., Esperanc¸a, P. M., and Holmes, C. C. (2015).
A review of homomorphic encryption and software
tools for encrypted statistical machine learning. arXiv
preprint arXiv:1508.06574.
Boyd, D. and Crawford, K. (2012). Critical questions for
big data: Provocations for a cultural, technological,
and scholarly phenomenon. Information,
communication & society, 15(5):662–679.
Brakerski, Z., Gentry, C., and Vaikuntanathan,
V. (2011). Fully homomorphic encryption
without bootstrapping. Cryptology ePrint
Archive, Report 2011/277. Available at
https://eprint.iacr.org/2011/277.
Brenner, M., Dai, W., Halevi, S., Han, K., Jalali, A., Kim,
M., Laine, K., Malozemoff, A., Paillier, P., Polyakov,
Y., Rohloff, K., Savas¸, E., and Sunar, B. (2017). A
standard api for rlwe-based homomorphic encryption.
Technical report, HomomorphicEncryption.org,
Redmond WA.
Cao, X., Moore, C., O’Neill, M., Hanley, N., and
O’Sullivan, E. (2014). High-speed fully homomorphic
encryption over the integers. In B
¨
ohme, R., Brenner,
M., Moore, T., and Smith, M., editors, Financial
Cryptography and Data Security, pages 169–180,
Berlin, Heidelberg. Springer Berlin Heidelberg.
Chase, M., Chen, H., Ding, J., Goldwasser, S., Gorbunov,
S., Hoffstein, J., Lauter, K., Lokam, S., Moody,
D., Morrison, T., Sahai, A., and Vaikuntanathan,
V. (2017). Security of homomorphic encryption.
Technical report, HomomorphicEncryption.org,
Redmond WA.
Cousins, D., Rohloff, K., and Sumorok, D. (2017a).
Designing an fpga-accelerated homomorphic
encryption co-processor. IEEE Transactions on
Emerging Topics in Computing.
Cousins, D. B., Rohloff, K., and Sumorok, D. (2017b).
Designing an fpga-accelerated homomorphic
encryption co-processor. IEEE Transactions on
Emerging Topics in Computing, 5(2):193–206.
Dai, W. and Sunar, B. (2015). cuhe: A homomorphic
encryption accelerator library. Cryptology ePrint
Archive, Report 2015/818.
Diallo, M. H., August, M., Hallman, R., Kline, M., Au,
H., and Beach, V. (2015). Nomad: A framework for
developing mission-critical cloud-based applications.
In Availability, Reliability and Security (ARES), 2015
10th International Conference on, pages 660–669.
IEEE.
Diallo, M. H., August, M., Hallman, R., Kline, M.,
Au, H., and Beach, V. (2016). Callforfire: A
mission-critical cloud-based application built using
the nomad framework. In Clark, J., Meiklejohn, S.,
Ryan, P. Y., Wallach, D., Brenner, M., and Rohloff, K.,
editors, Financial Cryptography and Data Security,
pages 319–327, Berlin, Heidelberg. Springer Berlin
Heidelberg.
Diallo, M. H., August, M., Hallman, R., Kline, M., Au, H.,
and Slayback, S. M. (2017). Nomad: a framework
for ensuring data confidentiality in mission-critical
cloud-based applications. In Data Security in Cloud
Computing, Security, pages 19–44. Institution of
Engineering and Technology.
Dorz, Y., ztrk, E., and Sunar, B. (2015). Accelerating
fully homomorphic encryption in hardware. IEEE
Transactions on Computers, 64(6):1509–1521.
ElGamal, T. (1985). A public key cryptosystem and a
signature scheme based on discrete logarithms. IEEE
transactions on information theory, 31(4):469–472.
Esperanca, P., Aslett, L., and Holmes, C. (2017). Encrypted
accelerated least squares regression. In Singh, A. and
Zhu, J., editors, Proceedings of the 20th International
Conference on Artificial Intelligence and Statistics,
volume 54 of Proceedings of Machine Learning
Research, pages 334–343, Fort Lauderdale, FL, USA.
PMLR.
Fan, J. and Vercauteren, F. (2012). Somewhat
practical fully homomorphic encryption. Cryptology
ePrint Archive, Report 2012/144. Available at
https://eprint.iacr.org/2012/144.
Gentry, C. (2009). A fully homomorphic encryption
scheme. phd thesis, stanford university, 2009.
Gilad-Bachrach, R., Dowlin, N., Laine, K., Lauter, K.,
Naehrig, M., and Wernsing, J. (2016). Cryptonets:
Applying neural networks to encrypted data with
high throughput and accuracy. In Balcan, M. F.
and Weinberger, K. Q., editors, Proceedings of The
33rd International Conference on Machine Learning,
volume 48 of Proceedings of Machine Learning
Research, pages 201–210, New York, New York,
USA. PMLR.
Graepel, T., Lauter, K., and Naehrig, M. (2012). Ml
confidential: Machine learning on encrypted data. In
SPBDIoT 2018 - Special Session on Recent Advances on Security, Privacy, Big Data and Internet of Things
346

International Conference on Information Security and
Cryptology, pages 1–21. Springer.
Juvekar, C., Vaikuntanathan, V., and Chandrakasan, A.
(2018). Gazelle: A low latency framework for
secure neural network inference. arXiv preprint
arXiv:1801.05507.
Lauter, K., Laine, K., Rohloff, K., Chen, L., and
Zimmermann, R. (2017). Homomorphic
encryption standardization: An open
industry/government/academic consortium to
advance secure computation. Available at
http://homomorphicencryption.org/.
Lyubashevsky, V., Peikert, C., and Regev, O. (2013). On
ideal lattices and learning with errors over rings. J.
ACM, 60(6):43:1–43:35.
Migliore, V., Seguin, C., Real, M. M., Lapotre, V.,
Tisserand, A., Fontaine, C., Gogniat, G., and Tessier,
R. (2017). A high-speed accelerator for homomorphic
encryption using the karatsuba algorithm. ACM Trans.
Embed. Comput. Syst., 16(5s):138:1–138:17.
Miller, F. P., Vandome, A. F., and McBrewster, J. (2009).
Advanced Encryption Standard. Alpha Press.
Newman, L. H. (2017). 6 fresh horrors from the
equifax ceo’s congressional hearing. Available at
https://www.wired.com/story/equifax-ceo-congress-
testimony/.
Ng, A. and Musil, S. (2017). Equifax data breach
may affect nearly half the us population.
Available at https://www.cnet.com/news/equifax-
data-leak-hits-nearly-half-of-the-us-population/.
Paillier, P. et al. (1999). Public-key cryptosystems based on
composite degree residuosity classes. In Eurocrypt,
volume 99, pages 223–238. Springer.
Regev, O. (2010). The learning with errors problem. Invited
survey in CCC, page 15.
Rivest, R. L., Adleman, L., and Dertouzos, M. L.
(1978). On data banks and privacy homomorphisms.
Foundations of secure computation, 4(11):169–180.
Rohloff, K., Cousins, D. B., and Sumorok, D. (2017).
Scalable, practical voip teleconferencing with
end-to-end homomorphic encryption. IEEE
Transactions on Information Forensics and Security,
12(5):1031–1041.
Roy, S. S., J
¨
arvinen, K., Vercauteren, F., Dimitrov,
V., and Verbauwhede, I. (2015). Modular
hardware architecture for somewhat homomorphic
function evaluation. In International Workshop on
Cryptographic Hardware and Embedded Systems,
pages 164–184. Springer.
Shaul, H., Feldman, D., and Rus, D. (2018). Scalable
secure computation of statistical functions with
applications to k-nearest neighbors. arXiv preprint
arXiv:1801.07301.
Wang, W., Hu, Y., Chen, L., Huang, X., and Sunar, B.
(2012). Accelerating fully homomorphic encryption
using gpu. In 2012 IEEE Conference on High
Performance Extreme Computing, pages 1–5.
Yonetani, R., Boddeti, V. N., Kitani, K. M., and Sato,
Y. (2017). Privacy-preserving visual learning using
doubly permuted homomorphic encryption. In 2017
IEEE International Conference on Computer Vision
(ICCV), pages 2059–2069.
Zengerle, P. and Cassella, M. (2015). Estimate
of americans hit by government personnel
data hack skyrockets. Available at
https://www.reuters.com/article/us-cybersecurity-usa/
millions-more-americans-hit-by-government-
personnel-data-hack-idUSKCN0PJ2M420150709.
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