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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>AutoMPC: Efficient Multi-Party Computation for Secure and Privacy-Preserving Cooperative Control of Connected Autonomous Vehicles</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Tao Li</string-name>
          <email>taoli@purdue.edu</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Lei Lin</string-name>
          <email>lei.lin@rochester.edu</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Siyuan Gong</string-name>
          <email>sgong@chd.edu.cn</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Computer Science, Chang'an University</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Department of Computer Science, Purdue University</institution>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Goergen Institute of Data Science</institution>
          ,
          <addr-line>Rochester University</addr-line>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2016</year>
      </pub-date>
      <abstract>
        <p>The advent of connected autonomous vehicles provides opportunities for safer, smoother, and smarter transportation. However, broadcasting information to surrounding vehicles and infrastructures risks security and privacy. Moreover, control decisions relying on such information are vulnerable to malicious attacks. In this paper, we propose a cooperative control strategy incorporating with efficient multi-party computation (MPC). In an effort to perform secure MPC without third-party authentication while reducing latency, we integrate a function secret sharing scheme with a distributed oblivious random access memory. We further design an adaptive proportional-derivative controller to increase resilience toward latency and adversaries. Theoretical foundations and limitations are also discussed.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        Since the first competition of autonomous vehicles hosted by
the Defense Advanced Research Projects Agency (DARPA)
Grand Challenge in 2005
        <xref ref-type="bibr" rid="ref19">(Seetharaman, Lakhotia, and
Blasch 2006)</xref>
        , self-driving vehicle or autonomous vehicle
techniques have attracted tremendous attentions from both
academia and industry. An autonomous vehicle is equipped
with various powerful sensors like camera, radar, LiDAR,
GPS, ultrasonic and so on to detect and perceive its
surrounding environment. Autonomous vehicles have the
potential to change driving behavior and the travel
environment, providing opportunities for safer, smoother, and
smarter road transportation. However, the development of
autonomous vehicles has also raised disputations and
skepticism in terms of liability, ethics, cybersecurity, privacy and
so on. Especially, the fatal accident in March, 2018
involving an Ubers self-driving car where a pedestrian was killed
implies a large room to enhance autonomous vehicle
techniques and safety should always be considered with the
highest priority in this process
        <xref ref-type="bibr" rid="ref14 ref15 ref16 ref8">(Li et al. 2018a)</xref>
        .
      </p>
      <p>
        On the other hand, connected vehicle techniques are also
being deployed to improve the safety and mobility of our
transportation system by enhancing situational awareness
and traffic state estimation through vehicle-to-vehicle (V2V)
and vehicle-to-infrastructure communications, which can
enable applications like cooperative collision warning,
providing traffic signal status information in real time and so
on
        <xref ref-type="bibr" rid="ref22">(Shladover 2018)</xref>
        , These applications require low latency
and high reliability networking. Hence, efficient, secure, and
trustworthy data transmitting is of paramount importance.
      </p>
      <p>
        More recently, interesting opportunities appear through
the utilization of techniques from connected vehicles to
autonomous vehicles. The connectivity allows an autonomous
to have more detailed knowledge of the environment. The
sensing capability of the autonomous vehicle is hence
further expanded. A platoon formed by connected and
autonomous (CAVs) on the road can increase the capacity,
reduce energy consumption and improve safety. It was
predicted that the transition from the current human-driven
vehicles to a fully CAV traffic environment require a few
decades
        <xref ref-type="bibr" rid="ref10">(GSMA 2013)</xref>
        , during which the road traffic consist
of a mixed traffic flow (see Figure 1). Equipped with
multiple sensors and V2V communications, a CAV can track
the trajectories of other CAVs in its vicinity, and ideally, all
CAVs in communication range. Such CAV trajectory data
can be leveraged with advances in computing and machine
learning algorithms to potentially predict trajectories of
surrounding vehicles, such as acceleration and speed. Based on
these predictions, CAVs can react accordingly to avoid or
mitigate traffic flow oscillations and accidents.
      </p>
      <p>
        In reality, V2V communications are unreliable due to
factors such as interference, network congestion, and malicious
attacks; in the worst case, V2V networks undergo
Byzantine failures
        <xref ref-type="bibr" rid="ref13 ref14 ref15 ref16 ref22">(Lamport, Shostak, and Pease 1982; Li and Lin
2018)</xref>
        , which is the most general and severe failure model,
since attackers are fully aware of any information of the
entire system. Moreover, current architecutre of vehicular
ad-hoc networks (VANETs) communicate in an open-access
environment and thereby experience serious issues in
security and privacy
        <xref ref-type="bibr" rid="ref18">(Qu et al. 2015)</xref>
        . To tackle these, we propose
a novel cooperative control strategy, AutoMPC, by
leveraging advances in modern cryptography such as multi-party
computation (MPC). As V2V communication requires low
latency, we further adopt an efficient MPC scheme
incorporating with an adaptive proportional-derivative controller
and prove its effectiveness through numerical experiments.
      </p>
      <p>
        The rest of this paper is organized as follows: in Section 2
we introduce necessary background; Section 3 presents the
AutoMPC model; future works are discussed in Section 4;
we leave the experimental section and more theoretical
results in the full paper.
To formalize the problem, we suppose a multi-agent
system in which each party i has a secret input xi and a
function f (x1; x2; : : : ) can be jointly evaluated. Secure
multiparty computation (MPC) is a mechanism to ensure that each
party known the output of the function f while being
unaware of others’ inputs. Two-party computation (2PC) is a
special case of MPC, which was first introduced by
        <xref ref-type="bibr" rid="ref29">(Yao
1982)</xref>
        as a problem that two millionaires (Alice and Bob)
wish to know who is richer but don’t want to disclose their
own wealth. The famous solution is Yao’s Garbled Circuits
        <xref ref-type="bibr" rid="ref30">(Yao 1986)</xref>
        , which is based on honest-but-curious model or
semi-honest security model that curious adversaries and
outside observers may learn the secrets by analyzing protocol
transcripts.
2.2
      </p>
    </sec>
    <sec id="sec-2">
      <title>Oblivious Random Access Memory</title>
      <p>
        Oblivious random access memory (ORAM)
        <xref ref-type="bibr" rid="ref7">(Goldreich
and Ostrovsky 1996)</xref>
        is similar to random access memory
(RAM) but translates the sequence of logical access
instructions in certain ways so that preserves the observing of
physical access patterns from adversaries. An ORAM supports
READ(i) and W RIT E(i) functions that are able to
perform “read” and “write” operations with a private index i.
For the case of MPC, we consider a variant of ORAM,
distributed oblivious RAM (DORAM) (Lu and Ostrovsky
2013), which generalize ORAM to a scenario that the
memory is splited among m parties and has a security property
that no party can learn anything of the RAM by observing
their own share of the physical memory.
2.3
      </p>
    </sec>
    <sec id="sec-3">
      <title>Secret Sharing</title>
      <p>
        Secret sharing
        <xref ref-type="bibr" rid="ref21">(Shamir 1979)</xref>
        is a method in cryptography
that distributes a secret among a group of m parties by
dividing the secret into m shares, one for each of m parties,
so that none of the individual party has any insight of the
secret while all m shares as a group contain full information of
the secret.
        <xref ref-type="bibr" rid="ref6">(Franklin and Yung 1992)</xref>
        designed a multi-secret
sharing system where multiple points of the polynomial host
secrets.
        <xref ref-type="bibr" rid="ref17">(Parakh and Kak 2011)</xref>
        proposed a k-threshold
computational secret sharing scheme that divide a secret S into
shares of size KjSj1 for optimal space efficiency.
3
      </p>
      <sec id="sec-3-1">
        <title>The AutoMPC Model</title>
        <p>
          Inspired by existing works
          <xref ref-type="bibr" rid="ref24 ref4 ref9">(Gordon et al. 2012; Wang et al.
2014; Doerner and Shelat 2017)</xref>
          and aforementioned
techniques, we propose the AutoMPC model, which adopts a
function secret sharing (FSS) scheme following the
definition in
          <xref ref-type="bibr" rid="ref23">(Boyle, Gilboa, and Ishai 2016)</xref>
          that:
Definition 1. An m-party function secret sharing scheme is
a pair of algorithms (Gen, Eval) with the following syntax:
Gen(1 ; f ) is a PPT key generation algorithm, which
on input 1 (security parameter) and f 2 f0; 1g
(description of a function f ) outputs an m-tuple of keys
(k1; : : : ; km). f is assumed to explicitly contains an
input length 1n, group description G, and size parameter
S.
        </p>
        <p>Eval(i; ki; x) is a polynomial-time evaluation algorithm,
which on input i 2 [m] (party index), ki (key defining
fi : f0; 1gn ! G), and x 2 f0; 1gn (intput for fi) outputs
a group element yi 2 G (the value of fi(x), the i-th share
of f (x)).</p>
        <p>
          The setting of FSS ensures correctness and security that
each party’s key cannot individually reveal any information
of f
          <xref ref-type="bibr" rid="ref3">(Boyle, Gilboa, and Ishai 2015)</xref>
          . We further adopt a
distributed oblivious RAM
          <xref ref-type="bibr" rid="ref4">(Doerner and Shelat 2017)</xref>
          to
optimize the computational complexity to O(n) which
outperforms current state-of-the-arts such as circuit oblivious
RAM
          <xref ref-type="bibr" rid="ref28">(Wang, Chan, and Shi 2015)</xref>
          and square-root
oblivious RAM
          <xref ref-type="bibr" rid="ref31">(Zahur et al. 2016)</xref>
          .
        </p>
        <p>To mitigate the latency trade-offs given by MPCs and
increase resilience towards adversaries, we propose an
adaptive proportional-derivative (PD) controller based on a
twopredecessor-following scheme as shown in Figure 2, in
which we assume all CAVs in the platoon to be identical,
forming a homogeneous vehicle string. Below is the control
command</p>
        <p>Ui(s) = Ub;i(s) + Uf;i 1(s) + Uf;i 2(s)
(1)
which consists of control feedback Ub;i from the error Ei
and two extra feedforward terms Uf;i 1 and Uf;i 2 from
the acceleration rates Xi 1 and Xi 2, respectively. Xi is the
position output, Xi 1 is the feedback position information
from the immediate predecessor. Ki is the feedback
controller which generates a control command to rectify the
error. Gi represents the ideal longitudinal vehicle dynamics.
Hi denotes spacing policy (e.g., CD and CTH), and F1;i and
F2;i are feedforward filters to process the acceleration
information from the corresponding predecessor vehicles. and
are indicators for the success of V2V communications (
and are equal to 1 for a successful communication between
the CAV and the corresponding predecessor vehicles, and 0
otherwise). These terms will be explained in detail later.
4</p>
      </sec>
      <sec id="sec-3-2">
        <title>Discussion and Future Works</title>
        <p>The AutoMPC model leverages advances in cryptography
to control theory for safer, smoother, and smarter
transportation. The contributions lie in several ways: (i) security
and privacy are guaranteed via a MPC scheme, without the
presence of third-party authentication; (ii) the efficiency of
the MPC is achieved by a distributed oblivious RAM and
a function secret sharing scheme, and thereby avoids the
homomorphic encryption approach which is
computationally expensive; and (iii) an adaptive proportional-derivative
controller is proposed to increase the resilience toward
latency and adversarial attacks. Preliminary experimental
results also validate above findings by comparing control
performances in speed, spacing, and acceleration rate.
Theoretical properties in security and control as well as more
experimental results will be discussed in the full paper.</p>
      </sec>
      <sec id="sec-3-3">
        <title>Acknowledgments</title>
        <p>The authors thank Jian Wang, Yuntao Guo, Chaojie Wang,
and Anye Zhou for insightful discussions and anonymous
reviewers for their helpful comments.</p>
        <p>Li, T. 2018. Modeling uncertainty in vehicle trajectory
prediction in a mixed connected and autonomous vehicle
environment using deep learning and kernel density estimation.
In the Fourth Annual Symposium on Transportation
Informatics.</p>
        <p>Lin, L., and Li, W. 2018. A compressive sensing
approach for connected vehicle data capture and recovery
and its impact on travel time estimation. arXiv preprint
arXiv:1806.10046.</p>
        <p>Lin, L.; Wang, Q.; Huang, S.; and Sadek, A. W. 2014.
Online prediction of border crossing traffic using an enhanced
spinning network method. Transportation Research Part C:
Emerging Technologies 43:158–173.</p>
        <p>Lin, L.; Wang, Q.; and Sadek, A. W. 2015. A novel variable
selection method based on frequent pattern tree for real-time
traffic accident risk prediction. Transportation Research
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        <p>Lu, S., and Ostrovsky, R. 2013. Distributed oblivious ram
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