<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">IJCNS</journal-id><journal-title-group><journal-title>International Journal of Communications, Network and System Sciences</journal-title></journal-title-group><issn pub-type="epub">1913-3715</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/ijcns.2017.108B034</article-id><article-id pub-id-type="publisher-id">IJCNS-78418</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Computer Science&amp;Communications</subject></subj-group></article-categories><title-group><article-title>
 
 
  An Anonymous Authentication Scheme for Vehicle-to-Grid Networks
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zhongwei</surname><given-names>Sun</given-names></name><xref ref-type="aff" rid="aff1"><sub>1</sub></xref></contrib></contrib-group><aff id="aff1"><label>1</label><addr-line>School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, China</addr-line></aff><author-notes><corresp id="cor1">* E-mail:</corresp></author-notes><pub-date pub-type="epub"><day>14</day><month>08</month><year>2017</year></pub-date><volume>10</volume><issue>08</issue><fpage>316</fpage><lpage>323</lpage><history><date date-type="received"><day>August</day>	<month>7,</month>	<year>2017</year></date><date date-type="rev-recd"><day>Accepted:</day>	<month>August</month>	<year>11,</year>	</date><date date-type="accepted"><day>August</day>	<month>14,</month>	<year>2017</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  
    Vehicle to grid technology allows bidirectional energy exchange between electric vehicles and the power grid for achieving many known benefits. However, V2G networks suffer from certain security threats, such as EV’s privacy and authentication problem. In this paper, we propose an anonymous group authentication scheme for V2G communications. This scheme realizes dynamic joining and revocation of EVs, and greatly reduces the overhead of EV revocation. Through the theoretical analysis, this scheme can ensure identity privacy of EV user and security of data transmission in the process of charging and discharging. 
  
 
</p></abstract><kwd-group><kwd>Electric Vehicles</kwd><kwd> Vehicle to Grid</kwd><kwd> Group Signature</kwd><kwd> Anonymity  Authentication</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>Depletion of fossil fuel reserves and prominence of environment problem gives a wakeup call for finding the alternative energy sources for these sectors. Because the traditional power grid has the feature of high cost, easy to cause waste and unreliable system, and with the increasing user demand for electricity diversity, traditional power grid has already can’t meet the development needs of the future [<xref ref-type="bibr" rid="scirp.78418-ref1">1</xref>]. However, smart grid can meet this Long-term demand. Smart grid support and encourage integration of new energy power generation system (such as wind energy, tidal power, solar power generation system), but because of the discontinuity and randomness, new energy will cause the fluctuation of power grid, so in order to smooth the fluctuations and ensure the stability of power grid voltage and frequency, smart grid need other auxiliary system as a compensation of new energy system. Vehicle to grid can be used as a buffer of new energy.</p><p>Vehicle to grid technology allows bidirectional energy exchange between electric vehicles and the power grid under the unified dispatch and control of power grid, and it is an integral part of the smart Grid. The core idea of V2G is using the storage energy of a large number of EV as a buffer of power Grid and new energy. When the power load is high, EV will feedback the surplus electricity to the power grid, and when the load is low, a large number of EV battery pack can be used to store excess power grid electricity. In this way, the V2G technology not only can be used as a buffer of new energy, but also play the role of peak shifting. Advantages of V2G: 1) using EV as a power grid buffer, and providing ancillary services for power grid, such as peak shaving, spinning reserve, reactive power compensation, etc., 2) providing EV owners with an extra income, and offsetting part of the cost to buy electric cars, which is conducive to the popularization of clean vehicles, 3) increasing power grid stability and reliability, and reducing the power system operating costs [<xref ref-type="bibr" rid="scirp.78418-ref2">2</xref>].</p><p>The V2G communications infrastructure can facilitate better power load management, and hence improve energy efficiency and reliability. However, the infrastructure may suffer from severe security attacks and vulnerabilities. In the literature, there are only a few studies on privacy and security issues in V2G networks, although several studies have been performed to enhance security and preserve privacy in the smart grid in general. H. R. Tseng et al. [<xref ref-type="bibr" rid="scirp.78418-ref3">3</xref>] noticed the privacy concerns created by EV owners’ identity information leakage. They utilized a restrictive partially blind signature to protect the identities of the owners. The protocol has been proven to preserve identity and location privacy, and to achieve data confidentiality and integrity. Yang et al. [<xref ref-type="bibr" rid="scirp.78418-ref4">4</xref>] identified the emerging privacy issues in V2G networks, and secure communication architecture was built to achieve privacy-preserving EV monitoring, in which an ID-based blind signature was introduced to enhance anonymity. References [<xref ref-type="bibr" rid="scirp.78418-ref3">3</xref>] and [<xref ref-type="bibr" rid="scirp.78418-ref4">4</xref>] based on the blind signature to ensure the safety of the electric car users’ privacy information, but blind signature algorithm is very complex, and it will bring huge delays to identity verification in V2G network. Miao He et al. [<xref ref-type="bibr" rid="scirp.78418-ref5">5</xref>] propose a privacy-preserving multi-quality charging (PMQC) scheme to evaluate the EV’s attributes, and authenticate its service eligibility and generate its bill without revealing the EV’s private information. This scheme reduces the delays of identity verification in references [<xref ref-type="bibr" rid="scirp.78418-ref3">3</xref>] and [<xref ref-type="bibr" rid="scirp.78418-ref4">4</xref>]. Hong Liu [<xref ref-type="bibr" rid="scirp.78418-ref6">6</xref>] distributes EVs into home mode and visiting mode, discusses the privacy security requirement of EVs in these two models, and designs security authentication scheme for each model. Guo et al. [<xref ref-type="bibr" rid="scirp.78418-ref7">7</xref>] proposed an authentication protocol to deal with multiple responses from a batch of vehicles. The proposed scheme introduced the concept of interval time for an aggregator verifying multiple vehicles, and the aggregator broadcasts a signed confirmation message to inform multiple vehicles using only one signature. The batch verification scheme employs a modified digital signature algorithm. Reference [<xref ref-type="bibr" rid="scirp.78418-ref8">8</xref>] distributed EVs into: charging, fully-charged (FC), and discharging, proposed a battery status-aware authentication scheme (BASA) to address the issue for V2G networks. References [<xref ref-type="bibr" rid="scirp.78418-ref7">7</xref>] [<xref ref-type="bibr" rid="scirp.78418-ref8">8</xref>] introduced batch authentication, which greatly reduces authentication delays of V2G. Because of pure anonymous, pseudonym technology is not a very good way to solve the security problem of vehicle privacy, and the above solutions are based on mixed scheme of anonymous technology and encryption technology, which will also bring great communication delay and computational over-head to LAG, so they are not suitable for V2G networks with a large number of users.</p><p>The remainder of paper is organized as follows: section II introduces security threats and requirement of V2G communication. Section III presents an anonymous group signature authentication scheme. Section IV shows the security analysis of our scheme. Finally, section V makes a conclusion.</p></sec><sec id="s2"><title>2. Security Threats and Requirements of V2G Communication</title><p>V2G should follow a fundamental principle: V2G cannot reduce or damage the security of smart grid. Lu et al. [<xref ref-type="bibr" rid="scirp.78418-ref9">9</xref>] divided the threat of SG into three categories: 1) availability of communication network; 2) integrity of communication data; 3) confidentiality of communication data. These security threats are also exist in V2G. Here we present some specific V2G security threat scenarios and serious consequences.</p><p>・ When V2G communication network is under attack and data have been tampered, security control center will make wrong decision, which will influence the stability of power grid and charging/discharging plan of EVs. If a wide range of communication networks are subject to this type of attack, it will lead to the entire power system run under the conditions of fault data, and bring serious threat to the safety of power grid.</p><p>・ When V2G communications network is under distributed denial of service attack (DDOS), related data information will be delayed, blocked, or even damaged. PEV/PHEV charge and discharge cannot be reasonably arranged so as to adapt to the current network conditions, which is likely to aggravate the load on the grid. Users can’t get the vehicle energy state, the state power load and billing information etc. in time, and thus they cannot make full use of time-sharing electricity to charge and discharge EVs.</p><p>・ Data privacy of V2G in the process of communication include: the vehicle’s location information, the user’s identity, battery type, the user’s payment information, ST process information, etc. Regardless of the privacy protection would be likely to lead to leakage of users’ personal identity and electric car location information. A malicious attacker can also deduce user’s habits (activities range of the user, and, driving path and distance information) by basing on a lot of user data, such as charging time, charging locations and charging amount information [<xref ref-type="bibr" rid="scirp.78418-ref10">10</xref>].</p><p>・ When malicious terminal connected to the electricity grid in the form of V2G, the data of DSO can be tapped, forged and damaged, so it is needed to firstly verify identity in DSO communication network, which requires authentication protocol which has efficient design and can resist various attacks to meet the needs of real-time and security of V2G communication network.</p></sec><sec id="s3"><title>3. An Anonymous Group Authentication Scheme for V2G</title><p>Boneh’s group signature has advantages of short signature and save communication bandwidth [<xref ref-type="bibr" rid="scirp.78418-ref11">11</xref>], here we take the group signature as cryptography foundation of the proposed scheme.</p><sec id="s3_1"><title>3.1. System Model</title><p>The system model is described in <xref ref-type="fig" rid="fig1">Figure 1</xref>. There are five kinds of entities involved in the architecture, including trusted authority (TA), central aggregator (CAG), local aggregator (LAG), charging/discharging station (ST), electric vehicles (EV). TA is responsible for assignment of public/private key, certificate of EV, and tracing of signature. CAG divide the recharge area into a number of LAG subsets. LAG carries out register of EV, distribute group for EV, and generates group public key and private key of group member. ST can directly monitor and communicate with each EV and send the collected monitoring data to LAG, and then provides charging or discharging service for EV.</p></sec><sec id="s3_2"><title>3.2. Authentication Scheme</title><p>Boneh’s [<xref ref-type="bibr" rid="scirp.78418-ref11">11</xref>] group signature has advantages of short signature and save communication bandwidth, so we make the group signature as cryptography foundation of this scheme.</p><p>1) System initialization</p><p>a) CAG divides itself into a number of subsets, like LAG1, LAG2, ・・・, and announces them in the public.</p><p>b) EV sends its identity information ID<sub>EV</sub> to TA. TA generates public/private key pair for every entity (EV, ST, LAG, and CAG). EV’s public/private key pair:<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x2.png" xlink:type="simple"/></inline-formula>,<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x3.png" xlink:type="simple"/></inline-formula>. LAG’s public/private key pair:</p><fig id="fig1"  position="float"><label><xref ref-type="fig" rid="fig1">Figure 1</xref></label><caption><title> Centralized V2G model</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/78418x4.png"/></fig><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x5.png" xlink:type="simple"/></inline-formula>,<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x6.png" xlink:type="simple"/></inline-formula>. S is the system key, which is only known by TA.</p><p>c) TA issues certificate <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x7.png" xlink:type="simple"/></inline-formula> to EV, where<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x8.png" xlink:type="simple"/></inline-formula>.</p><p>2) EV joins the group</p><p>EV complete register at LAG, LAG distributes a group for EV, and generates group public key and private key of group member. More specifically, when EV wants to join to V2G network via ST, EV sends message “<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x9.png" xlink:type="simple"/></inline-formula>” to LAG, t is a timestamp. After verifying the validity of the certificate, LAG generate generates group public key and private key of group member according to the following steps.</p><p>a) LAG selects a generator:<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x10.png" xlink:type="simple"/></inline-formula>, and set<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x11.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x12.png" xlink:type="simple"/></inline-formula>is a calculation homomorphic mapping of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x13.png" xlink:type="simple"/></inline-formula> to<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x14.png" xlink:type="simple"/></inline-formula>.</p><p>b) LAG selects <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x15.png" xlink:type="simple"/></inline-formula> at random, and sets<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x16.png" xlink:type="simple"/></inline-formula>, and announces w.</p><p>c) <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x17.png" xlink:type="simple"/></inline-formula>selects <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x18.png" xlink:type="simple"/></inline-formula> as its secret at random, and then sends this <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x19.png" xlink:type="simple"/></inline-formula> to</p><p>TA after encrypting it with its private key. TA computes:<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x20.png" xlink:type="simple"/></inline-formula>,</p><p>(<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x21.png" xlink:type="simple"/></inline-formula>), and sends <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x22.png" xlink:type="simple"/></inline-formula> secretly to LAG.</p><p>The group public key is<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x23.png" xlink:type="simple"/></inline-formula>, each<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x24.png" xlink:type="simple"/></inline-formula>’s private key is <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x25.png" xlink:type="simple"/></inline-formula>. The revocation token corresponding to a<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x26.png" xlink:type="simple"/></inline-formula>’s key <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x27.png" xlink:type="simple"/></inline-formula> is<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x28.png" xlink:type="simple"/></inline-formula>. No party is allowed to possess<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x28.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x29.png" xlink:type="simple"/></inline-formula>, it is only known to LAG.</p><p>3) Signature computing</p><p>EV computes group signature of message M through the following steps:</p><p>a) Picking a random nonce<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x30.png" xlink:type="simple"/></inline-formula>, and computing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x31.png" xlink:type="simple"/></inline-formula></p><p>b) Computing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x32.png" xlink:type="simple"/></inline-formula></p><p>c) Selecting <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x33.png" xlink:type="simple"/></inline-formula> at random, and compute <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x34.png" xlink:type="simple"/></inline-formula></p><p>d) Setting <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x35.png" xlink:type="simple"/></inline-formula></p><p>e) Picking blinding values:<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x36.png" xlink:type="simple"/></inline-formula>, and compute<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x36.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x37.png" xlink:type="simple"/></inline-formula>, where</p><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x38.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x38.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x39.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x38.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x39.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x40.png" xlink:type="simple"/></inline-formula></p><p>f) Computing a challenge value <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x41.png" xlink:type="simple"/></inline-formula></p><p>g) Computing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x42.png" xlink:type="simple"/></inline-formula></p><p>h) Outputting signature<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x43.png" xlink:type="simple"/></inline-formula>, and EV sends <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x43.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x44.png" xlink:type="simple"/></inline-formula> to ST.</p><p>4) Signature verification</p><p>When receiving<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x45.png" xlink:type="simple"/></inline-formula>, ST<sub>i</sub> verifies the signiture according to the following steps:</p><p>a) Computing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x46.png" xlink:type="simple"/></inline-formula></p><p>b) Computing</p><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x47.png" xlink:type="simple"/></inline-formula>,</p><disp-formula id="scirp.78418-formula501"><graphic  xlink:href="http://html.scirp.org/file/78418x48.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.78418-formula502"><graphic  xlink:href="http://html.scirp.org/file/78418x49.png"  xlink:type="simple"/></disp-formula><p>c) Checking if the challenge c is correct.</p><disp-formula id="scirp.78418-formula503"><graphic  xlink:href="http://html.scirp.org/file/78418x50.png"  xlink:type="simple"/></disp-formula><p>If it is, the signature is verified, and ST<sub>i</sub> makes revocation check, i.e. for each element<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x51.png" xlink:type="simple"/></inline-formula>, ST<sub>i</sub> checks whether <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x52.png" xlink:type="simple"/></inline-formula> is encoded in<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x53.png" xlink:type="simple"/></inline-formula>, by <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x54.png" xlink:type="simple"/></inline-formula>. If no element of RL is encoded in<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x54.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x55.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x54.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x55.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x56.png" xlink:type="simple"/></inline-formula>has not been revoked.</p><p>The overall process is shown in <xref ref-type="fig" rid="fig2">Figure 2</xref>.</p></sec><sec id="s3_3"><title>3.3. Batch Authentication</title><p>Batch validation method can judge whether the signature collection contains invalid signature, thus reduce the verification time. When large-scale EVs connect to power grid, it is needed to use batch authentication to reduce verification time.</p><p>Let<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x57.png" xlink:type="simple"/></inline-formula>, after ST received collection of messages <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x57.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x58.png" xlink:type="simple"/></inline-formula> and signatures<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x57.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x58.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x59.png" xlink:type="simple"/></inline-formula>, it verifies the signature collection using batch authentication by</p><p>1) Computing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x60.png" xlink:type="simple"/></inline-formula></p><p>2) Checking<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x61.png" xlink:type="simple"/></inline-formula>, If equality holds, continue. Otherwise, return “false”;</p><p>3) Select n numbers (the length is b):<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x62.png" xlink:type="simple"/></inline-formula>, checking:</p><disp-formula id="scirp.78418-formula504"><graphic  xlink:href="http://html.scirp.org/file/78418x63.png"  xlink:type="simple"/></disp-formula><p>If it is, return “true”. Otherwise, return “false”.</p></sec></sec><sec id="s4"><title>4. Security Analysis</title><p>Firstly, LAG, TA or malicious EV cannot fake other entities to generate group signature, so this scheme has strong unforgeability. For example, suppose a malicious EV has forged a signature<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x64.png" xlink:type="simple"/></inline-formula>. However, ST will compute c’ and check whether c’ is equal to c signature scheme. If the signature is forged, it cannot pass the verification process.</p><fig id="fig2"  position="float"><label><xref ref-type="fig" rid="fig2">Figure 2</xref></label><caption><title> Vehicle to grid schematic diagram</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/78418x65.png"/></fig><p>Secondly, it is not feasible for other entities to determine the vehicle status according to the result of group signature. Other group members only know group public key<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x66.png" xlink:type="simple"/></inline-formula>, but they do not know private key <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x66.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/78418x67.png" xlink:type="simple"/></inline-formula> of each group member. Although everyone can verify each signature is generated by group member, they cannot confirm who is signer. And only LAG can open the signature to confirm the identity of the signer. So our scheme has strong anonymity, and it can ensure that the identity information of EV user cannot be leaked. So this scheme has the characteristics of anonymity.</p><p>Thirdly, due to the unforgeability of this group signature, only group members can generate valid group signature. Moreover, this scheme use Hash function, and it is not feasible that outside attackers want to get EV’s private key through collecting common parameters to compute inverse operation of Hash function. So, our scheme can resist outside attack and protect data security of EV users.</p></sec><sec id="s5"><title>5. Conclusion</title><p>This paper has proposed an anonymous group authentication scheme based on revocable group signature in view that EVs are frequently join and leave from ST, in which the signature scheme is dynamic, and EVs can dynamically join and withdraw. Algorithm overhead is essentially same with ordinary group signature algorithm. ST only need to add the vehicle information to revocation list RL when EV logs out ST, and other EVs can anonymously prove that they are not revocable group members. Besides, this scheme solves the problem that ST revocation management is complicated.</p></sec><sec id="s6"><title>Cite this paper</title><p>Sun, Z.W. (2017) An Anonymous Authentication Scheme for Vehicle-to-Grid Networks. Int. J. Communications, Network and System Sciences, 10, 316-323. https://doi.org/10.4236/ijcns.2017.108B034</p></sec></body><back><ref-list><title>References</title><ref id="scirp.78418-ref1"><label>1</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Wang</surname><given-names> X. </given-names></name>,<etal>et al</etal>. (<year>2011</year>)<article-title>The Bottleneck Problems and Countermeasures of Current EVs’ Development</article-title><source> Energy Technology Econo-my</source><volume> 23</volume>,<fpage> 1</fpage>-<lpage>5</lpage>.<pub-id pub-id-type="doi"></pub-id></mixed-citation></ref><ref id="scirp.78418-ref2"><label>2</label><mixed-citation publication-type="other" xlink:type="simple">Liu, X., Zhang, Q. and Cui, S. (2012) Vehicle to Grid Review. Transactions of China Electro-Technical Soci-ety, 27, 121-127.</mixed-citation></ref><ref id="scirp.78418-ref3"><label>3</label><mixed-citation publication-type="other" xlink:type="simple">Tseng, H.R. (2012) A Secure and Privacy-Preserving Communication Protocol for V2G Networks. IEEE Wireless Communications and Networking Conference (WCNC), Shanghai, 1-4 April 2012, 2706-2711.  
https://doi.org/10.1109/WCNC.2012.6214259</mixed-citation></ref><ref id="scirp.78418-ref4"><label>4</label><mixed-citation publication-type="other" xlink:type="simple">Yang, Z., Yu, S., Lou, W. and Liu, C. (2012) P2: Privacy-Preserving Communication and Precise Reward Architecture for V2G Networks in Smart Grid. IEEE Trans. Smart Grid, 2, 697-706. https://doi.org/10.1109/TSG.2011.2140343</mixed-citation></ref><ref id="scirp.78418-ref5"><label>5</label><mixed-citation publication-type="other" xlink:type="simple">He, M., Zhang, K. and Shen, X.M. (2014) PMQC: A Privacy-Preserving Multi-Quality Charging Scheme in V2G Network. IEEE Global Communications Conference, Austin, 8-12 December 2014, 675-680.  
https://doi.org/10.1109/GLOCOM.2014.7036885</mixed-citation></ref><ref id="scirp.78418-ref6"><label>6</label><mixed-citation publication-type="other" xlink:type="simple">Liu, H., Ning, H.S., Zhang, Y. and Yang, L.T. (2012) Aggregat-ed-Proofs Based Privacy Preserving Authentication for V2G Networks in the Smart Grid. IEEE Transactions on Smart Grid, 3, 1722-1733. https://doi.org/10.1109/TSG.2012.2212730</mixed-citation></ref><ref id="scirp.78418-ref7"><label>7</label><mixed-citation publication-type="other" xlink:type="simple">Guo, H., Wu, Y., Bao, F., Chen, H. and Ma, M. (2012) UBAPV2G: A Unique Batch Authentication Protocol for Vehicle-to-Grid Communications. IEEE Transactions on Smart Grid, 2, 707-714. https://doi.org/10.1109/TSG.2011.2168243</mixed-citation></ref><ref id="scirp.78418-ref8"><label>8</label><mixed-citation publication-type="other" xlink:type="simple">Liu, H., Ning, H.S., Zhang, Y. and Guizani, M. (2013) Battery Status-Aware Authentication Scheme for V2G Networks in Smart Grid. IEEE Transactions on Smart Grid, 4, 99-110. https://doi.org/10.1109/TSG.2012.2224387</mixed-citation></ref><ref id="scirp.78418-ref9"><label>9</label><mixed-citation publication-type="other" xlink:type="simple">Lu, Z., Lu, X. and Wang, W. (2010) Review and Evaluation of Security Threats on the Communication Networks in the Smart Grid. IEEE Military Communications Conference, Sa Jose Convention Center, CA, 31 October-3 November 2010, 1830- 1835. https://doi.org/10.1109/MILCOM.2010.5679551</mixed-citation></ref><ref id="scirp.78418-ref10"><label>10</label><mixed-citation publication-type="other" xlink:type="simple">McDaniel, P. (2009) McLaughlin S. Security and Privacy Challenges in the Smart Grid. IEEE Security &amp; Privacy Magazine, 7, 75-77.  
https://doi.org/10.1109/MSP.2009.76</mixed-citation></ref><ref id="scirp.78418-ref11"><label>11</label><mixed-citation publication-type="other" xlink:type="simple">Boneh, D., Boyen, X. and Shacham, H. (2004) Short Group Signatures. Proc. of Advances in Cryptology, Vol. 3152, Springer-Verlag, Berlin, 41-55.  
https://doi.org/10.1007/978-3-540-28628-8_3</mixed-citation></ref></ref-list></back></article>