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2.3 Intermediate step
Regarding the GPSR protocol, the best neighbor node is the nearest node to the destination. We modify this rule in GPSR and add a restriction for selecting the best neighbors based on the list of private keys. 2.3中间步骤 对于GPSR协议来说,最佳邻居节点是到目的地的最近的节点。我们在GPSR协议中修改这个规则, 并且基于私人密钥列表对选择最佳的邻居节点添加一个限制。 In other words, when node A finds the best neighbor B from its neighborhood table, the list of private keys of node A needs to be compared with the list of private keys of node B. Then, node B is selected as a next node if and only if at least one private key of node A and B is selected from the same matrix. If they have no similar matrices, node B is eliminated from the neighborhood table and this phase repeats again to find the best neighborhoods.

换句话说,当节点 A 从它的邻居节点表中找到最好的邻居节点 B 时,A 节点的私钥 列表需要和 B 节点的私钥列表进行比对。 然后,节点 B 将会被选择作为下一跳节点当且仅当节点 A 和 B 的至少一个私钥是 选自同一矩阵。 如果节点 A 和节点 B 没有相似的矩阵,那么节点 B 将从节点 A 的邻居节点列表中 移除,这个相位会继续重复以找到节点 A 最好的邻居节点。
where the list of private keys of node B is PrB and PrA is the list of private keys of node A.

2.3.1 Shared key generation phase When the best neighbor is selected, the node needs a shared key to communicate with its neighbors securely. The shared key is created for each pair of two nodes that have a private key from the same matrix Pi. For example, if nodes i and j have a key form matrix P1, the shared key can be calculated by: 2.3.1 共享密钥生成阶段 当最好的邻居节点被选中时,该节点需要一个共享的密钥来安全地与它的邻居节点 进行通信。 对于每一对拥有来自同一矩阵 Pi 的私有密钥的两个节点,共享密钥都会被创建。 例如,如果节点 i 和节点 j 有一个来自矩阵 P1 的密钥,那么节点 i 和节点 j 之间的 共享密钥可以通过下式进行计算: 11 月 9 日翻译至此

We have mentioned it earlier that Pr is symmetric matrix,

我们已经提到过它公关是对称矩阵,

Then, the result of P1 _ kP is a symmetric matrix with size N × N in which SKij = SKji is the shared key between nodes i and j. 然后,结果 P1 * kP 是一个大小为N × N的对称矩阵,在这个矩阵中

SKij ? SKji ,并且它们是节点i和节点j之间的共享密钥。
After generating the shared secret key, the packet and the selected index are sent to the best neighbor by using the shared key. 当产生共享密钥后,数据包和选定的索引通过使用共享密钥被送到最好 的邻居节点。 It is important to mention that we assume our network is completely dense and each node has at least one neighbor with the same specification.
在此有必要提到的是,我们假设我们的网络是完全致密的,并且每个节点至少有一 个具有相同规格的邻居节点。
2.3.2 Verification phase When the packet is received by the best neighbor (for example node B), this node extracts the index from the packet and regenerate the shared key. 2.3.2 验证阶段 当数据包被最佳邻居节点(例如节点B)接收后,那么该节点将从数据包中提取索引,并且再生共享 密钥。 Then, node B creates an ACK message, signs it by using a shared key, and sends it to node A. 然后,节点B创建一个ACK消息,通过使用共享的密钥将该消息进行标记,并将其发送给节点A。 If the ACK message is verified by node A, node B is a trusted node, otherwise node B is a malicious node. 如果这个ACK消息通过了节点A的验证,那么节点B就被认为是一个可受信任的节点,否则节点B被 认为是一个恶意节点。 Therefore, Node A generates an alarm message and broadcast to the network that the node for eliminating the malicious node from their neighborhood tables. 因此,节点A将产生一个报警信息,并向网络进行广播,告知网络中其它节点应该从他们的邻居表

中消除该恶意节点。

2.4 Destination Step When a packet is received by the destination node, the probability of wormhole attack happening is checked based on the distance between source node to the destination node and the number of hops from source to destination. A necessary condition for detecting wormhole in destination node is:

2.4 目标步 当数据包被目标节点接收后,根据源节点到目的节点之间的距离和源节 点到目的节点之间的跳数,虫洞攻击发生的概率可以被测算到。用于检 测目标节点的虫洞的必要条件是:
where the location of the source node is (xs, ys), (xd, yd) is the location of the destination, R is the radio range of nodes, number of hops from source to destination is shown by h. When the wormhole is detected, a request packet is sent to source node in order to send a packet again from another path. 上式中,

?x s , ys ? 是源节点的位置, ?xd , yd ? 是目的节点的位置。R

是节

点的无线广播范围半径,从源节点到目的节点的跳数由 h 显示。当检测 到该虫洞时,一个请求数据包将被发送到源节点,以便源节点从另一个 路径中再次发送一个数据包给目的节点。

3.1 Miss detection probability analysis 3.1 漏误检测概率分析 Miss detection probability is a crucial metric to evaluate wormhole detection methods. 漏误检测概率是评价虫洞检测方法的一个重要指标。

According to key distribution of this method, there are y potential private keys for N sensor nodes in the network and each sensor node randomly selects α private keys ( α≤y ). 根据该方法的主要分布, 在网络中的 N 个传感器节点中有 y 个 潜在的私人密钥,并且每个传感器节点随机选择 α 个私人密钥 (α≤y)。

Therefore, the probability of a specific key belonging to one node is equal to bay c while the malicious nodes do not have a private key.
?? 因此,一个特定的密钥属于一个节点的概率是等于 ? ? ? ,而恶
?y?

意节点没有一个私人密钥。

If the adversary is able to compromise x nodes, the probability that just m nodes from x nodes (m ≤ x ≤ N) contain the specific key

( Ki ) from y potential private keys is computed by:
如果对手能够向 x 节点妥协, 仅仅是 m 节点从 x 节点(m ≤ x ≤

N) 包

含从潜在的私人密钥 y 的概率可以通过下面公式计算:

Therefore, the probability of breaking one link by an adversary is calculated in below formula: 因此, 被对手打破一个链接的概率可以通过下面的公式来计算:

Where x is the number of compromised nodes, numbers of selected nodes are shown by m, y is the number of potential private keys and α is equal to the number of private keys for each node.

其中,x 是妥协节点的数目,选定的节点的数目由 m 表示,y 是潜在私人密钥的数,α 是每个节 点的私钥数目

To create a wormhole in geographic routing protocol necessitates two or more malicious nodes to receive packets at one point of the network and forward those packets to another location by a wireless or wired tunnel.

在地理路由协议中创建一个“虫洞”,需要 2 个或多个恶意节点在网络的一个节点处接收这些 数据包,并且通过无线或有线通道将这些数据包转发到另一个位置。

Therefore, as shown in Fig. 8, the adversary needs to break more than 1 link to create the wormhole attack in the network. 因此,如图 8 所示,对手需要突破 1 个以上的链接来创建网络中的“虫孔”攻击。

Figure 8. Creating wormhole by breaking two link in geographic routing protocols.
图 8 在地理路由协议中通过断开链接来创建虫洞 If there are h hops from source node to destination, the adversary needs to break j link (j < h) to create wormhole attack. Then, the probability of creating wormholes by the attacker is: 如果有从源节点到目的地的跳数为 h,对手需要打破 j 条链路(j < k),以创建虫洞攻击。 那么,由攻击者创建虫洞的概率为:

where h = the number of hops, j = the number of broken links, x = the number of compromised nods, α indicates the number of private keys for each node and y is the number of potential private Keys. 此处,h 为跳数,j 为断开链接的数目,x 为妥协节点的数目,α 表示每个节点的私钥数量,而 y 为潜在私人秘钥的数目。 (11 月 4 日翻译至此) Fig. 9 shows the probability of a broken link where the number of potential private keys is 6 (y = 6), the number of private keys is 3, 4, or 5 (α = 3, 4, or 5), the maximum number of compromised nodes is 100 (x = 100) and the number of hops from source to destination node is equal to 10 (h = 10). 图 9 显示了一个断开连接的概率情况,其中潜在的私钥的数目是 6(y= 6),

私有密钥的数量是 3,4,或 5(α= 3,4,或 5),妥协节点的最大数目为 100(x= 100),从 源到目的节点的跳数等于 10(h=10)。

It can be seen that when the amount of compromised nodes are less than 55, the attacker cannot break the link, but with the increase of the number of compromised nodes, the probability of broken link is increasing too till the number of compromised node is equal to 70 and the attacker can break the link. 可以看出,当妥协节点的数量少于 55 时,攻击者无法打破连接,但是,随着妥协节点数量的增 多,断开链接的概率也越来越高,直到直到被损害的节点的数目等于 70 为止,此时攻击者可以 打破连接。

Fig. 9 also shows that when the number of compromised nodes is less than 55 or more than 65, the adversary cannot create the wormhole attack otherwise the maximum rate of miss detection wormhole is about 0.3 when the number of compromised nodes is from 55 to 65 (S1 Table). 图 9 还表明,当被损害的节点的数目是小于 55 或超过 65 时,对手无法创建“虫洞攻击”。 否则当损害的节点的数目是从 55 到 65(S1 表)时,误检虫洞的最大速率约为 0.3。

图 9 在 y = 6 和(3、4 或 5)时,断开连接的概率 图 10 y=6(α=3、4 或 5)时的误检率 In Fig. 10, the comparison of the probability of miss detection is illustrated when the number of private keys is 3, 4, or 5 (α = 3, 4, or 5) and the number of hops from source to destination node is equal to 10 (h = 10). As it is shown, our method is able to detect almost all wormhole attacks (S2 Table). 在图 10,对误检率的比较说明,当私钥数目为 3、4 或 5(α=3、4、或 5)时,从源节点到目的 节点的跳数等于 10(h=10)。正如它所示,我们的方法是能够检测到几乎所有的虫洞攻击(S2 表)。

3.2 Simulation Setup

3.2 仿真设置 We use simulator NS-2 to evaluate the performance of our scheme for detecting wormhole attack in geographic routing protocols. 我们使用模拟器 NS-2 去评估在地理路由协议中我们用于检测虫洞攻击的计划的性能。 We deploy 200 nodes randomly in a square area of size 1000 *1000 平方米 square area with multiple holes inside. 我们将 200 个节点随机部署在一个面积为 1000*1000 平方米的正方形区域的多个洞里面。

The transmission range of each node is set to 150 m. The number of malicious nodes is considered between 2 to 10 nodes, which can change their location to create the wormhole attack. 每个节点的传输范围被设置为 150 米。恶意节点数目被认为是 2 到 10 个节点之间,这些恶意节 点可以改变自己的位置,以创建“虫洞”攻击。

We implement the GPSR routing protocol and then improve the structure of beacon and neighborhood table based on our method. 我们实现了 GPSR 路由协议,然后基于我们的方法,改善了信标结构和邻域表。

Each node broadcasts the beacon packets periodically with a nominal interval of 0.3 seconds to update its neighborhood table. 每个节点定期广播信标数据包,并以 0.3 秒的时间间隔更新其邻域表。 We present our results after averaging of 100 simulation runs. All simulation parameters are shown in the Table 1. 平均每 100 个模拟运行后,我们发布一次结果。所有的仿真参数如表 1 所示。 (11 月 5 日翻译至此) Before simulating our method, the impact of wormhole attacks on geographic routing protocols is illustrated in Fig. 11.

在模拟我们的方法之前,图 11 中已说明了网络攻击对地理路由协议的影响。

We transfer 1250 packets within 20 hops and monitor the network to find the number of packets that are sent through the malicious nodes, are called untrusted packets. 我们在 20 个跳数内传输 1250 个数据包并且监控这个网络以找到那些通过恶意节点发送的被称 为不受信任的数据包的数量。 As it is clear, the wormhole attack is capable of transferring nearly 60% of the packets. Since the malicious nodes are able to change or drop the packets, it is necessary to protect this network against wormhole attack (S3 Table). 因为它是透明的,所以该虫洞攻击是能够传输近 60%的数据包的。由于恶意节点能够改变或放 弃这些数据包,所以有必要保护这个网络免受虫洞攻击(S3 表)。

表 1 仿真参数 仿真参数 路由协议 节点数目 传输范围 恶意节点数 数据包大小(字节) 交通类型 停顿时间 运动模型 值 GPSR 200 150 米 2—10 512 CBR 50 秒 随机路点

虫洞数目 模拟区域(平方米)

1—5 1000 * 1000

Figure 11. The effect of wormhole attack on geographic routing protocols

图 11 虫洞攻击对地理路由协议的影响
3.2.1 Wormhole detection rate 3.2.1虫洞检测率 The wormhole detection rate is defined as the ratio of the number of detected wormhole over the total number of attacks by the adversaries in the network. 虫洞检测率被定义为被检测到的虫洞攻击的数目和网络中的敌人发动攻击的总数的比值。 Fig. 12 plots the wormhole detection rate versus the tunnel length. We randomly place one wormhole in the network in each run. 图12展示了检测率随着隧道长度的变化而发生变化的情况。我们在每一次运行中在网络中随机放置 一个虫洞。 It can be seen that our scheme (DWGRP) is able to detect all wormhole attacks (100%). However, the rate of wormhole detection in ANS method is approximately 80 percent. 可以看出,我们的方案(DWGRP)能够检测到几乎所有的虫洞攻击(100%)。 然而,在ANS方法中的虫洞检测率约百分之80。 RRS method has the minimum rate of wormhole detection which is about 50 percent when the length of the tunnel reaches to 10. RRS法虫洞检测率最低的时候是当隧道的长度达到10时,此时大约只有50%。 Generally, the performance of the DWGRP method to detect the wormhole attack is satisfactory and better than the other methods (S4 Table).

总体来说,DWGRP 方法对于检测虫洞攻击的表现是令人满意的,并且和其它方法比起来也较好一
些(S4 表)。 Then, we compare the rate of wormhole detection for our scheme (DWGRP) with WHOP [56] and WDI [57]. We simulate the WHOP and WDI methods on GPSR protocols to compare their performance. 然后,对于虫洞检测率我们就我们的方案和WHOP [56] 和 WDI [57]做一些比较。我们在GPRS协议 上对WHOP和WDI方法进行模拟,来对它们的性能进行比较。 As it is shown in Fig. 13, the wormhole detection rate in WDI method has a slightly downward trend in which by increasing the tunnel length, the detection rate decreases from 90% to 70%. In WHOP scheme, the detection rate rises up to nearly 85% when the number of hops approaches 10. 如图13所示, 通过增加隧道长度, WDI方法的虫洞检测率略有下降趋势, 从90%下降到70%。 在WHOP 方案中,当节点间跳数接近10时,检测率上升到近85%。 Since the DWGRP scheme is able to detect 100% of wormhole attacks, the performance of our scheme is

better than WHOP and WDI in geographic routing protocols (S5 Table). 由于DWGRP方案能够100%的检测到虫洞攻击,所以在地理路由协议中我们的方案的性能是优于 WHOP和WDI的。(S5表)。
Figure 12. Wormhole detection rate against different tunnel length. 图12 不同隧道长度的虫洞检测率 Figure 13. Wormhole detection rate versus tunnel length in WDI, WHOP and DWGRP 图13 WDI, WHOP和DWGRP三种方案下不同隧道长度对应的虫洞检测率 Figure 14. The rate of re-send packets against different tunnel length. 图14 对应不同隧道长度重新发送数据包的速率。

3.2.2 Resend packet rate 3.2.2重发数据包率 If a wormhole attack is detected by the sink in our scheme, this packet will be eliminated and the packet will be re-sent. 在我们的方案中如果接收器检测到一个“虫洞攻击”,那么该数据包将被淘汰,并将重新发送该数 据包。 The ratio of the number of re-send packets over the total number of packets from source to destination is defined as the rate of re-send packets. 从源节点到目的节点需要重新发送的数据包的数目和所发送数据包的总数目的比值被定义为重发数 据包率。 Therefore, by increasing the rate of re-send packets, the rate of wasted energy is increased in the network. 作为结果,随着重发数据包率的增加,网络能量的浪费也会增加。 Fig. 14 shows the rate of re-send packets against different tunnel lengths for DWGRP, ANS and RRS. 图14显示的是三种不同方案DWGRP, ANS和RRS时,不同的隧道长度所对应的数据包重发率。 The rate of re-send packets in our scheme is zero when the tunnel length is less than 7. 在我们的方案中,当隧道长度不超过7时,重发数据包率为零。 When the tunnel length reaches to 10, less than 5 percent of packets need to be re-sent in DWGRP because the attacker cannot break the link in the network. 当隧道长度达到10时,在DWGRP方法中也只有不到5%的数据包需要重新发送,因为此时攻击者还 无法打破网络中的连接。 However, approximately 15 percent of packets which arrive to the sink will be re-sent in ANS method when the tunnel length is equal to 10. 然而作为对比,当隧道长度等于10时,在ANS方案中,已经有大约15%的数据包在到达汇聚节点后 依然需要重新发送。 In the RRS scheme, the sink node cannot detect the wormhole attack and request re-sending packets. Therefore, this rate is zero for RRS (S6 Table).
而在RRS方案中, 汇聚节点根本无法检测到虫洞攻击, 也不能请求重新发送数据包。 因此, RRS的重发数据包基本上为零 (S6 表)。

(11 月 7 日翻译至此)

4 Conclusion 4结论
Wormhole attack is recognized as a severe threat to wireless sensor networks and geographic routing protocols. 虫洞攻击被认为是对无线传感器网络和地理路由协议的一个严重威胁。 Detection of wormhole attack is difficult because such attacks appear in various modes. 在各种模式下,这种攻击是很难检测到的。 In this paper we categorize the wormhole attacks based on their characteristics and impact on different routing protocols. 在本文中我们根据其特点及对不同路由协议的影响对各种虫洞攻击进行分类。 Then, we present a novel detection method of wormhole attacks in geographic routing protocols by improving the pairwise key pre-distribution scheme based on the beacon packets. 然后,在地理路由协议中我们通过改进基于信标数据包的成对密钥预分配方案,从而提出一种新的 关于虫洞攻击的检测方法。 Our scheme has the capability to detect the malicious nodes before receiving the message. 我们的方案有能力在收到消息之前检测到恶意节点。 The proposed scheme does not need any special hardware devices and additional assumptions, such as network synchronization, special guard nodes, or unit disk communication model. 我们的建议方案不需要任何特殊的硬件设备和附加假设条件,诸如网络同步,特殊保护节点,以及 单元磁盘通信模型等。 Simulation results and analytical modeling show that DWGRP approach achieves superior performance and applicability with the minimum restrictions compared with the related works in geographic routing protocols or wireless sensor networks. 仿真结果和分析模型显示DWGRP方法在地理路由协议或无线传感器网络中和其他相关方案相比, 实 现了优越的性能,适用性也有了最低的限制。 For the future work, we intend to improve this method by modifying the pairwise key pre-distribution scheme to detect all malicious nodes. We will also improve our method to prevent the Sybil attack. 对于未来的工作,我们打算通过修改成对密钥预分配方案来改进这种方法以便能够检测所有的恶意 节点。我们也将提高我们的方法来防止Sybil攻击。

(11 月 8 日翻译至此)

Supporting Information

S1 Table. Probability of breaking in different scenarios. (XLSX) S2 Table. Probability of miss detection in different scenarios. (XLSX) S3 Table. The effect of wormhole attack on geographic routing protocols. (XLSX) S4 Table. Comparison of wormhole detection rate in ANS, RRS, and the proposed method based on length of tunnel. (XLSX) S5 Table. Comparison of wormhole detection rate in WDI, WHOP and the proposed method based on length of tunnel. (XLSX) S6 Table. Comparison of re-send packets in traditional and the proposed method based on length of tunnel. (XLSX) 支持信息 S1表 在不同的场景下连接被打破的概率 (XLSX) S2表 不同场景下的误检率 (XLSX) S3表 虫洞攻击对地理路由协议的影响 S4表 基于隧道长度的条件下,本文所提出的方法和ANS、RSS在虫洞检测率方面的比较 S5表 基于隧道长度的条件下,本文所提出的方案和WDI、WHOP在虫洞检测率方面的比较 S6表 基于隧道长度的条件下,本文所提出的方案和传统的方法在重发数据包方面的比较

Acknowledgments
This work was carried out as part of the Mobile Cloud Computing research project funded by the Malaysian Ministry of Higher Education under the University of Malaya High Impact Research Grant, reference number UM.C/HIR/MOHE/FCSIT/03. 致谢 这项工作是作为移动云计算研究项目的一部分的,该项目是由马来西亚高等教育部下的马来亚大学 高影响研究计划资助的,参考号码UM.C/HIR/MOHE/FCSIT/03。 This work was partly supported by the National Natural Science Foundation of China under Grant no. 61300220 and NSFC project 61371098. 这项工作也得到了中国国家自然科学基金的部分资助,资助金编号:61300220,国家自然科学基金 项目编号61371098。

Author Contributions

Conceived and designed the experiments: AG MKK MS. Performed the experiments: MS XL XW. AG AA. Analyzed the data: AS ME MS MKK. Contributed reagents/materials/analysis tools: Wrote the paper: MS. 作者贡献 构思和设计的实验:AG MKK MS 进行实验:MS XL XW 数据分析:AS ME MS MKK 贡献试剂/材料/分析工具:AG AA。 写的论文:MS

(11 月 8 日翻译完毕,开始翻译前面唐某部分)


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