1、Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,Jinbei Zhang, Luoyifu, Xinbing Wang Department of Electronic Engineering Shanghai Jiao Tong University Aug. 13, 2013,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,2,Outline,Introduction Motivations Re
2、lated works Objectives Network Model and Definition Secrecy Capacity for Independent Eavesdroppers Secrecy Capacity for Colluding Eavesdroppers Discussion Conclusion and Future Work,3,Motivations,Secrecy is a Major Concern in Wireless Networks. Mobile Phone Wallet Military networks ,Asymptotic Analy
3、sis on Secrecy Capacity in Large-Scale Wireless Networks,4,Related works I/II,Properties of Secrecy Graph,4 M. Haenggi, “The Secrecy Graph and Some of Its Properties”, in Proc. IEEE ISIT, Toronto, Canada, July 2008. 5 P. C. Pinto, J. Barros, M. Z. Win, “Wireless Secrecy in Large-Scale Networks.” in
4、Proc. IEEE ITA11, California, USA, Feb. 2011.,Cited From 5,Cited From 5,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,5,Related works II/II,Secrecy Capacity in large-scale networks, Mobile Networks 16 Guard Zone 13 Artificial Noise+Fading Gain(CSI needed) 12,16 Y. Liang, H
5、. V. Poor and L. Ying, “Secrecy Throughput of MANETs under Passive and Active Attacks”, in IEEE Trans. Inform. Theory, Vol. 57, No. 10, Oct. 2011. 13 O. Koyluoglu, E. Koksal, E. Gammel, “On Secrecy Capacity Scaling in Wireless Networks”, submitted to IEEE Trans. Inform. Theory, Apr. 2010. 12 S. Vasu
6、devan, D. Goeckel and D. Towsley, “Security-capacity Trade-off in Large Wireless Networks using Keyless Secrecy”, in Proc. ACM MobiHoc, Chicago, Illinois, USA, Sept. 2010.,Cited from 12,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,6,Objectives,Several questions arise: CSI
7、 information is difficult to obtainArtificial noises also degrade legitimate receivers channelsCost on capacity is quite large to utilize fading gain How to effectively improve the secrecy capacity?,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,7,Outline,Introduction Netwo
8、rk Model and Definition Secrecy Capacity for Independent Eavesdroppers Secrecy Capacity for Colluding Eavesdroppers Discussion Conclusion and Future Work,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,8,Network Model and Definition I/II,Legitimate Nodes: Self-interference c
9、ancelation16 adopted 3 antennas per-node CSI information unknown Eavesdroppers: Location positions unknown CSI information unknown,Cited from 17,17 J. I. Choiy, M. Jainy, K. Srinivasany, P. Levis and S. Katti, “Achieving Single Channel, Full Duplex Wireless Communication”, in ACM Mobicom10, Chicago,
10、 USA, Sept. 2010.,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,9,Network Model and Definition II/II,Network Model: Extended networks: n nodes randomly distributed in a network with size n. Static Physical channel model,where,Definition of secrecy capacity,where,Asymptotic
11、 Analysis on Secrecy Capacity in Large-Scale Wireless Networks,10,Outline,Introduction Network Model and Definition Secrecy Capacity for Independent Eavesdroppers Lower Bound Upper Bound Secrecy Capacity for Colluding Eavesdroppers Discussion Conclusion and Future Work,Asymptotic Analysis on Secrecy
12、 Capacity in Large-Scale Wireless Networks,11,Independent Eavesdroppers,Capacity for Eavesdroppers,Lemma 1: When a legitimate node t is transmitting to a legitimate receiver r, the maximum rate that an independent eavesdropper e can obtain is upper-bounded by,where is the Euclidean distance between
13、legitimate node t and node r and is the distance between legitimate node t and eavesdropper e.,Received Power,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,12,Independent Eavesdroppers,Case 1: when and both greater 1,Case 2-4:,Asymptotic Analysis on Secrecy Capacity in Lar
14、ge-Scale Wireless Networks,13,Independent Eavesdroppers,Capacity for Legitimate Nodes,Lemma 2: When a legitimate node t is transmitting to a legitimate receiver which is located d cells apart, the minimum rate that the legitimate node can receive is lower-bounded by , where is a constant.,when choos
15、ing and is a constant.,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,14,Independent Eavesdroppers,Secrecy Capacity for Each Cell,Choose,Theorem 1: For any legitimate transmitter-receiver pair which is spaced at a distance of d cells apart, there exists an , so that the rec
16、eiver can receive at a rate of securely from the transmitter.,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,15,Independent Eavesdroppers,Highway System Draining Phase Highway Phase Delivery Phase,Theorem 2: With n legitimate nodes poisson distributed, the achievable per-no
17、de secrecy throughput under the existence of independent eavesdroppers is .,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,16,Independent Eavesdroppers,Optimality of Our Scheme,18 P. Gupta and P. Kumar, “The Capacity of Wireless Networks”, in IEEE Trans. Inform. Theory, Vol
18、. 46, No. 2, pp. 388-404, Mar. 2000.,Theorem 2: When n nodes is identically and randomly located in a wireless network and source-destination pairs are randomly chosen, the per-node throughput (n) is upper bounded by .,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,17,Outli
19、ne,Introduction Network Model and Definition Secrecy Capacity for Independent Eavesdroppers Secrecy Capacity for Colluding Eavesdroppers Lower Bound Upper Bound Discussion Conclusion and Future Work,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,18,Colluding Eavesdroppers,E
20、avesdroppers Collude Assume that the eavesdropper can employ maximum ratio combining to maximize the SINR which means that the correlation across the antennas is ignored. Theorem 4: If eavesdroppers are equipped with A(n) antennas, the per-node secrecy capacity is .,Asymptotic Analysis on Secrecy Ca
21、pacity in Large-Scale Wireless Networks,1,Colluding Eavesdroppers,Eavesdroppers Collude Assume that each eavesdropper equipped with one antenna and different eavesdroppers can collude to decode the message.,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,20,Colluding Eavesdr
22、oppers,Lower Bound Theorem 5: Consider the wireless network B where legitimate nodes and eavesdroppers are independent poisson distributed with parameter 1 and respectively, the per-node secrecy capacity is,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,21,Colluding Eavesdr
23、oppers,Lower Bound Lemma 5: When the intensity of the eavesdroppers is for any constant 0, partitioning the network into disjoint regions with constant size c and denoting by the number of nodes inside region i, we have where Theorem 6: If eavesdroppers are poisson-distributed in the network with in
24、tensity for any constant 0, the per-node secrecy capacity is .,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,22,Colluding Eavesdroppers,Upper Bound,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,23,Colluding Eavesdroppers,Upper Bound,Asymptotic An
25、alysis on Secrecy Capacity in Large-Scale Wireless Networks,24,Colluding Eavesdroppers,Upper Bound Theorem 7: Consider the wireless network B where legitimate nodes and eavesdroppers are independent poisson distributed with parameter 1 and respectively, the per-node secrecy capacity is,Asymptotic An
26、alysis on Secrecy Capacity in Large-Scale Wireless Networks,25,Outline,Introduction Network Model and Definition Secrecy Capacity for Independent Eavesdroppers Secrecy Capacity for Colluding Eavesdroppers Discussion Conclusion and Future Work,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wi
27、reless Networks,26,Discussions,Secrecy Capacity in Random Networks Random networks: total node number is given Poisson networks: node numbers in different regions are independent When n goes to infinity, they are the same in the sense of probability Our results still hold in random networks,27 M. Pe
28、nrose, “Random Geometric Graphs”, Oxford Univ. Press, Oxford, U.K., 2003.,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,27,Discussions,Multicast Secrecy Capacity Corollary 1. Assume that legitimate nodes and eavesdroppersare independent poisson distributed with parameter 1
29、 and respectively. For each legitimate node, k 1 nodes are randomly chosen as its destinations. For independent eavesdroppers case, the aggregated multicast secrecy is when and is when .,24 X. Li, “Multicast Capacity of Wireless Ad Hoc Networks”, in IEEE/ACM Trans. Networking, Vol. 17, No. 3, pp. 95
30、0-961, 2009.,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,28,Discussions,Secrecy Capacity in i.i.d Mobility Networks Corollary 2. Consider a cell-partitioned network under thetwo-hop relay algorithm proposed in 19, and assume thatnodes change cells i.i.d. and uniformly ov
31、er each cell everytimeslot. For independent eavesdroppers case, the per-nodesecrecy capacity is and the corresponding delay is For colluding case, the per-node secrecy capacity isand the corresponding delay is .,19 M. J. Neely and E. Modiano, “Capacity and Delay Tradeoffs for Ad Hoc Mobile Networks”
32、, in IEEE Trans. Inform. Theory, Vol. 51, No. 6, pp. 1917-1937, 2005,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,29,Discussions,Secrecy Capacity under Random Walk Networks Corollary 3. Under random walk mobility model, nodes canonly move to adjacent cells every timeslot.
33、 For independenteavesdroppers case, the per-node secrecy capacity is and the corresponding delay is . For colludingcase, the per-node secrecy capacity is and the corresponding delay is .,30 A. Gamal, J. Mammen, B. Prabhakar, and D. Shah, “Throughput-delay trade-off in wireless networks”, In Proceedi
34、ng of IEEE INFOCOM, Hong Kong, China, Mar. 2004.,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,30,Outline,Introduction Network Model and Definition Secrecy Capacity for Independent Eavesdroppers Secrecy Capacity for Colluding Eavesdroppers Discussion Conclusion and Future
35、Work,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,31,Conclusions,We derive the upper bound for secrecy capacity in large-scale wireless networks by capturing the underling SINR relationship of eavesdroppers and legitimate nodes.The proposed scheme is order optimal for bot
36、h the independent eavesdroppers and the colluding case.Our model relies weakly on the specific settings such as traffic pattern and mobility models of legitimate nodes and can be flexibly applied to more general cases and shed insights into the design and analysis of future wireless networks.,Asympt
37、otic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,32,Future Work,Secrecy capacity under active attacksThe impact of heterogeneity networksThe impact of dense networks and CR networks,Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks,Thank you !,34,Backup,Revolve on its ownUsing 4 antennas,Impact of Secrecy on Capacity in Large-Scale Wireless Networks,
