Impact of Secrecy on Capacity in Large-Scale Wireless Networks

1. Impact of Secrecy on Capacity in Large-ScaleWireless Networks Jinbei Zhang, Luoyifu, Xinbing Wang Department of Electronic Engineering Shanghai Jiao Tong University Mar 15, 2012

2. Outline • Introduction • Motivations • Related works • Objectives • Network Model and Definition • Secrecy Capacity for Independent Eavesdroppers • Secrecy Capacity for Colluding Eavesdroppers • Discussion • Conclusion and Future Work Impact of Secrecy on Capacity in Large-Scale Wireless Networks

3. Motivations • Secrecy is a Major Concern in Wireless Networks. • Mobile Phone Wallet • Military networks • … Impact of Secrecy on Capacity in Large-Scale Wireless Networks

4. Related works – I/II • Properties of Secrecy Graph Cited From [5] Cited From [5] [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 Proc. IEEE ITA’11, California, USA, Feb. 2011. Impact of Secrecy on 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] Cited from [12] [16] Y. Liang, H. 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. Vasudevan, 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. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

6. Objectives • Several questions arise: • CSI information is difficult to obtain • Artificial noises also degrade legitimate receivers’ channels • Cost on capacity is quite large to utilize fading gain • What’s the upper bound of secrecy capacity? • What’s the impact of other network models? Impact of Secrecy on Capacity in Large-Scale Wireless Networks

7. Outline • Introduction • Network Model and Definition • Secrecy Capacity for Independent Eavesdroppers • Secrecy Capacity for Colluding Eavesdroppers • Discussion • Conclusion and Future Work Impact of Secrecy on Capacity in Large-Scale Wireless Networks

8. Network Model and Definition – I/II • Legitimate Nodes: • Self-interference cancelation[16] 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 Mobicom’10, Chicago, USA, Sept. 2010. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

9. Network Model and Definition – II/II • Network Model: • Extended networks • Static • Physical channel model where • Definition of secrecy capacity where Impact of Secrecy on 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 Impact of Secrecy on 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 Received Power where is the Euclidean distance between legitimate node t and node r and is the distance between legitimate node t and eavesdropper e. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

12. Independent Eavesdroppers Case 1: when and both greater 1, Impact of Secrecy on Capacity in Large-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 choosing and is a constant. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

14. Independent Eavesdroppers • Secrecy Capacity for Each Cell Theorem 1: For any legitimate transmitter-receiver pair which is spaced at a distance of d cells apart, there exists an , so that the receiver can receive at a rate of securely from the transmitter. Choose Impact of Secrecy on 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-node secrecy throughput under the existence of independent eavesdroppers is . Impact of Secrecy on Capacity in Large-Scale Wireless Networks

16. Independent Eavesdroppers • Optimality of Our Scheme 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 λ(n) is upper bounded by . [18] P. Gupta and P. Kumar, “The Capacity of Wireless Networks”, in IEEE Trans. Inform. Theory, Vol. 46, No. 2, pp. 388-404, Mar. 2000. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

17. Outline • Introduction • Network Model and Definition • Secrecy Capacity for Independent Eavesdroppers • Secrecy Capacity for Colluding Eavesdroppers • Lower Bound • Upper Bound • Discussion • Conclusion and Future Work Impact of Secrecy on Capacity in Large-Scale Wireless Networks

18. Colluding Eavesdroppers • Eavesdroppers 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 . Impact of Secrecy on Capacity in Large-Scale Wireless Networks

19. Colluding Eavesdroppers • Eavesdroppers Collude • Assume that each eavesdropper equipped with one antenna and different eavesdroppers can collude to decode the message. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

20. Colluding Eavesdroppers • 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 Impact of Secrecy on Capacity in Large-Scale Wireless Networks

21. Colluding Eavesdroppers • Lower Bound • Lemma 5: When the intensity of the eavesdroppers is for any constant β>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 intensity for any constant β>0, the per-node secrecy capacity is . Impact of Secrecy on Capacity in Large-Scale Wireless Networks

22. Colluding Eavesdroppers • Upper Bound Impact of Secrecy on Capacity in Large-Scale Wireless Networks

23. 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 Impact of Secrecy on Capacity in Large-Scale Wireless Networks

24. Outline • Introduction • Network Model and Definition • Secrecy Capacity for Independent Eavesdroppers • Secrecy Capacity for Colluding Eavesdroppers • Discussion • Conclusion and Future Work Impact of Secrecy on Capacity in Large-Scale Wireless Networks

25. 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. Penrose, “Random Geometric Graphs”, Oxford Univ. Press, Oxford, U.K., 2003. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

26. Discussions • Multicast Secrecy Capacity [24] X. Li, “Multicast Capacity of Wireless Ad Hoc Networks”, in IEEE/ACM Trans. Networking, Vol. 17, No. 3, pp. 950-961, 2009. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

27. Discussions • Secrecy Capacity in i.i.d Mobility Networks [19] M. J. Neely and E. Modiano, “Capacity and Delay Tradeoffs for Ad Hoc Mobile Networks”, in IEEE Trans. Inform. Theory, Vol. 51, No. 6, pp. 1917-1937, 2005.. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

28. Discussions • Secrecy Capacity under Random Walk Networks [30] A. Gamal, J. Mammen, B. Prabhakar, and D. Shah, “Throughput-delay trade-off in wireless networks”, In Proceeding of IEEE INFOCOM, Hong Kong, China, Mar. 2004. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

29. Outline • Introduction • Network Model and Definition • Secrecy Capacity for Independent Eavesdroppers • Secrecy Capacity for Colluding Eavesdroppers • Discussion • Conclusion and Future Work Impact of Secrecy on Capacity in Large-Scale Wireless Networks

30. Conclusions • In the non-colluding case, the optimal per-node secrecy capacity is achievable in the presence of eavesdroppers. • In the colluding case, we establish the relationship between the secrecy capacity and the tolerable number of eavesdroppers. More importantly, we first derive the upper bound for secrecy capacity which is achievable. • We identify the underlying interference model to capture the fundamental impact of secrecy constraints. This model relies weakly on the specific settings such as traffic pattern and mobility models of legitimate nodes. Hence, our study can be flexibly applied to more general cases and shed insights into the design and analysis of future wireless networks. Impact of Secrecy on Capacity in Large-Scale Wireless Networks

31. Future Work • Secrecy capacity under active attacks • The impact of dense networks • The impact of heterogeneity networks • The impact of social networks Impact of Secrecy on Capacity in Large-Scale Wireless Networks

32. Thank you !

33. Backup • Details on the Models of Legitimate nodes • Revolve on its own • Using 4 antennas Impact of Secrecy on Capacity in Large-Scale Wireless Networks