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

3
Motivations

• Secrecy is a Major Concern in Wireless Networks.
  
• Mobile Phone Wallet
• Military 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 ITA11, California, USA,
Feb. 2011.
5
Related works II/II

• Secrecy Capacity in large-scale networks,
• Mobile Networks 16
• Guard Zone 13
• Artificial NoiseFading 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.
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
• Whats the upper bound of secrecy capacity?
• Whats the impact of other network models?

7
Outline

• Introduction
• Network Model and Definition
• Secrecy Capacity for Independent Eavesdroppers
• Secrecy Capacity for Colluding Eavesdroppers
• Discussion
• Conclusion and Future Work

8
Network Model and Definition I/II

• Legitimate Nodes
• Self-interference cancelation16 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, USA, Sept. 2010.
9
Network Model and Definition II/II

• Network Model
• Extended networks
• Static
• Physical channel model

where

• Definition of secrecy capacity

where
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

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.
12
Independent Eavesdroppers
Case 1 when and both greater 1,
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.
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
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 .
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 ?(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.
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

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 .

19
Colluding Eavesdroppers

• Eavesdroppers Collude
• Assume that each eavesdropper equipped with one
  antenna and different eavesdroppers can collude
  to decode the message.

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

21
Colluding Eavesdroppers

• Lower Bound
• Lemma 5 When the intensity of the eavesdroppers
  is for any constant ßgt0,
  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 ßgt0, the
  per-node secrecy capacity is .

22
Colluding Eavesdroppers

• Upper Bound

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

24
Outline

• Introduction
• Network Model and Definition
• Secrecy Capacity for Independent Eavesdroppers
• Secrecy Capacity for Colluding Eavesdroppers
• Discussion
• Conclusion and Future Work

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.
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.
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..
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.
29
Outline

• Introduction
• Network Model and Definition
• Secrecy Capacity for Independent Eavesdroppers
• Secrecy Capacity for Colluding Eavesdroppers
• Discussion
• Conclusion and Future Work

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.

31
Future Work

• Secrecy capacity under active attacks
• The impact of dense networks
• The impact of heterogeneity networks
• The impact of social networks

32
Thank you !
33
Backup

• Details on the Models of Legitimate nodes
• Revolve on its own
• Using 4 antennas