Physical Layer Security from Inter-Session Interference in Large Wireless Networks

Transcription

1 Physical Layer Security from Inter-Session Interference in Large Wireless Networks Azadeh Sheikholeslami, Dennis Goeckel, Hossein Pishro-Nik, Don Towsley University of Massachussets, Amherst

2 Outline 1. Motivation 2. Introduction 3. First scenario: Equal path-loss between all pairs of nodes 4. Second scenario: General case 5. Conclusion 2

3 Motivation Conventional way to achieve secrecy: Cryptography Computationally unlimited eavesdropper Breaking encryption system later Perfect Secrecy [Shannon]: Unconditional secrecy One time pad 3

4 Motivation Wiretap Channel [Wyner]: Eve s channel degraded with respect to Bob s channel General Wiretap channel: Bob s channel better than Eve s channel 4

5 Motivation Gaussian wiretap channel: C S = log 1 + γ M log(1 + γ E ) Choosing γ M < γ E ensures a positive secrecy capacity γ E so small that Eve s decoder can never recover the message Problems in wireless networks: Close eavesdropper Eavesdropper with unknown location or channel gain 5

6 Motivation Cooperative jamming: Jammer s signal in the null space of Bob s channel Degrades Eve s channel with high probability Drawbacks: Low power efficiency Power expended on artificial noise Low throughput Only one node can transmit at each time slot. The location and/or CSI of Eve is known. 6

7 Motivation 1. Can we do something more power efficient? 2. Can we achieve higher throughput? 3. Can we achieve secrecy without knowing the location and channel gain of the eavesdropper? 7

8 Introduction Multipath fading: Reflectors in the environment Receiver sees the superposition Rayleigh fading Fading gain has an Exponential distribution Fact: Y 1,, Y n be a sequence of n i.i.d. exponential r.v.s with parameter λ, max(y 1,, Y n ) log n λ as n a.s. 8

9 Introduction Large wireless network: Many system nodes Many eavesdroppers 9

10 Introduction Cooperative jamming + relay [Goeckel, et. al., JSAC 2011]: A source-destination pair choose a relay node with large gain to both The other helper nodes chatter 10

11 First Scenario Equal path loss between all pairs of nodes Outline of protocol 1: Relay selection Transmission from Sources to relays Transmission from Relays to destinations The interference of other transmitters hides each message Multiple nodes can transmit in each time slot 11

12 First Scenario Equal path loss between all pairs of nodes Theorem: For the proposed protocol, m(n) eavesdroppers can be tolerated (S D) guaranteeing P OUT 0, for each source S which transmits a message, (E) and P OUT 1 as n is: nlog(1+γe) 2et m n = o log n where n is the number of system nodes, γ E is the required SINR threshold at each eavesdropper, and t is a constant. 12

13 Second Scenario General case Extended network Multi-hop in Gupta-Kumar framework Secure communication between two adjacent cells Tessellate the active cell into square sub-cells: 13

14 Second Scenario General case Outline of protocol 2: Choose one relay with fading greater that log N A group of nodes transmit messages simultaneously The interference of other transmitters hides each message Multiple nodes can transmit in each time slot 14

15 Second Scenario General case Theorem: By applying the proposed protocol, m(n) eavesdroppers can be (S R) tolerated guaranteeing P OUT 0, for each source S which transmits (E) a message, and P OUT 1 as N is: Nlog(1+γE2 α) 8et m N = o log N where N is the number of nodes in each cell, γ E is the required SINR threshold at each eavesdropper, α is the path-loss exponent, and t is a constant. 15

16 Conclusion 1. Equal path-loss between all pairs of nodes: A protocol for two hop communication between a large number of source-destination pairs via one relay for each pair is proposed. 2. General case in an extended network: A multi-hop strategy in a Gupta-Kumar framework is considered. In contrast to other cooperative jamming schemes, all the energy is used to transmit messages. No extra energy required to obtain secrecy. A large number of nodes share the same bandwidth simultaneously and achieve a higher bandwidth efficiency. 16