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Adversarial Models for Wireless Communication

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Andrea W. RichaArizona State University

SIROCCO'13, Andrea Richa

Channel availability hard to model:

- Mobility
- Packet injection
- Temporary Obstacles
- Background noise
- Physical Interference
- Co-existing networks
- Jammer

SIROCCO'13, Andrea Richa

- A physical jammerlistens to the open medium and broadcasts in the same frequency band as network
- can lead to significant disruption of communication at low cost for the jammer

jammer

honest nodes

SIROCCO'13, Andrea Richa

Channel availability hard to model:

- Mobility
- Packet injection
- Temporary Obstacles
- Background noise
- Physical Interference
- Co-existing networks
- Jammer

all contribute to some form of “background noise”

SIROCCO'13, Andrea Richa

Ideal world:

Usual approach adopted in theory.

: noise level

Background noise

0

time

SIROCCO'13, Andrea Richa

Ideal world:

OR

Usual approach adopted in theory.

: noise level

Background noise

0

time

SIROCCO'13, Andrea Richa

Ideal world:

OR (bounded, predictable)

Usual approach adopted in theory.

: noise level

Background noise

0

time

SIROCCO'13, Andrea Richa

: noise level

Real world:

How to model this???

background

noise

0

time

SIROCCO'13, Andrea Richa

X

X

X

Background noise (microwave, radio signal, etc.)

Intentional jammer

Temporary Obstacles (cars etc.)

Co-existing networks …

X

X

SIROCCO'13, Andrea Richa

- Idea: model unpredictable behaviors via adversary (a.k.a. adversarial jammer)!

X

X

X

X

X

SIROCCO'13, Andrea Richa

- Adaptive adversary
- Single-hop scenario
- Simple (yet powerful) idea
- MAC protocol

- Fairness

SIROCCO'13, Andrea Richa

- single frequency: e.g., sensor nodes
- at each time step, a node may decide to transmit a packet (nodes continuously contend to send packets)
- a node may transmit or sense the channel at any time step (half-duplex)
- when sensing the channel a node v may
- sense an idle channel
- receive a packet
- sense a busy channel (due to interference or adversarial jamming)

v

SIROCCO'13, Andrea Richa

- [Awerbuch, R., Scheideler, PODC’08]
- nreliable honest nodes and ajammer (adversary); all nodes within transmission range of each other and of the jammer

jammer

SIROCCO'13, Andrea Richa

- knows protocol and entire history
- (T,λ)-bounded adversary, 0 < λ < 1: in any time window of size w ≥ T, the adversary can jam ≤ λw time steps

steps jammed by adversary

other steps

w

0 1 …

SIROCCO'13, Andrea Richa

- a protocol is called constant-competitive against a(T,λ)-bounded adversary if the nodes manage to perform successful transmissions in at least a constant fraction of the steps (w.h.p. or on expectation), for any sufficiently large number of steps

successful transmissions

steps jammed by adversary

other steps (idle channel, message collisions)

w

0 1 …

SIROCCO'13, Andrea Richa

- symmetric local-control MAC protocol that is constant-competitive against any (T,1-ε)-bounded adaptive adversary after Ω (T / ε) steps w.h.p., for any constant 0<ε<1and anyT.
- energy efficient:
- converges to bounded amount of energy consumption due to message transmissions by nodes under continuous adversarial jamming (ε=0)

- fast recovery from any state

~

SIROCCO'13, Andrea Richa

Pros:

- no prior knowledge of global parameters
- nodes do not know ε

- no IDs needed
Cons:

- nodes know rough estimate γ=O(1/(log T + loglog n))
- allow for superpolynomial change in n and polynomial change in T over time

- fair channel use is not guaranteed
- we will see how to fix that later

SIROCCO'13, Andrea Richa

- spread spectrum & frequency hopping:
- Many references in the literature (specially more applied work)…
- rely on broad spectrum (large number of available frequencies). However, sensor nodes or common wireless devices based on 802.11 have narrow spreading factors
- Our approach is orthogonal to broad spectrum techniques, and can be used in conjunction with those.

SIROCCO'13, Andrea Richa

- random backoff:
- adaptive adversary too powerful for MAC protocols based on random backoff\tournaments (including the 802.11 standard [Bayrataroglu, King, Liu, Noubir, Rajaraman, Thapa, INFOCOM’08])

- [Gilbert, Guerraoui, Newport, OPODIS’06]: cannot handle adaptive adversaries with high jamming rate
- more general scenario (adversary can also introduce malicious messages)
- nodes know n
- not energy efficient

- Others (channel surfing, coding strategy,etc.): also cannot handle adaptive adversary

SIROCCO'13, Andrea Richa

- Adaptive adversary
- Single-hop scenario
- Simple (yet powerful) idea
- MAC protocol

- Fairness

SIROCCO'13, Andrea Richa

- each node v sends a message at current time step with probability pv≤pmax, for constant 0 < pmax<< 1.p = ∑ pv(aggregateprobability) qidle=probability the channel is idleqsucc=probability that only one node is transmitting (successful transmission)
- Claim.qidle. p ≤qsucc≤(qidle. p)/ (1-pmax)
if (number of times the channel is idle)=(number of successful transmissions)p = θ(1)qsucc= θ(1) ! (what we want!)

~

SIROCCO'13, Andrea Richa

- a node v adapts pv based only on steps when an idle channel or a successful message transmission are observed, ignoring all other steps (including all the blocked steps when the adversary transmits!)

time

idle steps

successful transmissions

steps jammed by adversary

steps where collision occurred but no jamming

SIROCCO'13, Andrea Richa

- a node v adapts pv based only on steps when an idle channel or a successful message transmission are observed, ignoring all other steps (including all the blocked steps when the adversary transmits!)!

time

idle steps

successful transmissions

steps jammed by adversary

steps where collision occurred but no jamming

SIROCCO'13, Andrea Richa

Each time step:

- Node vsends a message with probability pv . If v does not send a message then
- if the wireless channel is idle then pv = (1+ γ) pv
- if vreceived a message thenpv = pv /(1+ γ)
(Recall thatγ = O(1/(log T + loglog n)).)

SIROCCO'13, Andrea Richa

- Basic problem:Aggregate probability p could be too large.
- all time steps blocked due to message collisions w.h.p.

time

idle steps

successful transmissions

steps jammed by adversary

steps where collision occurred but no jamming

SIROCCO'13, Andrea Richa

- Basic problem:Cumulative probability pcould be too large.
- all time steps blocked due to message collisions w.h.p.

time

idle steps

successful transmissions

steps jammed by adversary

steps where collision occurred but no jamming

SIROCCO'13, Andrea Richa

- Basic problem:Cumulative probability p could be too large.
- all time steps blocked due to message collisions w.h.p.

- Idea: If more than T consecutive time stepswithout successful transmissions (or idle time steps), then reduce probabilities, which results in fast recovery of p.
- Problem: Nodes do not know T. How to learn a good time window threshold?
- It turns out that additive-increase additive-decrease is the right strategy!

SIROCCO'13, Andrea Richa

- each node vmaintains
- probability valuepv,
- time window thresholdTv, and
- countercv

- Initially, Tv = cv = 1andpv = pmax (< 1/24).
- synchronized time steps (for ease of explanation)
- Intuition:wait for an entire time window (according to current estimate Tv) until you can increase Tv

SIROCCO'13, Andrea Richa

In each step:

- node v sends a message with probability pv . If v decides not to send a message then
- if v senses an idle channel, then pv= min{(1+γ)pv , pmax}
- if vsuccessfully receives a message, then pv= pv /(1+ γ)and Tv= max{Tv - 1, 1}

- cv= cv + 1. If cv> Tvthen
- cv= 1
- ifvdidnot receive a messagesuccessfullyin thelast Tv steps thenpv= pv /(1+ γ)andTv= Tv +1

SIROCCO'13, Andrea Richa

- Let N = max {T,n}
- Theorem. Our MAC protocol is constant-competitive under any (T,1-ε)-bounded adversary if the protocol is executed for Ω(log N . max{T,log3N/(εγ2)}/ε) steps w.h.p., for any constant 0<ε<1and anyT.

SIROCCO'13, Andrea Richa

- Show competitiveness for time frames of F = θ((log N . max{T,log3N/(εγ2)}/ε) many steps If we can show constant competitiveness for any such time frame of size F, the theorem follows
- Use induction over the number of sufficiently large time frames seen so far. We subdivide each frame:

I’

I

f =θ(max{T,log3N/(εγ2)})

F = (log N / ε) . f

SIROCCO'13, Andrea Richa

- p > 1/(f2(1+γ)2√f) and Tv< √F, in each subframe I’ w.h.p.
- p<12 and p>1/12 within subframe I’ with moderate probability (so that adaptive adversarial jamming not successful)
- Constant throughput in I’ with moderate probability
- Over a logarithmic number of subframes, constant throughput in frame I of size F w.h.p.

SIROCCO'13, Andrea Richa

Moreover, under a more powerful adversary that can perform continuous jamming (afterΩ(T)steps):

Lemma. The total energy consumption (sending out messages) during an entire continuous jamming attack is O(√T), independent of the length of the attack.

Exhaust adversary’s energy resources

~

~

SIROCCO'13, Andrea Richa

33

- Adaptive adversary
- Single-hop scenario
- Simple (yet powerful) idea
- MAC protocol

- Fairness

SIROCCO'13, Andrea Richa

- [R.,Scheideler, Schmid, Zhang, ICDCS’11]
- Fully adaptive adversary that in addition can quickly observe the channel at the current time step, before deciding to jam
- i.e., the adversary has some knowledge about the random choices at current time step
- Distinguishes between idle and non-idle time steps, but cannot distinguish between successful transmissions and collisions (e.g., if packets are encrypted)

SIROCCO'13, Andrea Richa

- Need to “synchronize” transmission probabilities pv, as well as counters cv and Tv
- Piggyback pv, cv, Tvto a message sent by v
- Better understanding on how aggregate probability changes every time step
- Achieve fairness for free (basically all nodes have the same transmission probability)!

- Once nodes are synchronized (plus some other smaller changes), one can show that the basic protocol is also robust against reactive adversaries

SIROCCO'13, Andrea Richa

Theorem.The AntiJam protocol achieves:

- fairness: the channel access probabilities among nodes do not differ by more than a factor of (1+γ) after the first message was sent successfully.
- eθ(1/ ε )-competitiveness w.h.p., under any (T,1-ε)-bounded reactive adversary if the protocol is executed forΩ(T/ε) steps w.h.p., for any constant 0<ε<1and anyT(constant in throughput now depends on ε)

2

~

SIROCCO'13, Andrea Richa

- Fact:
- Right after u sends a message successfully along with the tuple (pu ,cu ,Tu), (pv, cv, Tv)= (pu / (1+ γ), cu,Tu) for all receiving nodes v, while the sending node values stay the same. In particular, for any time step tafter a successful transmission by node u, (cv, Tv) = (cw, Tw) for all nodes v and w V
- This implies that after a successful transmission, the access probabilities of any two nodes in the network will never differ by more than a factor in the future.

SIROCCO'13, Andrea Richa

ε = 0.5

SIROCCO'13, Andrea Richa

SIROCCO'13, Andrea Richa

SIROCCO'13, Andrea Richa

SIROCCO'13, Andrea Richa

SIROCCO'13, Andrea Richa

- Adaptive adversary
- Single-hop scenario
- Simple (yet powerful) idea
- MAC protocol

- Fairness

SIROCCO'13, Andrea Richa

Physical interference

Jammed

SIROCCO'13, Andrea Richa

Powerful jammer

- A message sent by nodeu is received at node v iff- N: Gaussian variable for background noise- S: set of transmitting nodes- : constant that depends on transmission scheme- d(x,y):Euclidean distance between x and y
- Well-accepted model (in theory, at least ) for physical interference

P/d(u,v)

>

N + w inSP/d(w,v)

SIROCCO'13, Andrea Richa

- (B,T)-bounded adaptive adversary: has an overall noise budget of BT that it can use to increase the noise level at node v and that it can distribute among the time steps as it likes.
- At any point in time, the adversary makes independent decisions for each node on whether to jam it (provided it does not exceed its noise budget over a window of size T).
- many noise phenomena can be covered under this model

SIROCCO'13, Andrea Richa

- [Ogierman, R., Scheideler, Schmid, Zhang, 2013]: SINR model
- Also achieve constant throughput :
Throughput =

(Earlier, [R., Scheideler, Schmid, Zhang, DISC’10]: unit-disk graph model.)

SIROCCO'13, Andrea Richa

- Adaptive adversary
- Single-hop scenario
- Simple (yet powerful) idea
- MAC protocol

- Fairness

SIROCCO'13, Andrea Richa

- [R., Scheideler, Schmid, Zhang, MobiHoc’11]
- Our goal: select a leader among the nodes
- Challenges: we may start in any state; there is adaptive adversary

leader

SIROCCO'13, Andrea Richa

- Goal: design a self-stabilizing protocol that elects a single node as the leader, irrespective of the jamming activity
- Challenges:
- a leader node should let the others (followers or other leaders) know that he is still around
- the followers should be able to notice when there is no leader in the network

SIROCCO'13, Andrea Richa

Why is leader election difficult under an adaptive jammer?

Example: exponential/polynomialbackoff

: jammingactivity

channel

activity

(expected)

: messages

0

time

constantsuccessprobability

SIROCCO'13, Andrea Richa

Example 1: exponential/polynomial backoff

: jammingactivity

channel

activity

(expected)

: messages

0

time

constantsuccessprobability

SIROCCO'13, Andrea Richa

Example 2: reserved leader slot to notify nodes about leader

: jammingactivity

channel

activity

(expected)

: leadermessage

0

time

SIROCCO'13, Andrea Richa

Example 2: reserved leader slot to notify nodes about leader

: jammingactivity

channel

activity

(expected)

: leadermessage

0

time

SIROCCO'13, Andrea Richa

- Adversary: used to model external world
- More bening:
- Control packet injection rates
- Control mobility

- Intentionally disruptive:
- jammers

- More disruptive: malicious adversaries
- Undermine security
- Control Byzantine nodes (introduce fake messages)

SIROCCO'13, Andrea Richa

- Adversarial packet injection/queueing:
- [Chlebus, Kowalski, Rokicki, PODC’06],[Andrews, Jung, Stolyar, STOC’07],[Anantharamu, Chlebus, Rokicki, OPODIS’09],[Chlebus, Kowalski, Rokicki, Distributed Computing’09],[Lim, Jung, Andrews, INFOCOM’12]

- Multi-channel access with adversarial jamming:
- [Dolev, Gilbert, Guerraoui, Newport, DISC’07], [Anantharamu, Chlebus, Kowalski, Rokicki, SIROCCO’11],[Dolev,Gilbert, Khabbazian, Newport, DISC’11], [Daum, Gilbert, Kuhn, Newport, PODC’12], [Ghaffari, Gilbert, Newport, Tan, OPODIS’12]

SIROCCO'13, Andrea Richa

- Broadcasting\Gossiping with adversarial jamming:
- [Dolev, Gilbert, Guerraoui, Newport, DISC’07], [Dolev,Gilbert, Khabbazian, Newport, DISC’11], [Daum, Gilbert, Kuhn, Newport, PODC’12], [Ghaffari, Gilbert, Newport, Tan, OPODIS’12]

- Capacity Maximization with adversarial jamming: [Dams, Hoefer, Kesselheim, unpublished]
- Malicious adversary:
- [Dolev, Gilbert, Guerraoui, Newport, DISC’07], [Gilbert, Young, PODC’12]

- Infection spreading with adversarial mobility: [Wang,Krishnamachari, ]
- Etc.

SIROCCO'13, Andrea Richa

- Jamming-resistant protocols with power control:
- Increasing power increases chance that signal will overcome jamming activity, however…
- Increasing power also generates more interference…
- Also adapt noise threshold level?

- How about reactive jammers in multihop environments, under SINR?
- Can the protocols be modified so that no rough bound on n and T are required?
- stochastic/oblivious jammers: Simpler to handle? E.g., a constant gamma seems to work fine here.

- Other applications of the MAC protocol (e.g., broadcast)?

SIROCCO'13, Andrea Richa

- What would be your application of an adversary in wireless communication?

SIROCCO'13, Andrea Richa

- Baruch Awerbuch (John Hopkins); Stefan Schmid (TU Berlin\Telekom Labs); Christian Scheideler and Adrian Ogierman (U. of Paderborn); Jin Zhang (Google)
- Papers available from my webpage (for recent – and maybe not so recent -- submissions, please send me email) at [email protected]

SIROCCO'13, Andrea Richa

Thank you!

Questions?

SIROCCO'13, Andrea Richa

SIROCCO'13, Andrea Richa

SIROCCO'13, Andrea Richa