adversarial models for wireless communication

Adversarial Models for Wireless Communication

Andrea W. RichaArizona State University

SIROCCO'13, Andrea Richa 1

MotivationChannel availability hard to model:

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

2SIROCCO'13, Andrea Richa


Physical layer jamming● A physical jammer listens 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

honest nodes jammer

MotivationChannel 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”

Motivation

Ideal world:

Usual approach adopted in theory.

0 time

Background noise

: noise level


Motivation

Ideal world:

OR


0 time

Background noise

: noise level


Motivation

Ideal world:

OR (bounded, predictable)


0 time

Background noise

: noise level


Motivation

Real world:

How to model this???

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backgroundnoise

: noise level


Our Approach: Adversarial Jamming

Background noise (microwave, radio signal, etc.)Intentional jammer

Temporary Obstacles (cars etc.)Co-existing networks …

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Our Approach: Adversarial Jamming

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

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X

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Overview● Adaptive adversary

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

● Reactive adversary– Fairness

● Adaptive adversary in multi-hop networks● Application: Leader Election● Other adversarial models● Future work



Wireless communication model● 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


Single-hop wireless network● [Awerbuch, R., Scheideler, PODC’08]● n reliable honest nodes and a jammer (adversary); all

nodes within transmission range of each other and of the jammer

jammer


Adaptive adversary● 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

0 1 … w

steps jammed by adversary

other steps


Constant-competitive protocol

● 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


0 1 … w

other steps (idle channel, message collisions)


Our main contribution● 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<1 and any T.

● 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

~


Pros and ConsPros:● 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

Physical Layer Traditional Jamming Defenses

● 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.


MAC Layer Jamming Defenses● 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



Simple (yet powerful) idea● each node v sends a message at current time step with

probability pv ≤ pmax, for constant 0 < pmax << 1. p = ∑ pv (aggregate probability) 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!)

~


Basic approach

● 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!)


idle steps


steps where collision occurred but no jamming

time


Basic approach

● 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!)!


idle steps



time


Naïve protocol

Each time step:● Node v sends 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 v received a message then pv = pv /(1+ γ)

(Recall that γ = O(1/(log T + loglog n)). )


Problems

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


idle steps



time


Problems

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


idle steps



time


Problems

● 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 steps without 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!


MAC protocol● each node v maintains

– probability value pv , – time window threshold Tv , and – counter cv

● Initially, Tv = cv = 1 and pv = 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


MAC protocolIn 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 v successfully receives a message, then pv = pv /(1+ γ)

and Tv = max{Tv - 1, 1}

● cv = cv + 1. If cv > Tv then– cv = 1– if v did not receive a message successfully in the last Tv

steps then pv = pv /(1+ γ) and Tv = Tv +1


Our results● 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,log3 N/(ε γ2)}/ ε) steps w.h.p., for any constant 0<ε<1 and any T.


Proof sketch● Show competitiveness for time frames of F =

θ((log N . max{T,log3 N/(ε γ2)}/ 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:

II’

f = θ(max{T,log3 N/(ε γ2)})

F = (log N / ε) . f


Proof sketch

● 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.

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Continuous jamming● Moreover, under a more powerful adversary that

can perform continuous jamming (after Ω(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

~

~


Reactive adversary● [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)


AntiJam: Reactive jamming-resistant MAC protocol

● Need to “synchronize” transmission probabilities pv, as well as counters cv and Tv

– Piggyback pv, cv, Tv to 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


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Our resultsTheorem. 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 for Ω(T/ε) steps w.h.p., for any constant 0<ε<1 and any T

(constant in throughput now depends on ε )

~

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SIROCCO'13, Andrea Richa

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Proof sketch: Fairness● 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 t after 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.


AntiJam: Throughput for ε = 0.5

ε = 0.5


AntiJam: Convergence Time


AntiJam: Fairness


AntiJam vs. Non-reactive protocol: Fairness


AntiJam vs 802.11


Multihop wireless networks

SIROCCO'13, Andrea Richa 45Powerful jammer

Physical interference

Jammed

Signal-to-Interference-Noise-Ratio (SINR)


● A message sent by node u 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 in S P/d(w,v)>

Multihop Adversarial Model

● (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


Throughput in multihop networks

● [Ogierman, R., Scheideler, Schmid, Zhang, 2013]: SINR model

● Also achieve constant throughput :

Throughput =

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


for v steps timejammed-non #

by v received msgs successful#

v

v

Leader Election in Adversarial (Single-hop) Networks

●[R., Scheideler, Schmid, Zhang, MobiHoc’11]

●Our goal: select a leader among the nodes

●Challenges: we may start in any state; there is adaptive adversary50SIROCCO'13, Andrea Richa

leader

51

Self-stabilizing Leader Election● 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


Leader Election

Why is leader election difficult under an adaptive jammer?Example: exponential/polynomial backoff

0 time

channelactivity

(expected)

: jamming activity

: messages

constant success probability52SIROCCO'13, Andrea Richa

Why is leader election difficult under an adaptive jammer?

Example 1: exponential/polynomial backoff

0 time

: jamming activity

: messages

constant success probability

channelactivity

(expected)



Example 2: reserved leader slot to notify nodes about leader

0 time

channelactivity

(expected)

: jamming activity

: leader message


Other adversarial modeling in wireless networks

● 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)



● 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]



● 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.


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Future work: Adversarial Jamming

● 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)?


Future Work

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


Collaborators

● 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 www.public.asu.edu/~aricha

[email protected]


http://www.public.asu.edu/~aricha


Thank you!Questions?

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