Jamming-Resistant MAC Protocol1 A Jamming-Resistant MAC Protocol for Single-Hop Wireless Networks...

Jamming-Resistant MAC Protocol 1

A Jamming-Resistant MAC Protocol for Single-Hop

Wireless Networks

A Jamming-Resistant MAC Protocol for Single-Hop

Wireless Networks

Baruch Awerbuch (JHU)Andrea W. Richa (ASU)

Christian Scheideler (Uni PB)


Wireless jamming

● blocking of the wireless channel due to interference, noise or collision at the receiver side

wireless nodes

XXXX


Adversarial physical layer jamming● a jammer listens to the open medium and broadcasts

in the same frequency band as the network– no special hardware required

– can lead to significant disruption of communication at low cost for the jammer

honest nodes jammer


Single-hop wireless network

● n reliable honest nodes and one jammer; all nodes within transmission range of each other and of the jammer

jammer


Wireless communication model

● 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

v


Adaptive adversary● knows protocol and entire history● nodes cannot distinguish between adversarial

jamming or a message collision – i.e., a node senses a busy channel in both cases

● (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 transmission in at least a constant fraction of the non-jammed 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 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 common 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


Further contributions

Leader election protocol:● robust and efficient

● all nodes agree on a leader in O(T/ε) steps w.h.p.

Fair use of the wireless channel: ● share the channel fairly among all nodes (some

nodes may dominate transmission probabilities in our MAC protocol)

● converges in O(n/ε) steps w.h.p.

~


Traditional defenses

● spread spectrum: frequency hopping over a wide frequency band– hard for a jammer to detect the used frequency fast

enough in order to jam it

– Problem: commonly used wireless devices (e.g., 802.11) have relatively narrow frequency bands

● random backoff:– adaptive adversary too powerful for MAC protocols

based on random backoff or tournaments (including the standard MAC protocol of 802.11 [BKLNRT’08])


Further related work

● MAC protocol in [GGN’06] would not be able to sustain constant-competitive ratio if adversary can jam more than ½ the time steps.– more general scenario (adversary can also introduce

malicious messages)– nodes know n– not energy efficient

● reliable broadcast in grid [KBKV’06]– eventually terminates– honest nodes consume energy at much higher rates

than adversary


Overview● Jamming

● Model

● Our contributions

● Related work

● MAC protocol

– Basic Approach

– MAC protocol

– Fast recovery

– Energy Efficiency

● Leader Election & Fair Use of the Channel

● Future work


Simple idea● each node v sends a message at current time step with

probability pv ≤ pmax, for constant 0 < pmax << 1. p = ∑ pv (cumulative probability) qidle = probability the channel is idleqsuccess = probability that only one node is transmitting (successful transmission)

● Claim. qidle . p ≤ qsuccess ≤ (qidle . p)/ (1- pmax)

if (number of times the channel is idle) = (number of successful transmissions) p = 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: Cumulative probability p could be too large. – all time steps blocked due to message collisions w.h.p.


idle steps



time


Problems



idle steps



time


Problems


● Idea: If more than T consecutive time steps without successful transmissions, 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 protocol

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 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


Example: Low value of p

● pv = 1/n2, Tv = 3, cv = 1

v Wireless Channel (Idle)Sensing



● pv = (1+ γ) /n2, Tv = 3, cv = 2


TAMU'08, Andrea Richa 25


● pv = (1+ γ)2 /n2, Tv = 3, cv = 3


25Jamming-Resistant MAC Protocol



● pv = (1+ γ) 3/n2, Tv = 3, cv = 4

v

pv = (1+ γ) 2/n2, Tv = 4, cv =1

Wireless Channel (Jammed)Sensing



● ~ polylog (n) idle steps later:– pv = c/n, Tv ≤ √T polylog (n)

v Wireless Channel

~


Example: Large p

● pv = 1/c, Tv = 2, cv = 1

v Wireless ChannelSending

Message


Example: Large p

● pv = 1/c, Tv = 2, cv = 2

v Wireless Channel (collision)Sensing


Example: Large p

● pv = 1/c, Tv = 2, cv = 3

v Wireless Channel (Jammed)Sensing

pv = 1/[c(1+ γ)], Tv = 3, cv = 1


Example: Large p

● pv = 1/[c(1+ γ)], Tv = 3, cv = 1

v Wireless ChannelSending

Message


Example: Large p

● pv = 1/[c(1+ γ)], Tv = 3, cv = 2

v Wireless Channel (Collision)Sensing


Example: Large p

● pv = 1/[c(1+ γ)], Tv = 3, cv = 3



Example: Large p

● pv = 1/[c(1+ γ)], Tv = 3, cv = 4


pv = 1/[c(1+ γ) 2], Tv = 4, cv = 1


MAC protocol

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}


● 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

Why only successful steps??

Counterexample

Suppose that v pv is very low.

Repeat indefinitely:


Channel jammed for Tv steps

Channel idle for one step

pv

Tv

Channel jammed for Tv-1 steps

no progress!


Our results

● Let N = max {T,n}

● Theorem. The 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.


Overview● Jamming

● Model


● Related work

● MAC protocol

– Basic Approach

– MAC protocol

– Fast recovery



● Future work



Fast recovery

● Our protocol quickly recovers from any (Tv,cv,,pv)-values.

● Theorem. For any initial p0= ∑ pv and T0 = max Tv, it

takes O([log(1+ γ) (1/ p0 )]/ ε + T02) w.h.p. until the

MAC protocol satisfies again p ≥ 1/(f2(1+γ)2√f) and Tv < √F for all v.


Proving fast recovery: p

● p0 < 1/(f2(1+γ)2√f)

● we show that it takes roughly [log(1+ γ) (1/ p0 )]/ ε steps to get down from p0 to (p0)1/2; another [log(1+ γ) (1/ p0 )]/ (2ε) steps to get to (p0)1/4; …

roughly at most 2[log(1+ γ) (1/ p0 )]/ ε until cumulative probability p ≥ 1/(f2(1+γ)2√f)


Proving fast recovery: T

● Once cumulative probability p ≥ 1/(f2(1+γ)2√f) , count number of steps until Tv < √F for all v

– repeated applications of similar inductive argument as MAC protocol’s, by repeatedly selecting appropriately geometric decreasing frame sizes (starting from 4 max Tv ).


Energy efficiency

● Corollary. For any time frame of size F = Ω((log N max{T,log3 N/(ε γ2)} / ε), the total energy spent by all nodes together on sending out messages is bounded by O(F) whp.

● Total amount of energy spent proportional to number of successful transmissions.


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

~

~



Proving Lemma

● First we show that the total energy consumption is O(p0 . T0/ γ + log N) whp, where p0=∑ pv and T0 = max Tv at the start of the attack

– compute expected number transmissions out of each node given that pv decreases by 1/(1+ γ) every T0 +1, then T0 +2 , then T0 +3, … number of steps under continuous jamming

– sum up expected values over all nodes and use Chernoff bounds

● Note that for an attack starting after Ω(T) steps, p0

=O(1) and T0 = O(√F)= O(√T), whp. ~

~


Overview● Jamming

● Model


● Related work

● MAC protocol

– Basic Approach

– MAC protocol

– Fast recovery



● Future work



Leader election

● all nodes agree on a leader in O(T/ε) steps w.h.p.● robust and efficient

– tournament based leader election protocols are not robust against adversarial jamming

● Basic Idea: – each node will keep a counter for the number of

successful transmissions received so far; – the node that receives the least amount of successful

transmissions (and hence sent the largest amount of successful transmissions) will become the leader node

~


Leader election: Basic Ideas

● In addition to the triples (pv,Tv ,cv) each node v maintains – counter sv for estimate on total number of successful

transmissions so far

– one of the states {unknown, leader, follower}

● Initially, all nodes are at unknown.


Leader election protocol

● Modify the MAC protocol slightly: …


if v is still in the state unknown, then v checks if:

(1) sv ≥ sw, then v becomes a follower

(2) sv < sw, then v becomes a leader

v sets sv := max{sv, sw}+1

…


Example: Leader election

v

sv = 0 sw = 0

Message, sv = 0

all other nodes w



v

sv = 0 sw = 0

Message, sv = 0

all other nodes w



v

sv = 0

all other nodes w

sw = 0

Message, sv = 0



v

sv = 0

w

sw = 0

sw ≥ sv, then w becomes a “follower” and sw = max{ sw , sv } + 1 = 1

sw = 1

follower

Message, sv = 0



v

sv = 0

w

sw = k+1

Message, sw = k+1

After v continues successfully transmitting for k more steps. Now the first node w ≠ v is transmitting a message to v, with sw = k+1.



v

sv = 0

w

sw = k+1

Message, sw = k+1

After v continues successfully transmitting for k more steps, until first node w ≠ v successfully transmits a message. Now sw = k+1,

and sv = 0.sv < sw, then v becomes a “leader”

leader

sv = k+2


Our results: Leader election

● Let N = max {T,n}

● Theorem. Within O(log N max{T,log3 N/(ε γ2)} / ε) many steps, the leader election protocol reaches a state in which there is exactly one leader and the other nodes are followers, w.h.p.

● Proof: It takes O(log N max{T,log3 N/(ε γ2)} / ε) until two distinct nodes transmit a message.


Fairness

● share the channel fairly among nodes– MAC protocol can be rather unfair

– some probabilities may eventually dominate others

● simple counter-based mechanism (as in the leader election protocol) would fail here…


Fairness: Basic ideas

● each node v also maintains an additional counter mv of the different nodes which had successful transmissions so far

● the protocol aims at setting pv = pmax /2mv, which will eventually converge to pv = pmax /2n (= θ(1/n))

● converges in O(n/ε) steps w.h.p.


Future work

● Can the MAC protocol be extended to multihop wireless networks?

● How can we adapt to node join and leave operations?● Can the MAC protocol 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?


Questions?

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