Universe Detectors for Sybil Defense in Ad Hoc Wireless Networks

1
Universe Detectors for Sybil Defense in Ad Hoc
Wireless Networks

• Adnan Vora
• Mikhail NesterenkoSébastien Tixeuil
• Sylvie Delaët
• Detroit, Michigan
• November 21, 2008

2
Sybil Attack and Ad Hoc Wireless Networks

• Sybil attack Doceur02 faulty node (or
  attacker) compromisesthe system by creating
  multiple identities that system perceives as
  separate
• attacker can
• overwhelm systems resources by turning attack
  into denial-of-service
• subvert routing infrastructure, message
  transmission, etc.
• problem is related to Byzantine fault tolerance
  (faulty node behaves arbitrarily) and straddles
  fault-tolerance and security domains
• Ad Hoc wireless networks potential target
• ad hoc no initial topological knowledge
• wireless - broadcast medium allows identity
  creation
• Sybil defense is lumped together with DoS,
  considered intractable and seldom addressed

3
Sybil in Wireless What to Do?

• critical aspects
• asynchrony allows faulty node to create
  arbitrary number of identities
• broadcast medium difficulty to ascertain sender
  identity
• problematic solution approaches
• cryptography e.g. sender digitally signs
  messages, receiver verifies and discards
  incorrect ids problem
• needs key-based infrastructure
• requires nodes to handle cryptographic operations
• reputation nodes observe each other, if one
  deviates from protocol, others notice and report
• implicitly presumes reliable identify recognition
• wireless features that enable Sybil defense
• broadcast medium message is received by all
  nodes in vicinity
• received signal strength (RSS) allows distance
  estimation
• note that faulty node may change transmission
  signal strength (TSS)
• need to only discover nodes in range further
  topology discovery is already possible NT06

4
Outline

• model and notation
• problem definition
• impossibility of standalone solution
• universe detectors
• bounds on detectors
• necessary node density
• necessary transmission range
• Sybil attack resilient neighborhood discovery
  algorithm SAND
• detector interface issues
• algorithm description
• detector optimality
• related work
• extensions and further work

5
Outline

• model and notation
• problem definition
• impossibility of standalone solution
• universe detectors
• bounds on detectors
• necessary node density
• necessary transmission range
• Sybil attack resilient neighborhood discovery
  algorithm SAND
• detector interface issues
• algorithm description
• detector optimality
• related work
• extensions and further work

6
Model

• asynchronous execution model (faulty node can
  create infinitely many ids)
• all nodes know their geographic coordinates, no
  other ids
• nodes
• real - either correct or faulty
• fictitious introduced by faulty nodes
• neighborhood of node u set of nodes within
  distance d of u
• free space model of signal propagation R cT/r2
• Tr - fixed TSS at which correct nodes broadcast,
  TSS of faulty nodes - arbitrary
• Rmin minimum RSS at which signal is received
• nodes can accurately measure the RSS above Rmin,
• on basis of RSS and assuming Tr can compute
  distance to sender, range rt max legit
  distance to receive message
• conflict - distance does not match nodes id
  (coordinates)
• message receipt is reliable, every message
  contains senders id
• universe subset of nodes (transmissions) that
  do not conflict
• real no fictitious nodes
• complete contains all correct nodes
• locality - each process ignores messages from
  nodes out for range rt and outside its
  neighborhood distance d

rt
u
dn
7
The Neighborhood Discovery Problem

• each correct node u needs to output a set of its
  neighbors
• safety a set contains all correct neighbors and
  no fictitious ones
• liveness eventually, u outputs a set containing
  all correct neighbors
• problem variants
• strong (SNDP) safety and liveness as above
• weak (WNDP) safety is relaxed to allow a subset
  of correct neighbors
• eventual (?NDP) safety satisfied only
  eventually
• a solution to ?NDP is a solution WNDP which in
  turn is a solution to SNDP

8
Outline

• model and notation
• problem definition
• impossibility of standalone solution
• universe detectors
• bounds on detectors
• necessary node density
• necessary transmission range
• Sybil attack resilient neighborhood discovery
  algorithm SAND
• detector interface issues
• algorithm description
• detector optimality
• related work
• extensions and further work

9
Neighborhood Discovery Is Impossible

• Theorem 1. In an asynchronous system, none of the
  three variants of the neighborhood discovery
  problem are deterministically solvable in the
  presence of a single Byzantine fault.

• intuition two cases k is real, k is
  fictitious.
• f ensures u gets the same sequence of messages
  with the same RSS forcing u to make identical
  decision

f
f
k
k
u
u
dn
dn
10
Abstract Universe Detectors

• need to augment the model to make the problem
  solvable
• correct node may detect conflicts and separate
  nodes into universes however cannot decide which
  universe is real
• universe detector points to real universe
• properties
• completeness if computation contains a suffix
  where node outputs a real and complete universe
  in every state, this computation also contains a
  suffix where the detector points to it
• accuracy if a detector points to the universe,
  it is real and complete
• detector classes
• strongly perfect (SPU) both completeness and
  accuracy as above
• weakly perfect (WPU) may point to real
  universe even if it is incomplete
• eventually perfect (?PU) completeness and
  accuracy only eventual
• SPU ? WPU ? ?PU
• solution is conflict aware if two nodes that do
  not conflict always belong to the same universe
• disallows trivial solution node creates all
  possible combinations of nodes that is it is
  aware of one of the universes has to be real
  and complete

11
Outline

• model and notation
• problem definition
• impossibility of standalone solution
• universe detectors
• bounds on detectors
• necessary node density
• necessary transmission range
• Sybil attack resilient neighborhood discovery
  algorithm SAND
• detector interface issues
• algorithm description
• detector optimality
• related work
• extensions and further work

12
Snare

• a retinue Ef of a faulty node f is assignment of
  correct nodes if x belongs to Ef , then every
  node y such that yf lt xf also belongs to Ef
• deception field of a retinue Ef is an area where
  f can place fictitious nodes without retinue
  members detecting conflicts
• snare - a point k in the neighborhood of u such
  that
• exists retinue assignment to faulty nodes in the
  neighborhood
• the intersection of the deception fields contains
  k
• perfect snare all correct neighborhood
  nodesare in retinues

retinue of f1
retinue of f2
retinue of f1
retinue of f2
f1
y
y
f1
f2
f2
x
x
z
z
u
dn
u
dn
ab/(b-a)
deception field
z
f
fz
x
a
min(fy,fx)
b
y
f
min(rt,dn)
x
y
min(rt,dn)
fz
deception field
min(rt,dn)
deception field
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Necessary Node Density

• Theorem 2. There is no conflict aware well-formed
  deterministic solution to any of the neighborhood
  discovery problems despite the availability of
  the universe detectors if one of the considered
  layouts contains a perfect snare.

• intuition a faulty node may place a fictitious
  node in the snare

ab/(b-a)
deception field
z
f
fz
x
a
min(fy,fx)
b
y
f
min(rt,dn)
x
y
min(rt,dn)
fz
deception field
min(rt,dn)
deception field
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Necessary Transmission Range

• Theorem 3. There is no conflict-aware
  deterministic solution for any of the
  neighborhood discovery problems despite the
  availability of universe detectors and lack of
  snares if the node transmission range rt is less
  than double the neighborhood distance dn.
• intuition faulty node may force separation of
  correct nodes into different universes

if f1 invents node k, y conflicts with k forcing
x to put k and y into separate universes
f2 sends the same message as f1 making y to
issue a conflict andforcing x to separate k and y
f1
rt
rt
f2
k
k
y
y
dn
dn
x
x
fictitious
real
15
Outline

• model and notation
• problem definition
• impossibility of standalone solution
• universe detectors
• bounds on detectors
• necessary node density
• necessary transmission range
• Sybil attack resilient neighborhood discovery
  algorithm SAND
• detector interface issues
• algorithm description
• detector optimality
• related work
• extensions and further work

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Detector Interface Issues

• encoding universes
• every conflict message may potentially split
  existing universes ? naïve encoding produces
  exponential size input for detector
• pass conflicts themselves instead, detector can
  reconstruct universes
• impossible to ascertain sender, detector has to
  handle it
• ? detector has to output universes rather than
  justpoint to them

universe U
conflict between x and y
conflict between u and v
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SAND Sybil attack resilient neighborhood
discovery algorithm

• message receipt properties
• receives announce from every correct node in the
  neighborhood
• announce from each correct node is confirmed by
  every correct node in the neighborhood
• messages from correct nodes do not conflict
• a message from a fictitious node is always gets a
  conflict from a correct node
• DEP
• matches each message with confirm or conflict
• note
• matching may not be unique
• there may not be an original message to match
• there may be cycles
• DEP may grow infinitely

• algorithm SAND
• messages announce, confirm, conflict
• confirm and conflict sent in
  reply and carry initiating
  messages information
• once send announce
• receive message ?
• if message from inside the range and about the
• node in the neighborhood then
• if correct announce then send confirm
• if incorrect message then send conflict
• update dependency graph DEP
• universe detector points to a universe ? output
  universe

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Concrete Detectors

• define concete detectors that accept DEP and
  output universes as abstract ones
• cSPU always outputs real and complete universe
• cWPU may output incomplete universe, but
  eventually outputs complete
• ?cPU eventually outputs real and complete
• Theorem 4. Assuming absence of simple snares and
  assuming that transmission range is at least
  twice as large as neighborhood distance SAND
  provide a conflict-aware deterministic solution
  to the Neighborhood Discovery Problem as follows
  SNDP if cSPU detector is used WNDP if cWPU is
  used, ?NDP if ? cPU is used.
• Chandra et al CHT96 defined weakest detector U
  to solve a problem P. Similar reasoning can be
  applied to universe detectors.
• there is an algorithm A that uses U to solve P
  (this is due to theorem 4)
• there is another algorithm B that uses an
  arbitrary solution S to P to implement U
• output of a neighborhood discovery problem can be
  immediately used to implement the corresponding
  detector
• ? Proposition 1 Concrete universe detectors
  cSPU, cWPU and ?cPU are the weakest detectors
  required to solve SNDP, WNDP and ?NDP
  respectively.

19
Related Work

• Demirbas and Song DS06 describe an experiment
  of using RSS for Sybil attack detection.
• Delaet et al DMRT08 and Hwang et al HHK07
  consider Sybil attack in synchronous wireless
  networks
• Nesterenko and Tixeuil NT06 study how, despite
  Byzantine faults, each node can discover the
  complete topology of the system once all the
  neighborhoods are known.
• There is a large body of literature on secure
  location identification CH06, KZ03, LPC05,
  SSW03, VN06. Secure communication between
  identifying correct nodes is assumed.

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Detector Implementation and Future Research

• implementation may vary depending on application
  properties
• bounds of faulty nodes speed, transmission power
  
• selective use of security
• exploiting topological knowledge of network (e.g.
  all nodes know it is a grid)
• future research
• what are the properties of SAND? can it provide
  more info to detectors? We suspect not
• extend discussion to more realistic radio models
• comparing fault and universe detectors
• fault detectors is all that is necessary to solve
  consensus
• universe detectors need topological constraints

21
Thank You

• Questions?