Polygonal Broadcast, Secret Maturity and the Firing Sensors

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Polygonal Broadcast, Secret Maturity and the
Firing Sensors

• Shlomi Dolev BGU
• Ted Herman UIOWA
• Limor Lahiani BGU

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Sensor Networks

• Collaborative effort of large number of sensor
  nodes densely deployed inside (close to) the
  phenomenon.
• Each sensor has sensing, processing transceiver
  and power units.
• (location finder, power generator, mobilizer,
  etc.)

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Sensor Networks
Wireless Communication
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Sensor Networks

• Limitations
• Low-power (small battery)
• Short memory
• Transmission radius

Primal Focus power conservation
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Related Work

• Agriculture, military, environment
• SmartDust (Berkeley)
• Millimeter scale sensor network
• Oxygen (MIT)
• Computational support of daily activities

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Related Work

• Flood ( AS02)
• Maximum number of hops
• Receiver is the destination
• Random Protocols
• Gossiping AS02
• Rumor routing BE02
• (May end up in flood)
• Two tier flood YLCLZ02 (UCLA)
• Restricted to grid
• Global location awareness
• Routing to sinks

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Talk Outline

• System Model and Settings
• Polygonal broadcast schemes
• Polygonal flood schemes
• Local broadcast/flood and remote transmission
• Sense of direction
• Secret maturity and sensor activation

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System Model Settings

• Sensors are (uniformly) distributed
• No GPS / Global Location
• No global orientation (NESW),
• Decentralized (neighbors relative location)
• Limited energy (transmitting gtgt receiving)

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System Model Settings

• Communication with a particular neighbor
• Directed communication technology (no id)
• Laser
• Directed antenna
• Local broadcast (sensor id)
• GPS ? local broadcast with location identifier

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Polygon Relative View

• A message either arrives through an edge, namely
  the S direction, or through a vertex (angle),
  namely the SW direction.
• The other directions are implicitly defined.

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Ad-Hoc Polygonal Tiling

• Virtual tiling of polygons
• Trade-off memory and energy (edge size)
• Initiator implicitly defines the tiling
• Backbone of polygons representatives on the fly
• Only representative transmit
• Message is routed along the backbone
• No overuse
• Local transmission inside the polygon

• Plane coverage

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Initiator
Local transmission
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Polygon Representative

• Tiling construction info ? neighboring polygons
• Optimization parameter/function
• (e.g., maximum power available)

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Polygonal Broadcast Schemes

• Imaginary (all regular) polygonal tiling
• Impossibility results
• Zero bit for all regular polygons
• One bit for triangles
• One bit broadcast scheme for square tiling
• One bit broadcast scheme for hexagon tiling
• Two bits broadcast scheme for triangle tiling

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Polygonal Broadcast Schemes

• A tuple S ltT,I,Fgt where
• T is the imaginary polygonal tiling defined by
  the initiator
• I is the algorithm of the initiator
• F specifies to each sensor how to forward the
  received message according to the broadcast
  bit(s) attached to it

?Goal Plane coverage, no cycles, reach
all polygons exactly once.
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Impossibilities

• No zero-bit broadcast scheme for
• Triangles
• Squares
• Hexagons
• No one-bit broadcast scheme for
• triangles

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Zero Bit Broadcast Scheme
All sensors forwards at the same
direction (except for the initiator)
No broadcast bit
Edges-only / Vertices-only scheme

• Edge/Vertex bit

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Zero Bit Broadcast Scheme Impossible for Square
Tiling
Edges only
Vertices only
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Zero Bit Broadcast SchemeImpossible for Triangle
Tiling
Edges only
Vertices only
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Zero Bit Broadcast Scheme Impossible for Hexagon
Tiling
Edges only
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One Bit Broadcast for Square Tiling

• T Square tiling (edge size e)
• I (N,1),(E,1),(S,1),(W,1),
• (NE,0),(NW,0),(SE,0),(SW,0)
• F
• F (SW,0) (NE,0), (N,1), (NE,1)
• F (S,1) (N,1)

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One Bit Broadcast Scheme for Square Tiling
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One Bit Broadcast Scheme for Hexagon Tiling
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Two Bits Broadcast Scheme for Triangle Tiling
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Polygonal Flood Scheme

• Irregular distribution ? Deserted polygons
• Forward message to all edge neighbors
• Except the receiving edge
• Local memory to avoid cycles
• One bit flag
• Message identifier

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Flood-Tree for Square Tiling
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Local Broadcast and Local FloodSquares and
Hexagons

• Restricted distribution region (flood/broad.)
• Polygonal distance/radius
• BroadcastFollowing the scheme with polygonal
  hope counter
• FloodSmart use of radius counters ltCN,CE,dgt
• Forward with probability
• Probability p to forward the message

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Distribution Range R(d,i)
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Local Broadcast Squares and Hexagons

• Broadcast to distribution range R(d,i)
• Polygons who are d-far from pi receive message
  after d polygonal hops
• Hop counter attached to the message
• Stop forwarding when hop counter reaches zero

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Polygonal Local FloodSquares

• Smart counter ltcN,cE,dgt for squares
• cN Polygonal distance at the N direction
• cE Polygonal distance at the E direction
• d radios

• init lt1,0, dgt
• cNlt d ? forward at direction N with
  ltcN1,cE,dgt
• cE lt d ? forward at directions E and W with
  ltcE1,cN,,dgt and ltcE-1,cN,,dgt
  relatively

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Local Flood for Square Tilingdistribution radius
2
Smart Counter ltCN,CE,dgt
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Local Broadcast with Probability Squares and
Hexagons

• Forward message with probability p (except the
  initiator) avoid counters
• PrpR(d,i) The probability of a local
  broadcast initiated by si to reach all the
  polygons in R(d,i)
• PrpR(1,i) 1
• PrpR(d,i) PrpR(d-1,i)pN(d-1,i)
• N(0,i) 1
• N(d,i) 8d for squares (d gt 0)
• N(d,i) 6d for hexagons (d gt 0)

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Remote TransmissionEnd-to-End

• Relative distance ? Polygonal distance
• CN and CE counters
• Greedy DFS towards destination
• Updating counters
• Greedy decision decrease polygonal distance
• Backtracking when meeting a deserted polygon
• Backtracking storage

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D
S
(-4,-3)
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Sense of Direction

• Motivation
• Data reply to query initiator
• Find emergency exit, fire core
• Technique
• Flood message (with unique identifier)
• Remember the direction of the first arriving
  message (the fastest)

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Sense of DirectionFind the Nearest Emergency Exit

• Different tiling for each initiator.
• Simplified for presentation

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Sense of DirectionFind The nearest Emergency Exit
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Sense of DirectionFind the Nearest Emergency Exit
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Secret Maturity and Sensor Activation

• Simultaneous activation
• Captured sensors do not reveal secrets
• Sensor does not know the content of the message
  until the actual activation
• Too late for the adversary

• Problem Flood propagation time
• Solution Outside entity (e.g., satellite)

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Secret Maturity and Sensor Activation

• Simultaneous activation
• Captured sensors do not reveal secrets
• Sensor does not know the content of the message
  until the actual activation
• Too late for the adversary

• Problem Flood propagation time
• Solution Outside entity (e.g., satellite)

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Secret Maturity and Sensor Activation

• Satellite transmits public key Kei and private
  key Kdi every ?t time units.
• Kei for secrets encryption at ti
• Kdi for decryption secrets encrypted with Kei -1

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Simultaneous Activation in ?t time

• Initiator at ti
• Encrypt activation message with Kei
• Throws the original message
• Floods the encrypted message
• All sensors (including the initiator)
• Wait till private key Kdi1 is published at ti1
• Decrypt message and act accordingly

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Simultaneous Activation in ?ta(a -time puzzle)

• Initiator
• Let M be the activation message
• Mp E (a ,M) a -time lock puzzle RSW96
• M E(Kei,Mp)
• Throws M and Mp
• Floods M

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Simultaneous Activation in ?t a time

• All sensors (including initiator)
• Get flooded message M
• Wait for Kdi1 to be published (at time ti1)
• Mp D(Kdi1,M)
• Solve time lock puzzle Mp and get M D(Mp)
  (takes a time units)
• Follow the activation message M

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The End
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Master Thesis of Limor Lahiani