1. Secure Location Verification and Stabilization
Adnan Vora and Mikhail Nesterenko
Kent State University r β k
acceptance zone

2. Location Verification
problem
description
have: protected asset
ensure: access to asset only if the principal is in correct location
applications:
wireless network access
keyless car starting
secure gate opening
perimeter protection and friendly force identification, etc.
appeal
immediate practical benefits
non-traditional approach to security
effective algorithmic solutions

3. Outline problem statement basic solution description and properties
immediate applications: securing arbitrary zones
extensions
improving efficiency
operating with non-circular signal propagation
protecting against directional antennas
using random sensor placement
stabilization and fault-tolerance

4. Problem Statement stated informally in[SSW’03] actors
(potentially malicious) prover(s)
arbitrary protection zone
a set of RF-capable verifiers
problem
specify:
placement rules for verifiers
prover  verifiers communication protocol
so that
the verifiers accept the correct prover only if it is inside the protection zone and reject otherwise
protocol is secure if a prover anywhere outside protection zone is rejected
protection zone
verifiers
prover
assumptions
prover authentication not required
verifiers are trusted
intra-verifier communication is reliable and secure
signal propagation is perfectly omni-directional (unit-disk)

5. Previous Approaches
use limited signal propagation speed (e.g. ultrasound)
a verifier radios prover
prover buzzes back
verifier computes roundtrip time and calculates distance
limitations
uncertainties of two mediums: sound and ether (echos, varying propagation speeds)
extra hardware needed: sounders and microphones
requires sequential verification (and time synchronization between verifiers) RF
prover
.01secs=4ft
sound
verifiers

6. Outline problem statement basic solution description and properties
immediate applications: securing arbitrary zones
extensions
improving efficiency
operating with non-circular signal propagation
protecting against directional antennas
using random sensor placement
stabilization and fault-tolerance

7. Basic Solution idea use broadcast nature of RF signal propagation
specifics
separate roles of verifiers
acceptor – receives signal from prover inside protection zone
rejector – receives signal from outside prover
solution
communication protocol:
prover broadcasts signal to distance x, if no decision – increases distance by x
prover is accepted if only acceptors hear from prover, rejected otherwise, informed of decision
placement rules: to come x x
accepted prover x
acceptors
rejector
rejected prover

8. Rejection Zone
rejection zone – prover (correct or malicious) is never accepted
Lemma 1 [VN04] a point on a plane is in rejection zone if it is closer to the nearest rejector than the nearest acceptor
Theorem 1 sensor placement is secure iff the rejectors’ Voronoi cells cover the area outside the protection zone
rejection zone
rejector
rejector
acceptor
Voronoi diagram
rejector
rejector

9. Acceptance and Ambiguity Zones
rejector
rejector
acceptance zone – correct prover is always accepted
ambiguity zone – prover may (not) be accepted
acceptor
acceptance
zone
ambiguity zone
rejector
rejector x
correct prover rejected
why ambiguity zone exists
malicous prover accepted
Lemma 2: a point is in acceptance zone if it is x closer to the nearest acceptor than to the nearest rejector

10. Securing Polygons
protection gap – largest distance from point in rejection zone to nearest point outside protection zone – measures how far rejection zone encroaches upon protection zone
protection is complete if protection gap is zero
Lemma 3 n-sided convex polygon is completely protected with n+1 verifiers
Lemma 4 in this case, if the protection zone contains a circle of radius r, the acceptance zone contains an open disk of radius r-x/2
Theorem 2 An arbitrary n-sided polygonal protection zone can be completely secured with O(n) verifiers
rejection zone
ambiguity zone
acceptance zone
x/2
protection zone boundary

11. Securing Arbitrary Protection Zones
ambiguity gap – largest distance from a point in ambiguity zone to nearest point outside protection zone
Theorem 3 the number of verifiers required to secure an arbitrary-shaped protection zone of area S and perimeter P with constant ambiguity gap is in O(P+S)
Proof outline:
divide protection zone in squares with constant side t (number of such squares is in O(P+S)) ,
protect each square individually with 5 verifiers t
acceptance zone x

12. Outline problem statement basic solution description and properties
immediate applications: securing arbitrary zones
extensions
improving efficiency
operating with non-circular signal propagation
protecting against directional antennas
using random sensor placement
stabilization and fault-tolerance

13. Protecting against Directional Antennas
assumption: fixed beamwidth β
Theorem 5 an arbitrary shaped protection zone can be secured against malicious provers using O(r) verifiers where r is radius of inscribed circle
proof outline: idea – place rejectors such that if acceptor is reached so is rejector
inscribe circle with radius r
place rejectors on circumference of co-centric circle of radius r-k, where k – constant, space rejectors 2k tan(β/2) apart
place acceptor in the middle,
 condition satisfied
rejectors
protection zone
acceptance zone
acceptor k r β
2k tan(β/2)
malicious prover

14. Logarithmic Verification Time
basic algorithm: number of verification attempts is d/x where d – protection zone diameter
with more acceptors can be made logarithmic
add acceptor placement rule: for every point in the acceptance zone, there exists integer i≥0, such that there are no rejectors closer to this point than x2i+1 and at least one acceptor between x2i and x2i+1
modify protocol: prover doubles its signal strength every verification attempt
Theorem 5 modified protocol is correct and the maximum number of broadcasts is in O(logd)

15. Shrinking Ambiguity Zone
basic algorithm: ambiguity zone size is proportional to x
can be made arbitrarily small with additional verification attempts
recall: ambiguity zone is due to discrete signal increments
idea: tune signal strength if rejected
modified protocol: if prover is rejected and the last signal increment is z, the prover decreases the signal strength by z/2 and rebroadcasts; if no decision, the prover increases the signal stregth by z/2 and rebroadcasts; process continues until prover accepted
Theorem 6 the modified protocol is correct and the number of extra broadcast attempts is proportional log(b-a)
prover a
x/4 … b
rejected
no decision
accepted

16. Complex Signal Propagation
basic signal propagation model: unit-disk
complex (more realistic) model: a ring of possible signal reception
zone delineation for complex model:
Lemma 6: a point is in rejection zone if it is at least y closer to nearest rejector than acceptor
Lemma 7: a point is in acceptance zone if it is at least x+y closer to nearest acceptor than rejector
results similar to basic model apply
signal reception
prover r
definite
never
basic model
prover r y
definite
possible
never
complex model

17. Random Verifier Placement
modified problem
verifiers are not aware of their location
they are informed if they are inside or outside protection zone
classification
an outside verifier is rejector
a verifier whose Voronoi neighbor is outside is rejector
rest are acceptors
Theorem 7 verification protocol with random placement of verifiers solves location verification problem
border of
protection zone
rejectors
boundary
acceptance+
ambiguity zones

18. Implementation of Random Placement
rejectors
boundary
acceptors
outside verifiers
inside verifers
in practice radio neighborhood can be used to approximate Voronoi neighborhood
need to ensure appropriate verifier density on the border of protection zone
placement procedure
verifiers have read-only bit signifying inside/outside placement
classification procedure
if verifier or its neighbors have outside bit set – verifier is rejector, acceptor otherwise

19. Outline problem statement basic solution description and properties
immediate applications: securing arbitrary zones
extensions
improving efficiency
operating with non-circular signal propagation
protecting against directional antennas
using random sensor placement
stabilization and fault-tolerance

20. Stabilization of Random Placement
observe: classification decision is local – depends only on neighborhood topology
 very robust
state correction – each verifier periodically checks the inside/outside bits of the neighbors and reevaluates its classification
 global state
stabilizes
fault-contains
adaptively
in constant time/space/energy
corrupt state

21. Other Extensions and Further Info
distributed decision making – an acceptor only needs to contact neighboring rejectors
fault-tolerant rejector sets – redundant rejector sets independently covering rejection zone provide extra security and fault-tolerance guarantees
limited power provers – can be serviced with appropriately dense acceptor location
details: A. Vora, M. Nesterenko "Secure Location Verification Using Radio Broadcast”, Techreport TR-KSU-CS ,