Robust Geotag Generation Algorithms from Noisy Loran Data

for Security Applications

Di Qiu, Sherman Lo, Dan Boneh, Per EngeStanford University

ILA 2009

Sponsored by FAA Loran Program CRDA 2000-G-028

Geo-security: Why?

Doesn’t require memorization• Users don’t have to memorize location dependent signal

characteristics.

Resistant to misplaced tokens• Users won’t forget to bring location.

Can’t be delegated• Users can’t lend location to someone else.

Low awareness

Don’t need physical access to attack

2

Geo-security: Big picture

Use location-dependent signal characteristics from multiple transmitters.Restrict access of information content or electronic devices.

3

Geo-security: How?

Receiver GeotagGeneration

Database

Application

Grant/Deny?

Matching

Calibration

Verification

Desired properties:

1.Hard to forge2.Reproducible

Desired properties:

1.Hard to forge2.Reproducible

GeotagGeneration

0111000…0111000… Location 1 = 011…Location 2 = 100…Location 3 = 101…

Location 1 = 011…Location 2 = 100…Location 3 = 101…

Matching

4

Geotag applications

Loopt• Social networking

Digital Manners Policy• Microsoft

Data access control• Geo-encryption

Geo-fencing• Laptop anti-theft technology

User A

User B

Central server

xA

xB

SMS

5

Performance standards

Two hypotheses• H0: accepting as authentic user• H1: rejecting as an attacker

Two errors• False reject: accepting hypothesis H1 when H0 is true• False accept: accepting hypothesis H0 when H1 is true

6

Geotag generation

Quantization-based

Fuzzy extractor-based Pattern classification-based• k-Nearest Neighbor (kNN)• Support Vector Machines (SVM)

⎪⎩

⎪⎨⎧

∑ =⊕=

Δ+Δ=∈=

=otherwise.0

1)(')(~1 if1)',~(

))1(,[;)(

1

n

i

iiki

iTiTnTTM

kkSxkiT

7

Quantization-based geotag reproducibility

Tamper-resistant device and self-authenticated signals for spoofing attacks.Temporal variation degrades performanceParameters --TD, ECD,SNR-- from GRI 9940Non-monotonic trend comes from quantization

2σ 3σ 4σ 5σ 6σ 7σ 8σ10

−2

10−1

100

Quantization Steps

False

Rej

ect R

ate

Reproducibility of Loran Tag

8

Fuzzy extractor

9

Generationx P Reproducex’P

…

T T’

Definition. A fuzzy extractor is a tuple (M, t0, Gen, Rep), where M is the metric space with a distance function dis, Gen is a generate procedure and Rep is a reproduce procedure, which has the following properties:

1.If dis(x, x’) ≤ t0, T’ = T.2.If dis(x, x’) ≥ t0, T’ ≠ T.

Y. Dodis el al., “Fuzzy extractors: How to generate strong keys from biometrics and other noisy data,” 2004.

Three fuzzy extractors for location data

Euclidean metric fuzzy extractor• Noise, bias, and quantization errors• Adjust offsets• Real numbers

Hamming metric fuzzy extractors• Constructions

░ Reed-Solomon based fuzzy extractor░ Secret Sharing based fuzzy extractor

• Offline transmitter• Inputs are integers: quantized values of location parameters

10

Performance of Euclidean fuzzy extractor

2σ 3σ 4σ 5σ 6σ 7σ 8σ10

−2

10−1

100

Quantization Steps

False

Rej

ect R

ate

Euclidean Metric Fuzzy Extractor Performance

without fuzzy extractorwith fuzzy extractor

84% reduction

11

RS-based fuzzy extractor – “Locking”

12

Receiver x Quantization qx

Mapping MatrixGeneration

QuantizationLevels

1 2 3 4 … n

q1

q2

q3

… … … … … …

c1

c2

c3

ContinuousQuantized

Random Generator

RSEncode c

T

xqc =

RS-based fuzzy extractor – “Unlocking”

13

q’x

… … … … … …

c1

c2

c3 c1

c2

c’3

cn

…RS

Decode T’

Receiver x’ Quantization q’x

ContinuousQuantized

T’=T if dis(q’x, qx) ≤ t, t is a design parameter

Performance analysis: RS-based

14

∑+=

−−⎟⎟⎠

⎞⎜⎜⎝

⎛=

n

tj

jnj ppjn

1)1(}failure decodeor error Pr{

p symbol error

t ≤ 2

Pattern classification

Goal: Extract decision rules from data to assign class labels to future data samples.• Maximize the difference between classes• Minimize the within-class scatter

The quality of a feature vector is essential to spatial discrimination/decorrelation.

“Good” features “Bad” features

Properties

Linear separability Non-linear separability Highly correlated Multi-modal15

Dimensionality reduction

“Curse of dimensionality” – high dimensional data are difficult to work with.• The added parameters or features can increase noise• Enough observations to get good estimates

Dimensionality reduction• Efficiency – computation and storage costs• Classification performance• Ease of modeling

16

Geotag generation using pattern classification

ClassificationSignal processingData collection Dimensionalityreduction

Model selection

T = f(ω)

Geotag database

Calibration

?Decisionmaking

Verification

T’=f(ω’)

T = f(ω)

Matching

17

K-Nearest Neighbor (kNN)

‘Memory’ based classification

No training phase is required: ‘lazy’ learning approach

Given data point x, find the k nearest training inputs x1, x2,…, xk to x using a distance metric.

Large k produces smoother boundaries and reduces the impact of noise.

Computational cost

x1

x2

x

18

Visualization of kNN, k=8

Easy to implement but computationally intensive.Euclidean distance metric

-30 -20 -10 0 10 20 30 40 50-10

-5

0

5

10

x1

x 2

KNN, k=8

Class 1Class 2Class 3

19

Support Vector Machines (SVM)

Optimal separating hyperplane – find a hyperplane with minimum misclassification rateNon-linear SVM• Perform a non-linear mapping of the feature vector x onto a

high-dimensional space• Construct an optimal separating hyperplane in the high-

dimensional spaceTradeoff – margin and capacity

ϕ(x) wTzx z y

x1

x2

Large Margin

x1

x2

Small Margin

20

Visualization of SVM

-30 -20 -10 0 10 20 30 40 50-10

-5

0

5

10

x1

x 2

SVM, Kernel argument=5

Class 1Class 2Class 3

Sequential Minimal Optimization (SMO) is applied to solve the optimization problem.Large kernel argument reduces misclassification errors but lowers discrimination ability.

-30 -20 -10 0 10 20 30 40 50-10

-5

0

5

10

x1

x 2

SVM, Kernel argument=1

Class 1Class 2Class 3

21

Data set to evaluate spatial discrimination

22

Classifier visualization

-0.2 -0.1 0 0.1 0.2 0.3-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

x1

x 2

SVM

Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12Class 13

-0.2 -0.1 0 0.1 0.2 0.3-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

x1

x 2

KNN, k=8

Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12Class 13

23

Spatial discrimination comparison

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

Separation [m]

Fals

e ac

cpet

rat

e (F

AR

)Performance Comparison

SVMkNN, k=8Quantization

24

85% reduction

Conclusion

Modeled geo-security and standardized the performance evaluation.• Geotag reproducibility and spatial discriminiation

Developed fuzzy extractors to reduce continuity risks.• Euclidean metric for noise, seasonal bias, and quantization error• Hamming metric for offline transmitters

Applied pattern classification for geotag generation to improve spatial discrimination.• kNN and SVM

25

Acknowledgment

The authors would like to thank Mitch Narins of the FAA, Dr. Greg Johnson and Ruslan Shalaev at Alion Science & Technology and USCG LSU for their support and help during the research.

26

Thank you!

Questions?

27

Backup slides

28

Geotag reproducibility

90-day seasonal monitor dataSame hypothesis problemTradeoff by varying kernel argument

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Kernel Argument

Fals

e re

ject

rat

e (F

RR

)

SVM

29