Sensor-based Wearable PUF

Kazuhide Fukushima, Seira Hidano and Shinsaku Kiyomoto

KDDI R&D Laboratories, Inc., 2-1-15 Ohara, Fujimino-shi, Saitama, 356-8502, Japan

Keywords:

Wearable, IoT, Smartphone, Sensor, Accelerometer, Gyroscope, PUF.

Abstract:

The Physically Unclonable Function (PUF) is a technique that generates unique device identiﬁers based on

variations in the manufacturing process. The Internet of Things (IoT) has become widespread, and various

kinds of devices are now available. Device authentication and key management are essential to provide a

secure service to these devices. We can use the unforgeable identiﬁer generated by the PUF as a key for

encryption and authentication. However, the existing PUFs require a dedicated hardware or low-level software,

i.e., driver. Thus, they are impractical to use on smartphones or IoT devices due to the severe limitations

of production cost and power consumption. In this paper, we propose a sensor-based PUF that utilizes the

accelerometer and gyroscope, which are widely available on smartphones and IoT devices. We implement

the proposed PUF on a smartwatch and show that accelerometer-based PUF achieves good usability, extreme

robustness, and a high entropy of 91.66 bits.

1 INTRODUCTION

Android is an open mobile platform developed by

the Open Handset Alliance (OHA) led by Google,

Inc (Open Handest Alliance, 2010). It had grown

to be the top-share smartphone platform in the

world (82.8% market share) in the second quarter

of 2015 (IDC, 2015), and more than 1,800,000 ap-

plications are available from the Android Market as

of November 2015 (Statista, 2015). Google have

announced the release of the Brillo, which is an

Android-based platform for the Internet of Things

(IoT) (Google, 2015). Users can add new features to

their smartphones and IoT devices by installing appli-

cations. However, an attacker may analyze applica-

tions to ﬁnd a secret key to decrypt protected content

or get authentication information illegally.

One approach is to generate the unique key dy-

namically based on the device information of smart-

phone or IoT device. For example, the MAC ad-

dress of a Wi-Fi adapter and Bluetooth adapter has

been used as the input to a key generation func-

tion. However, the MAC address can be eas-

ily modiﬁed in a device where the administrator

privilege is compromised. Furthermore, the cur-

rent version of Android and iOS prohibit general

applications from getting the MAC address. An-

droid 6.0 (API level 23) returns a ﬁxed value

02:00:00:00:00:00 for WiﬁInfo.getMacAddress()

and BluetoothAdapter.getAddress() that is a method

to get the MAC address of the Wi-Fi and Bluetooth

adapter respectively (Google, 2015). iOS7 returns the

same value for similar APIs (Apple, 2013). The pro-

tection of the key generation algorithm is another crit-

ical issue. The Android SDK contains an obfuscation

tool: ProGuard (Lafortune, 2002) to protect against

unauthorized analysis and modiﬁcation. Nonetheless,

this mechanism offers only limited protection since it

relies solely on a software mechanism.

Another approach is hardware-based protection,

and one idea is to use tamper-proof hardware. Mo-

bile phones have a tamper-proof device, such as a user

identity module (UIM) (3GPP2, 2000) or subscriber

identity module (SIM) (The 3rd Generation Partner-

ship Project (3GPP), 1990) that provides secure stor-

age for service-subscriber keys and secure computa-

tional capability. The serial number of the SIM card

can be used as a valid identiﬁer. Android provides

the getSimSerialNumber() method to get the identi-

ﬁer. The Trusted Computing Group (TCG) has estab-

lished technology speciﬁcations for the Trusted Plat-

form Module (TPM) that is available in smartphones

and PCs (Trust Computing Group, 2016). The TPM

provides the cryptographic functions to enhance the

security of the platform, and it is used as a root of

trust. However, most IoT devices, including wear-

ables, do not have dedicated hardware.

The Physically Unclonable Function (PUF),

which generates unique device identiﬁers based on

variation in the manufacturing process, is a promis-

Fukushima, K., Hidano, S. and Kiyomoto, S.

Sensor-based Wearable PUF.

DOI: 10.5220/0005946702070214

In Proceedings of the 13th International Joint Conference on e-Business and Telecommunications (ICETE 2016) - Volume 4: SECRYPT, pages 207-214

ISBN: 978-989-758-196-0

207

ing alternative. We can use the device identiﬁer as

a key. The device identiﬁer generated by the PUF

is hard to analyze since it does not appear in digital

format on the device. However, the existing PUFs

depend on additional and dedicated hardware; thus,

they are impractical to use in IoT devices due to

the severe limitations of production cost and power

consumption. The Static Random-Access Memory

(SRAM) PUF and Dynamic Random-Access Mem-

ory (DRAM) PUF utilize existing hardware, but they

are still infeasible since they require low-level soft-

ware, i.e., a driver.

Smartphones and IoT devices have various sen-

sors and hardware such as an accelerometer, gyro-

scope, proximity sensor, microphone, speaker, and

camera. Most wearables have an accelerometer and

gyroscope to change the behavior based on user ac-

tions. In this paper, we propose a sensor-based PUF

that utilizes the characteristic values of accelerometer

and gyroscope. The proposed PUF is widely available

on smartphones and IoT devices.

2 RELATED WORK

The Physically Unclonable Function (PUF) (Pappu

et al., 2002) is a technique that generates unique de-

vice identiﬁers based on variations in the manufactur-

ing process. The Arbiter PUF utilizes the difference

in the signal transmission delay (Gassend et al., 2004;

Lee et al., 2004), and the Glitch PUF is based on the

signal transition (Suzuki and Shimizu, 2010). Kumar

et al. proposed the Butterﬂy PUF, which uses the ini-

tial state of ﬂip-ﬂops (Kumar et al., 2008). Gassend

et al. proposed the Ring Oscillator PUF based on the

difference in the oscillating frequency of the ring os-

cillator (Gassend et al., 2002). Finally, Tuyls et al.

proposed the Coating PUF based on the capacitance

of the coating materials containing dielectric parti-

cles (Tuyls et al., 2006). These PUFs depend on addi-

tional and dedicated hardware; thus, they are imprac-

tical to use in smartphones or IoT devices.

Some PUFs based on the existing hardware have

been proposed. An SRAM PUF utilizes the initial

data in memory when the power is turned on (Chopra

and Colopy, 2009; Maes et al., 2009a; Maes et al.,

2009b). Krishna et al. proposed a memory-cell-based

PUF that uses intrinsic process variations in the read

and write reliability of cells in static memory (Krishna

et al., 2011). Liu et al. proposed a DRAM PUF that

uses the decay time and output stability (Liu et al.,

2014). Keller et al. proposed a PUF based on the

inﬂuence of temperature and time on the charge de-

cay (Keller et al., 2014). A DRAM PUF proposed

by Tehranipoor (Tehranipoor et al., 2015) uses initial

data similar to an SRAM PUF. However, the SRAM

and DRAM PUFs are still impractical in smartphones

or IoT devices. They require dedicated drivers to ex-

tract the characteristic features of devices, which im-

poses an additional cost.

Thus, we propose a sensor-based PUF for smart-

phones and IoT devices. The proposed PUF can ex-

tract the characteristic values of sensors through the

standard API of the OS. Thus, it does not require the

additional hardware and dedicated drivers.

3 PROPOSED METHOD

We propose a sensor-based PUF for smartphones and

IoT devices including wearables. The proposed PUF

acquires the maximum and minimum values of the ac-

celerometer and gyroscope as the characteristic values

of the sensors and generates device identiﬁers based

on these characteristic values. We describe the fea-

tures of the accelerometer and gyroscope in Section

3.1 and 3.2, respectively. Section 3.3 describes the

method to generate a device identiﬁer based on char-

acteristic values of the sensors.

3.1 Accerelometer

A 3-axis accelerometer measures the accelerations

along the x, y, and z-axis. Figure 1 shows the direc-

tion of these axes. Most smartphones and wearables

have an accelerometer that can measure up to ±2 G

(19.6 m/s

) or ±4 G (39.2 m/s

The maximum and minimum values of the ac-

celerometer along each axis differ from one device

to another. Thus, these values can be used to gen-

erate device identiﬁcation data. We construct a 6-

dimensional data set that consists of the maximum

and minimum values along the x, y, and z-axis and

extract digits that have enough variety. The charac-

teristic value of the accelerometer can be achieved by

concatenating these digits.

3.2 Gyroscope

A 3-axis gyroscope measures the angular velocities

around the x, y, and z-axis. Figure 2 shows the ro-

tation direction around these axes. Many wearables

have a gyroscope that can measure up to 2000 deg/s

(34.9 rad/s).

The maximum and minimum values of the gyro-

scope around each axis differ from one device to an-

other. Thus, these values can be used to generate de-

vice identiﬁcation data. We construct a 6-dimensional

SECRYPT 2016 - International Conference on Security and Cryptography

208

Figure 1: Axis direction of accelerometer.

Figure 2: Rotation direction of gyroscope.

data set that consists of the maximum and minimum

values around the x, y, and z-axis and extract digits

that have enough variety. The characteristic value of

the gyroscope can be achieved by concatenating these

digits.

3.3 Device Identiﬁer Generation

We now describe the detailed behavior of the sensor-

based PUF to generate the device identiﬁer. The iden-

tiﬁer generation process consists of the acquisition of

the characteristic values of the sensors (step 1) and

identiﬁer generation using a one-way function (step

2).

Step 1 Acquisition of the Characteristic Values of

the Sensors. The sensor-based PUF requires the

maximum values and minimum values of the ac-

celerometer and gyroscope. A user needs to shake

and twist the hand holding or wearing a device. This

process stores the tentative maximum and minimum

values of sensors. These tentative values are updated

when the current sensor value is larger or smaller than

the tentative maximum or minimum value, respec-

tively. We consider the tentative values as the actual

maximum and minimum values after a user shakes the

device for a speciﬁed time (a few seconds), and the

tentative values are stable. We show a sample imple-

Figure 3: Fuzzy extractor in registration phase.

mentation of this step in the appendix.

Step 2 Generation of Device Identiﬁer. The

sensor-based PUF uses a one-way function to gener-

ate a device identiﬁer from the concatenated charac-

teristic values of the accelerometer and gyroscope. A

device identiﬁer has to vary with each application or

service when the identiﬁer is used as a key. In this

case, applications or services can concatenate a seed

to the input to the one-way function to fulﬁll the re-

quirement.

We can use a fuzzy extractor (Dodis et al., 2008)

to deal with minor deviations of the characteristic val-

ues of the sensors. The fuzzy extractor generates and

registers a secure sketch SS for future identiﬁer ex-

tractions in the registration phase. It generates the

random number r, encoded with an error-correcting

code C. The secure sketch SS is the exclusive-or

of the characteristic value of sensor w, and C(r) or

SS = w ⊕C(r). The random number r is disposed of

when the registration process completes. In the de-

vice identiﬁer generation phase, the fuzzy extractor

recovers the original characteristic value w from the

secure sketch SS calculated from the current charac-

teristic value w

in the device. It calculates C(r) as

C(r) = EC(SS ⊕ w

) = EC[C(r) ⊕ (w ⊕ w

)],

where EC is the error-correcting component and w ⊕

denotes the minor deviation of the characteristic

values of the sensor. Finally, the fuzzy extractor gen-

erates the device identiﬁer as

DeviceID(w

,s) = h(w ⊕ s) = h(SS ⊕C(r) ⊕ s)

using the one-way function h. Figure 3 shows the

fuzzy extractor in the registration phase and Figure 4

shows the device identiﬁer generation phase.

The sensor values for each axis can be considered

as independent. Thus, the sensor-based PUF sepa-

rately applies the fuzzy extractor to each character-

istic value (maximum and minimum values for x, y,

and z-axis).

The proposed PUF encodes the characteristic val-

ues of the sensor to binary data with Gray code. The

Hamming distance between adjacent values is one en-

coding; thus, minor deviations up to ±t can be re-

covered with the error correcting code of t correction

Sensor-based Wearable PUF

209

Figure 4: Fuzzy extractor in device identiﬁer generation

phase.

Table 1: Maximum and minimum values of acceleration.

Maximum Minimum

x-axis 19.460205 m/s

-19.539200 m/s

y-axis 19.228836 m/s

-19.770569 m/s

z-axis 19.755707 m/s

-19.243698 m/s

capability. However, the robustness achieved by the

fuzzy extractor has a trade-off with entropy. We dis-

cuss the trade-off in section 5.2.

4 IMPLEMENTATION

We have implemented the sensor-based PUF as an

Android Wear application. The PUF application is

executed on an LG Watch Urbane smartwatch to eval-

uate the entropy and robustness.

The LG Watch Urbane has an accelerometer that

can measure from -2 G (-19.6 m/s

) to 2 G (-19.6

m/s

). The maximum and minimum values of the sen-

sor vary with the devices and axis. Table 1 shows an

example. The number in the second decimal place

and the following digits have enough variety. Thus,

the PUF application extracts the numbers in the sec-

ond to sixth decimal place as a character string with

ﬁve ﬁgures from each of the maximum and minimum

values of the accelerations along the x, y, and z-axis.

The application can acquire the characteristic value

of the accelerometer with 30 characters by concate-

nating these six character strings.

The LG Watch Urbane has a gyroscope that can

measure from -2,000 degree/s (-34.9 rad/s) to 2,000

degree/s (34.9 rad/s). Table 2 shows an example. The

number in the fourth decimal place and the following

digits have enough variety. Thus, the PUF applica-

tion extracts the numbers in the fourth to sixth deci-

mal place as a character string with three ﬁgures from

each of the maximum and minimum values of angular

velocities around the x, y, and z-axis. The application

can acquire a characteristic value of the accelerometer

with 18 characters by concatenating these six charac-

ter strings.

The PUF application generates a device identiﬁer

with 128-bit length from the characteristic value of

Table 2: Maximum and minimum values of angular veloc-

ity.

Maximum Minimum

x-axis 34.997101 rad/s -35.000763 rad/s

y-axis 34.997055 rad/s -35.000809 rad/s

z-axis 34.997803 rad/s -35.000061 rad/s

Figure 5: Screenshot of sensor-based PUF application.

an accelerator or gyroscope by using SHA-256 and

truncating the last 128 bits. We do not use the fuzzy

extractor in the application since it extracts the iden-

tical characteristic values from the accelerometer and

gyroscope consistently.

Figure 5 shows a photo of the PUF application on

the LG Watch Urbane. The application regenerates

and displays the generated device identiﬁer whenever

the tentative maximum and minimum values of sen-

sors are updated. The tentative maximum and mini-

mum values are reset to zero when the user presses the

reset button (RST). The application stores the device

identiﬁer when the register button (REG) is pressed,

and deletes the identiﬁer when the unregister button

(URG) is pressed. We can use this function to eval-

uate the robustness of the device identiﬁer. The ap-

plication compares the generated identiﬁer and stored

identiﬁer and displays ”OK” if they are identical or

”NG” otherwise.

We have compared the usability of the

accelerometer-based PUF and gyroscope-based

PUF in an LG Watch Urbane. The accelerometer-

based PUF can generate the same identiﬁer within

a few seconds. The measurement range of the ac-

celerometer is from -2 G to 2 G, and the sensor value

quickly reaches the maximum or minimum when a

user shakes the device. However, the identiﬁer gener-

ated by the gyroscope-based PUF is not stable. The

measurement range of the gyroscope is from -2,000

degrees/s to 2,000 degrees/s. A user has to rotate the

device around three axes at a rate of six revolutions

per second, which is difﬁcult if the user continues to

wear the device. As a result, the accelerometer-based

PUF is more useful than the gyroscope-based PUF in

SECRYPT 2016 - International Conference on Security and Cryptography

210

an LG Watch Urbane. Thus, we evaluate the entropy

and robustness of the accelerometer-based PUF in the

following section.

5 EVALUATION

We evaluate the compatibility of the sensor-based

PUF with the requirements for PUFs. Then, we evalu-

ate the robustness and entropy of the device identiﬁer

generated by the accelerometer-based PUF.

5.1 Compatibility with Requirements

Maes and Verbauwhede showed the requirements

for PUFs: evaluable, unique, reproducible, un-

predictable, one-way, unclonable and tamper evi-

dent (Maes and Verbauwhede, 2010). We show the

compatibility of the sensor-based PUF with these re-

quirements.

Evaluable. The sensor-based PUF uses the charac-

teristic values of the existing sensors, and these val-

ues can be acquired through the existing APIs. The

PUF can be implemented as a general application at

minimal cost. Furthermore, the sensor-based PUF

uses only the extraction and concatenation of charac-

ter strings, one-way function, and optional exclusive-

or and operations for the error-correcting code. Thus,

the PUF is feasible in resource-restricted devices.

Unique. The device identiﬁer generated by the

sensor-based PUF is unique since it has high entropy.

We evaluate the entropy of the proposed PUF in sec-

tion 5.2.

Reproducible. The device identiﬁer generated by

the sensor-based PUF is reproducible since it has high

robustness. We evaluate the robustness of the pro-

posed PUF in section 5.3.

Unpredictable. The sensor-based PUF is not appli-

cable to the challenge-response model. Thus, we can-

not evaluate the unpredictability of the proposed PUF.

One-way. The sensor-based PUF uses a one-way

function to generate the device identiﬁer from the

characteristic values. The one-way function guaran-

tees this requirement for the sensor-based PUF.

Unclonable and Tamper Evident. The sensor-

based PUF acquires the characteristic values of sen-

sors using software (application) and generates the

device identiﬁer. Thus, we have to protect against

acquisition and modiﬁcation of the characteristic val-

ues and generated device identiﬁcation. For exam-

ple, attackers can make a clone of the sensor-based

PUF by acquiring the characteristic values of the sen-

sor. They can also modify the values of the sensors or

the generated device identiﬁer in the memory. Thus,

we have to protect against these attacks by applying

memory protection techniques(Ostrovsky, 1990; Gol-

dreich and Ostrovsky, 1996; Nakano et al., 2012).

Attackers may modify the identiﬁer generation algo-

rithm so that it outputs an arbitrary identiﬁer. We have

to protect these attacks by applying software tamper-

proof techniques to prevent modiﬁcation of the appli-

cation. We will study the security against physical

attacks in our future research.

5.2 Entropy

We have evaluated the Quadratic Renyi entropy of the

device identiﬁer generated by an accelerometer-based

PUF. The Quadratic Renyi entropy is deﬁned as:

(B) = −log

∑

b∈B

(b)

(B) is a particular case (α = 2) of the Renyi entropy

(B), which is deﬁned as:

(B) =

1 − α

log

∑

b∈B

(b)

The Shannon entropy is deﬁned as

H(B) = −

∑

b∈B

(b)log

(b).

The Renyi entropy and Shannon entropy have the re-

lationship: lim

α→1

(B) = H(B). The Reyni en-

tropy is decreasing with respect to α. Thus, the

Quadratic Renyi entropy is smaller than or equal to

the Shannon entropy, or H

(B) ≤ H(B). The same

holds when the B is according to the uniform distri-

bution.

The

∑

b∈B

(b)

is the probability that the two

sampled values are identical, and the Quadratic Renyi

entropy is referred to as the collision entropy. The

Quadratic Renyi entropy can be written as

(B) = −log

(0)

with the probabilistic mass function of the distance D

between two sampled values p

(d).

The Quadratic Renyi entropy has been used to

evaluate the entropy of biometric information (Hi-

dano et al., 2010; Hidano et al., 2012). However, it is

Sensor-based Wearable PUF

211

difﬁcult to predict the probability p

(d) directly with

a limited number of samples. Thus, we used a non-

parametric approach with a speciﬁc kernel function

that can estimate p

(d) with a small error. Koko-

nendji (Kokonendji et al., 2007) proposed a non-

parametric estimation of probability mass functions

using discrete triangular distribution. The probability

mass function can be estimated as

ˆp

(x) =

∑

i=1

a,h,x

where X

, X

, . . . , X

are random samples from a

count distribution with an unknown probability mass

function. T

a,h,x

(X) is the probability mass function of

the discrete triangular distribution of the order h and

with the arm a. T

a,h,x

(X) is given as:

a,h,x

(X) =

(

(a+1)

−|X−x|

P(a,h)

(X −a ≤ x ≤ X + a)

0 (otherwise)

where P(a, h) = (2a + 1)(a + 1)

− 2

∑

k=0

is the

normalizing constant. p

(0) can be estimated as

ˆp

(0) =

∑

i=0

[(a + 1)

− i

]

P(a,h)

where n

is the number of samples whose distance is

i. The asymptotic mean integrated squared errors are

given by:

AMISE(a,h) =

(a + 1)

nP(a,h)

[V (a,h)]

∑

x∈N

(x)]

where V (a,h) is the variance of T

a,h,x

(X) as

V (a,h) =

P(a,h)

a(2a + 1)(a + 1)

− 2

∑

k=0

h+2

and p

(x) is the second derivative of p(x) as

(x) =











p(2) − 2p(1) + p(0) (x = 0)

p(3)−p(2)−p(1)+p(0)

(x = 1)

p(x+2)−2p(x)+p(x−2)

(otherwise)

AMISE(a,h) is increasing with respect to a; thus,

∗

= 1 is the optimal parameter for a. The optimal

parameter h

∗

for h is given by:

∗

= argmin

h>0

AMISE(1,h).

We acquired 90 strings, which are the characteris-

tic values of accelerometers described in section 3.1,

from 15 of the same wearables (LG Watch Urbanes).

Each string ranges from 00000 to 99999 and can be

encoded with a 17-bit binary value. We exhaustively

compared the binary values and studied the distribu-

tion of the Hamming distance.

Table 3: Distribution of Hamming distance.

Distance Frequency

0 0

1 2

2 5

3 24

4 92

5 193

6 394

7 646

8 711

9 729

10 572

11 354

12 187

13 70

14 22

15 3

16 1

17 0

Total 4,005

Table 3 shows the distribution of the Hamming

distance, and it is similar to the binomial distribution.

Thus, we used p(x) as the probabilistic mass function

of the binomial distribution B(17, 1/2) to ﬁnd the op-

timal parameter h

∗

. AMISE(1,h) is increasing with

respect to h; however, ˆp

(0) goes to 0 as h → 0. Thus,

∗

= 1 and h

∗

= 1/12 are used as the optimal param-

eters. The estimated Quadratic Renyi entropy of the

artiﬁcially generated histogram of the binomial distri-

bution B(17, 1/2) is 16.19 bits using the optimal pa-

rameter setting.

We can estimate ˆp

(0) = 2.52 × 10

−5

, from

the distribution of the Hamming distance in Ta-

ble 3. Thus, the Quadratic Renyi entropy is

(B) =

log

ˆp

(0) or 15.28 bits. The device identiﬁer based

on the accelerometer consists of six-dimensional data,

and the total entropy is 91.66 bits.

We discuss the trade-off between entropy and ro-

bustness in the case where the sensor-based PUF uses

the fuzzy extractor. The entropy loss of each char-

acteristic value of the sensors is at least log

∑

k=0





bits according to the Hamming bound. n is the bit

length of the encoded characteristic value, and t is

the correction capability of the error-correcting code.

The total entropy loss is at least 6log

∑

k=0





bits.

Table 4 shows the relationship between the correc-

tion capability of the error-correcting code and the up-

per bound of the total entropy of the device identiﬁer

generated by the sensor-based PUF. The device iden-

tiﬁer generated by the accelerometer-based PUF can

achieve more than 60 bits of entropy when the fuzzy

extractor is not used, or when the fuzzy extractor uses

the error-correcting code with one-bit correction ca-

pability.

SECRYPT 2016 - International Conference on Security and Cryptography

212

Table 4: Entropy loss due to error correction.

Capability Entropy

0 91.66

1 66.64

2 48.06

3 33.43

4 21.75

5 12.47

5.3 Robustness

The sensor-based PUF using an accelerometer and

gyroscope can generate the identical device identiﬁer

within the same device without the fuzzy extractor.

We conﬁrmed that the device identiﬁer generated by

the accelerometer-based PUF is consistent by the fact

that the same user generates the same identiﬁer more

than 1,000 times. Furthermore, more than ten users

can generate the same identiﬁcation within the same

device. The accelerometer-based PUF generates the

same device identiﬁer regardless of the surrounding

temperature. Finally, it generates the same identiﬁer

in -5 degrees Celsius and 90 degrees Celsius and at

2000 meters of altitude on a mountain.

6 CONCLUSION

In this paper, we proposed a sensor-based PUF. The

sensor-based PUF utilizes the accelerometer and gy-

roscope that are widely available in smartphone and

IoT devices. We implemented the proposed PUF on a

smartwatch and showed that the accelerometer-based

PUF achieves good usability, extreme robustness, and

a high entropy of 91.66 bits.

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@Override

public void onSensorChanged

(SensorEvent event) {

if (event.sensor.getType() ==

Sensor.TYPE_ACCELEROMETER) {

boolean upd = false;

float x = event.values[0];

float y = event.values[1];

float z = event.values[2];

if (x > maxX) { maxX = x; upd = true; }

if (x < minX) { minX = x; upd = true; }

if (y > maxY) { maxY = y; upd = true; }

if (y < minY) { minY = y; upd = true; }

if (z > maxZ) { maxZ = z; upd = true; }

if (z < minZ) { minZ = z; upd = true; }

if (upd) {

// Generate device identifier based

// on updated tentative values

deviceId = generateDeviceId();

}

Figure 6: Acquisition of maximum and minimum values of

the accelerometer.

APPENDIX

Figure 6 shows a sample implementation to acquire

the maximum and minimum values of the accelerom-

eter in an Android device. The ﬁelds maxX, minX,

maxY, minY, maxZ, and minZ are ﬁelds that store the

tentative maximum and minimum values of acceler-

ations along the x, y and z-axis. The method on-

SensorChanged is called when the sensor values have

changed. We retrieve the event from the accelerome-

ter by using the if statement. The acceleration along

the x, y, and z-axis is stored in the values array. The

same code where Sensor.TYPE ACCELEROMETER is

replaced with Sensor.TYPE GYROSCOPE can acquire

the maximum and minimum values of angular veloc-

ities around each axis.

The sensor-based PUF needs to set the highest

sampling frequency on the sensors so that we can ef-

ﬁciently acquire the maximum and minimum values.

We can set the sampling frequency through the reg-

isterListener method in Android. The method regis-

ters SensorEventListener that is used to receive no-

tiﬁcations from the SensorManager when the sen-

sor values have changed. The notiﬁcation frequency

is highest, and the period is a few milliseconds if

SENSOR DELAY FASTEST is passed to the method.

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