传感器的工厂校准指纹识别（Factory Calibration Fingerprinting of Sensors，IEEE TIFS） 原文标题：

IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 1

Factory Calibration Fingerprinting of Sensors

Jiexin Zhang, Alastair R. Beresford, and Ian Sheret

Abstract--Device fingerprinting aims to generate a distinctive any time and iOS also provides an option to limit access to
signature, or fingerprint, that uniquely identifies individual com- this identifier. Moreover, apps requesting this identifier but do
puting devices. Fingerprints may be a privacy concern since not serve any in-app advertisements will be rejected by the
apps and websites can use them to track user activity online. App Store. Last but not least, the advertising identifier is not
To protect user privacy, both Android and iOS have included a accessible from mobile browsers. Similarly, although Android
variety of measures to prevent such tracking. In this paper we still allows apps to access the ANDROID_ID, it cannot be
present a new type of fingerprinting, factory calibration finger- obtained from a website and its value is scoped by the signing
printing, that bypasses existing tracking protection. Our attack key and user since Android 8. Different apps on a device will
recovers embedded per-device factory calibration data from the have different values of ANDROID_ID and a factory reset
accelerometer, gyroscope, and magnetometer sensors that are or an APK signing key change may also change its value [1].
pervasive in modern smartphones by careful analysis of the Thus, it cannot be used to track users across apps and websites.
sensor output alone. We discuss the factory calibration behaviour
of each sensor and show that the calibration fingerprint is fast We have developed a new type of fingerprinting attack,
to generate, does not change over time or after a factory reset, the factory calibration fingerprinting attack, which can by-
and can be used to track users across apps and websites without pass these restrictions. Modern mobile devices are shipped
any special permission from the user. We find the calibration with a variety of embedded motion sensors that apps rely
fingerprint is very likely to be globally unique for iOS devices, on to provide rich functionality, including workout tracking,
with an estimated 67 bits of entropy for the iPhone 6S. In and improved user interaction. Natural variation during the
addition, we have analysed 146 Android device models from 11 manufacture of embedded sensors means that the output of
vendors and found the attack also works on recent Google Pixel each sensor is unique and therefore such natural variation may
devices. For Pixel 4/4 XL, we estimate the calibration fingerprint be exploited to create a device fingerprint.
provides about 57 bits of entropy. Following our disclosures,
Apple deployed a mitigation in iOS 12.2 and Google in Android Previous work applies machine learning techniques directly

1. We analyse Apple's fix and show that the mitigation is to sensor data in an attempt to create device fingerprints for

imperfect although it is likely to be sufficient in most threat smartphones; this has been shown to be ineffective (VII).
models. In our attack, instead of feeding sensor outputs into machine
learning algorithms, we infer the per-device factory calibration
I. INTRODUCTION data from the output of gyroscope, accelerometer, and mag-
netometer to construct a globally unique fingerprint. Overall,
When users visit a website, their web browser provides a our attack has the following advantages:
range of information to the website, including the name and
version of the browser, screen size, fonts installed, and so on. Practical the attack can be launched by any website or
Ostensibly, this information allows the website to provide a any app on a vulnerable device without requiring
great user experience. Unfortunately, this same information Efficient explicit confirmation or interaction by the user.
can also be used to track users. In particular, this information Unique the attack takes less than one second to generate
can be used to generate a distinctive signature, or device Robust a fingerprint.
fingerprint, to identify users. Similarly, mobile app developers Effective the attack generates a globally unique fingerprint
can also generate a device fingerprint using the idiosyncrasies for vulnerable devices.
of software and hardware. the calibration fingerprint never changes, even
after a factory reset.
Realising the potential risk to user privacy, both iOS and the attack provides an effective means to track
Android have included measures to prevent such tracking. On users as they browse across the web and move
iOS, developers do not have access to the UDID (Unique between apps on their device.
Device IDentifier), IMEI (International Mobile Equipment
Identity), and MAC address of hardware modules after iOS In our previous research we have focused mostly on iOS

1. Similar restrictions are also deployed on Android O; de- devices and demonstrated its effectiveness on gyroscope and

velopers cannot get access non-resettable unique hardware magnetometer data available in iOS [2]. This paper extends our
identifiers even if users grant the app dangerous permissions previous work: we present our latest findings on accelerometer
such as the READ_PHONE_STATE permission. While it is still calibration on iOS devices (III-E); we conduct a large-scale
possible to track users by the advertising identifier on both factory calibration behaviour analysis on popular Android
iOS and Android, this method comes with several drawbacks. device models (III-F); we compare the calibration fingerprint
First, both platforms allow users to reset this identifier at with the Fingerprintjs2 fingerprint for Google Pixel phones
(IV-B); we analyse the calibration fingerprint for vulnerable
J. Zhang and A. Beresford are with the Department of Computer Science Pixel devices and estimate entropy for each model (V-B).
and Technology, University of Cambridge, Cambridge, UK (email: {jz448,
arb33}@cl.cam.ac.uk).

I. Sheret is with Polymath Insight Limited, Stevenage, UK (email:
ian.sheret@polymathinsight.co.uk).
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2

We followed a coordinated disclosure procedure and re- Calibration aims to identify and remove the deterministic
ported the vulnerability to Apple on 3rd August 2018 and errors from the sensor. Many commercial sensors are fac-
Google on 10th December 2018. In iOS 12.2, Apple adopted tory calibrated and their calibration parameters are stored in
our suggestion and added random noise to sensor outputs firmware or non-volatile memory, providing accurate measure-
(CVE-2019-8541) while Google decided to round sensor out- ments off the shelf [5]. In the context of mobile devices, the
puts to a multiple of nominal gain in Android 11. In addition, main benefit of per-device calibration is that it allows more
Apple removed access to motion sensors from Mobile Safari accurate attitude estimation [6]. By contrast, sensors embedded
by default and in later versions also removed motion sensor in low-cost smartphones are usually poorly calibrated due to
access from WebKit. However, in this paper we show that the high cost and complexity of factory calibration [7]. For an
Apple's fix is imperfect since a calibration fingerprint can still individual manufacturer, the choice of sensor calibration is,
be extracted if more sensor data is available (VI). therefore, an engineering trade-off.

We make the following contributions in this paper: MEMS sensors usually convert and store the analogue

1. We introduce a new method of fingerprinting a device: measurement in a digital register through an Analogue-to- Digital Converter (ADC) module. For a triaxial motion sensor, the factory calibration fingerprinting attack. let A = [Ax, Ay, Az]T be the sensor ADC output. Considering
2. We describe how factory calibration data can be ex- all three kinds of deterministic errors, the output of the motion sensor can be represented by the following equation [8]: tracted from the accelerometer, magnetometer, and gy- roscope found on recent smartphones. Ox Sx 0 0 1 Nxy Nxz Ax + Bx
3. We demonstrate that the factory calibration data of the magnetometer and gyroscope together form a reliable Oy = 0 Sy 0 Nyx 1 Nyz Ay + By (1) fingerprint for iOS devices that does not change after factory reset or operating system updates. Oz 0 0 Sz Nzx Nzy 1 Az + Bz
4. We collect motion sensor data from 870 iOS devices and show that our approach can generate a globally unique Here, Si S is the scale factor; Nij N represents the identifier; we show that the calibration fingerprint of the nonorthogonality between axis i and j; and Bi B is the bias. iPhone 6S has about 67 bits of entropy. A sensor's sensitivity, or gain, is defined as the ratio between
5. We implement our approach as an iOS app and find the the output signal and measured property. A sensor's nominal approach is lightweight and efficient: data collection and gain is the intended operating sensitivity of the sensor. It is a processing typically takes less than one second in total. single value that is usually documented in the sensor datasheet.
6. We conduct a large-scale analysis on motion sensor We use F to denote a sensor's nominal gain in this paper. calibration in 146 Android device models from 11 If a sensor is ideal, its scale matrix S and nonorthogonality vendors. We find that all Google Pixel phones except matrix N should be F I and I, respectively, where I is an for Pixel 1/1 XL can be fingerprinted by our attack; we identity matrix. However, due to the existence of errors, the show that the calibration fingerprint of the Pixel 4/4 XL scale factors can be as large as 2% of the nominal gain [9]. has about 57 bits of entropy. The above equation can be further simplified as:
7. We analyse Apple's fix and show that it is imperfect: with ~50K samples the exact fingerprint can be ex- O = G(A + B) (2) tracted. where G = SN is referred to as the gain matrix. II. BACKGROUND A myriad of calibration techniques has been proposed to

Motion sensors used in modern smartphones, including the calculate the gain matrix and bias vector during manufac-
accelerometer, gyroscope, and magnetometer, are based on ture [3]. Vendors can also choose to only calibrate the bias
MEMS (Micro-Electro-Mechanical Systems) technology and vector to lower the cost. Once factory calibration is finished,
use microfabrication to emulate the mechanical parts. The the calibration parameters of the sensor will be stored in non-
accelerometer and gyroscope measure the proper acceleration volatile memory inside the device and should not change over
and rotation speed of a device in each of the axes, respec- time [10], [11]. Details of the calibration process used by
tively, while the magnetometer measures the Earth's magnetic manufacturers are not made public.
field relative to the device. These sensors are pervasive in
modern mobile devices. Although MEMS technology has III. ATTACK METHOD
greatly reduced the size and cost of motion sensors, MEMS
sensors are usually less accurate than their optical counterparts The goal of the adversary in this paper is to obtain a reliable
due to various types of error. In general, these errors can fingerprint from the built-in motion sensors of a smartphone.
be categorised as deterministic and random: random errors Our threat model is as follows. We assume an adversary is
are usually caused by electronic noise interfering with the able to record motion sensor samples from a smartphone. The
output of sensors, which change over time and have to attacker can do this if the user installs an app, or visits a
be modelled stochastically; deterministic errors are produced website (currently accelerometer and gyroscope only), under
by manufacturing imperfections and can be classified into the control of the attacker. Furthermore, we assume that
three categories: bias, scaling factor, and nonorthogonality the software embedded in the app or web page is able to
misalignment errors [3], [4]. communicate with a remote server under the control of the
attacker; this is typically the case for both apps and web pages.
We first look at the gyroscope in iOS devices; the calibration
fingerprinting for other sensors and devices is discussed later.
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 3

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Fig. 1: General steps to recover the device calibration fingerprint

TABLE I: Estimated gyroscope nominal gain for iOS devices Data Collection, Data Preprocessing, ADC Value Estimation,
Gain Matrix Estimation, Validity Check, and Fingerprint Gen-
Model Nominal Gain eration.
(mdps)
Data Collection. We collect a small number of samples
iPhone 5S/6/6 Plus/6S/6S Plus/7/7 Plus/8/8 Plus/SE from the gyroscope through a mobile app at the maximum
sampling frequency. Empirically, we find 100 samples col-
iPhone X/XS/XS Max 61 lected in less than 1 second is sufficient. We use O =
[O1, O2, , ON ] to denote the collected data, where Oi =
iPad Pro 9.7/10.5/12 inch [Oix , Oiy , Oiz ]T is a 3-by-1 vector.

iPhone 4/4S/5/5C/5S, 70 Data Preprocessing. After collecting the data, we calculate
iPad 3/Mini/Mini 4/Mini Retina/Air/Air 2 O by differencing the consecutive outputs for all three axes.
In other words, O is calculated by the following equation:
iPhone 5S devices have two possible nominal gain values.
O = [O2 - O1, O3 - O2, , ON - ON-1]
A. Gyroscope Calibration on iOS devices
Then, we select only a subset of the data, O i , where the
We have found that the gain matrix of the gyroscope in iOS absolute value of all its elements is lower than a multiplication
devices is factory calibrated and further estimated the nominal of the nominal gain:
gain for different device models based on the gyroscope
outputs [2]. In particular, Table I lists the nominal gain (in O i = {Oj O | max(|Oj|) < ( i + 0.5)FG}
mdps, millidegrees per second) of the gyroscope for all the
iOS devices that we have measured. The estimated nominal where i is the threshold. We start i from 1 and double its
gain of 61 mdps indicates that the sensor is likely configured value for each iteration (i.e., i+1 = 2 i) until the subset covers
to a measurement range of 2 000 dps and resolution of 16 the whole dataset (e.g., O i = O). In each iteration, we
bits (4 000/216 0.061). Furthermore, we have found that feed O i to the next step and update the value of G.
the fractional part of motion sensor outputs in iOS only has
16-bit resolution. There are a few possible reasons for this, ADC Value Estimation. In this step, we aim to recover
but the simplest is that the value in the gain matrix G is A i , which is the difference between consecutive ADC
stored as a signed integer with a resolution of 2-16 degrees outputs. From Equation 2 we have:
per second (dps). After investigation, we find that every device
that uses an M-series motion coprocessor, which was released A i = G-1O i
by Apple in September 2013 with the iPhone 5S, shows this
pattern. The purpose of the motion coprocessor is to offload where G-1 is the inverse of the gain matrix G. However,
the collection and processing of sensor data from the CPU. the value of G is unknown at the moment. Nevertheless, we
However, for older devices such as iPhone 4 and iPhone 4S, can estimate G by its ideal value G0 = FG I, where FG is
gain matrix values are stored with more precision and the the nominal gain of the gyroscope. That is to say, we have
calibration involves truncation down to 2-16 dps after the gain G = G0 in the first iteration, where G is the estimated gain
is applied. The complete set of devices that use the M-series matrix. Deterministic errors are comparatively small, and thus
motion coprocessor can be found online.1 G should be relatively close to G0. Since A i only has
integer values, we can estimate A i by:
B. Fingerprinting from Mobile Apps
A i = round(G-1O i )
In general, manufacturing imperfections introduce idiosyn-
crasies across different sensors. If factory calibration is carried where the round() function rounds each element to the
out on a per-device basis, then the calibration matrices may nearest integer. However, since G0 is not equal to G, the
also be unique. Therefore, the gain matrix G may be used as rounded value A i may not be the true value. Therefore, we
a robust device fingerprint. calculate the rounding error Er R3(N-1) by:

The general process to recover the device calibration finger- Er = |A i - G-1O i |
print is illustrated in Fig. 1, which consists of six major steps:
To ensure the estimated values are correct, we require that
1https://en.wikipedia.org/wiki/Apple_motion_coprocessors every value in Ekr , which means the k-th column in Er,
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 4

be lower than a threshold (e.g., 0.1). If not, we believe 0.4 0.4
Gyroscope Output (deg/s)
the rounding is ambiguous and thus remove both Aki 0.2 Difference between Gyroscope Outputs (deg/s) 0.2
and Oki from the dataset. Once all ambiguous values are
removed, A i can be regarded as a safe estimate of A i . 0.0 0.0
Nevertheless, if the device is moving rapidly (e.g., vigorous
shaking), rounding errors could be accumulated and cause -0.2 -0.2

rounding to an incorrect integer value (i.e., A i = A i ).
Gain Matrix Estimation. After estimating the ADC value

matrix A i , we can update the gain matrix estimate by:

2

G = arg min GA i - O i

G 2 -0.4 -0.4
0 0
2 100 200 300 400 500 100 200 300 400 500
where 2 is the squared Euclidean 2-norm function. Or in
Sequence Sequence

words, we use the least squares solution to GA i = O i Axis x y z Axis x y z

as the gain matrix estimate.

After each update of G, we check if we have processed all (a) Fused gyroscope data (b) After differencing

the output data. If so, we will pass the estimated G to the Fig. 2: Gyroscope data collected via JavaScript (iPad Air)

Validity Check process. Otherwise, the algorithm will go back

to the Data Preprocessing stage with an updated G, and a

new range of data will be processed with i+1 = 2 i. When the device does not contain an M-series coprocessor,
the GYROID is calculated by:
By way of an example, here is the G that we estimated
from an iPhone XS in the units of 2-16 dps: GYROID = G - round(G0)

4012.000000000001 -35.999999999999318 -10.999999999999677 because values in the gain matrix are not simply integers in
11.000000000000174 4030.999999999999 21.999999999999631 the units of 2-16 dps in this case.

-3.999999999999980 -25.000000000000011 4016.000000000000 Summary. In this section we present the general idea and
procedure to generate a calibration fingerprint. Overall, the
These numbers are extremely close to whole integers, calculations are light-weight and are easy to implement. The
indicating that the gain matrix is stored in the units of 2-16 attack works well under normal device interaction (e.g., device
is resting on a desk or held in hand when browsing a webpage);
dps. In fact, we found that all iOS devices with an M-series it typically requires only 100 data samples that can be collected
in less than 1 second to generate the GYROID (IV). If
coprocessor store the gain matrix this way. For these devices, the device is moving vigorously when collecting data, our
approach will detect fast movement, as the Validity Check will
we can simply round G to obtain the true gain matrix G. fail, and keep trying until the movement is reduced. This attack
is therefore practical since people rarely shake their device
Validity Check. To quantify the deviation between G and continuously and vigorously for extended periods.
the true value of G, we define the estimation error Ee R31

as follows:

O - GA

Ee = 2

N -1

If the estimation error is small (i.e., max(Ee) < ), then G C. Fingerprinting from Mobile Websites
should be close to the true gain matrix G. Otherwise, it means
the ADC value estimation is incorrect, which is likely a result JavaScript also provides APIs for web developers to access
of vigorous movement during the data collection. In this case, the fused gyroscope data. In this paper, we state the sensor data
we need to collect another batch of data and repeat the steps. is fused if its value is a result of applying a time-varying bias
correction to the raw sensor data. In practice, it is common to
Fingerprint Generation. The generation of the gyroscope use a Kalman filter to combine, or fuse, the accelerometer and
calibration fingerprint, GYROID, can be categorised into two gyroscope inputs to calculate the corrected bias values. Fig. 2
groups based on whether the device has an M-series copro- (a) presents the 500 sequential gyroscope samples collected
cessor. If the device does have an M-series coprocessor, the from an iPad Air through mobile Safari when the device is
GYROID is defined as follows: at rest on a desk. As shown in Fig. 2 (a), quantisation in the
fused data is still visible because the gyroscope ADC outputs
GYROID = round(G) - round(G0) (3) are integers. However, there is a slowly varying continuous
component added to the bias due to the bias correction. Fig. 2
where both G and G0 are in the units of 2-16 dps. Or in (b) shows that the bias part can be nearly eliminated by
words, the GYROID is the gain matrix G after subtracting the subtracting consecutive samples. Therefore, we can apply the
nominal gain in units of 2-16 dps. For instance, the GYROID same technique described in III-B to recover the gain matrix.

of the iPhone XS in the previous example is:

14 -36 -11

GYROID = 11 33 22 (4)

-4 -25 18
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 5

D. Practical Calibration Fingerprinting Attacks TABLE II: Magnetometer type of different iOS device models

To launch a calibration fingerprinting attack, an adversary Type Model Nominal Gain (T)
can collect gyroscope samples from any device using an app
written by the attacker or that visits any website under the Type I iPhone 4S/5/5C/5S/6/6 Plus 0.35/0.28/0.17
attacker's control. The attacker can then generate a device All iPad models
fingerprint (e.g., GYROID) from the samples and store it in
a database. Then, the adversary can query the database to Type II iPhone 6S/6S Plus/7/7 Plus/SE 0.075
determine when a particular physical device uses a particular
app or visits a particular website. The details of the generation Type III iPhone 8/8 Plus 0.075
and query of the GYROID in the database differ depending on
the collecting source (app or web) and device model. Type IV iPhone X/XS/XS Max 0.075

Specifically, for apps running on a device with an M-series Type I devices have three possible nominal gain values.
motion coprocessor, they can follow the steps in III-B to
recover the exact GYROID. Otherwise, if the device does not Difference between Accelerometer Outputs (g) iPhone 4S iPhone 5
have a motion coprocessor (e.g., iPhone 4/4S/5) or adversaries
only have access to fused gyroscope data (e.g., via JavaScript), 0.002
there are two options to determine whether two GYROID
entries in the database represent the same physical device. 0.000

Option 1 (Clustering): adversaries can directly use the -0.002
estimated gain matrix G as the GYROID and store it in a
database. For every new device with the same model, they 0 500 1000 1500 2000 0 500 1000 1500 2000
can calculate its G and compare the Euclidean distance
between its G and the ones in the databases. If they are Sequence
close, then adversaries know they came from the same
device (the entropy of G is discussed in V-A). Axis x y z

Option 2 (Rounding): adversaries can still use Equation 3 Fig. 3: Comparison between iPhone 4 and 5 (Accelerometer)
to generate the GYROID. However, the estimated GY-
ROID may deviate from the true one by at most 1 for devices, we can use the same approach described in III-B to
each of the 9 values. Therefore, adversaries can store the obtain the magnetometer fingerprint (i.e., MAGID). Although
estimated GYROID and perform a fuzzy query (i.e. accept the gain matrix of the magnetometer is not stored at 2-16 T
a 1 fluctuation for each element). Note that this option resolution, adversaries can use the same techniques discussed
provides less entropy compared with Option 1. in III-D to launch an attack by either clustering or rounding.
Compared with the gyroscope, the raw magnetometer data is
E. Fingerprinting Other Motion Sensors not currently accessible in major browsers. Nevertheless, the
MAGID provides additional entropy to the GYROID. Thus,
Magnetometer. We found that the magnetometer in iOS we can combine them as a finer-grained fingerprint when
devices can also be fingerprinted. Similar to the gyroscope, the analysing apps.
raw readings from the magnetometer only have a resolution
of 2-16 T (microtesla). After subtracting consecutive raw Accelerometer. We observed a similar quantisation pattern
magnetometer measurements for every device model in our for the accelerometer in older generations of iOS devices,
dataset, we observed four types of pattern: including the iPhone 4S and iPad Mini. For example, Fig. 3
shows the consecutive differences between 2 000 accelerome-
Type I (different sensitivity, negligible fluctuation): Type ter outputs from an iPhone 4S. The quantisation is clear and
I devices have a slightly different sensitivity for each axis. thus we can apply the same approach described in III-B to
recover the accelerometer fingerprint. Note that these devices
Type II (fixed sensitivity, moderate fluctuation): Type II do not use an Apple motion coprocessor, and thus adversaries
devices have the same sensitivity for every axis but there would need to use techniques described in III-D to launch
is a moderate fluctuation within each cluster. the attack. For newer versions of iOS devices, such as the
iPhone 5 also shown in Fig. 3, Apple uses a higher-resolution
Type III (different sensitivity, moderate fluctuation): Type accelerometer that conceals the quantisation in outputs. Our
III devices have a slightly different sensitivity for each attack currently does not directly apply to these devices.
axis and there is a moderate fluctuation within each
cluster; the quantisation of the data is evident in this case. In this paper, we define the SENSORID as a combination
of distinctive sensor calibration fingerprints. In the case of
Type IV (different sensitivity, intense fluctuation): Type iOS devices, the SENSORID includes both the GYROID and
IV devices show an intense fluctuation on the magne- MAGID. For older versions of iOS devices (e.g., iPhone 4S
tometer output. In this case, the quantisation of the data and iPad Mini), the SENSORID also includes the accelerom-
is not as evident as in other cases. eter fingerprint (i.e., ACCID).

We summarise the magnetometer type of different iOS
device models and their estimated nominal gain in Table II.
Overall, the observation of the four patterns reveals the dif-
ferent underlying calibration procedures. For all four types of
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 6

Difference between Accelerometer Outputs (ms-2) Pixel 3 Pixel 4 XL TABLE III: SENSORID composition
0.06
SENSORID Device Model
0.05 ACCID iPhone 4S, iPad Mini
GYROID Pixel 2/2 XL/3/3 XL/3a/3a XL/4/4 XL
MAGID iOS devices, Pixel 4/4 XL

iOS devices

0.04

0.03 500 1000 1500 2000 0 500 1000 1500 2000 of factory calibration is up to individual manufacturers.
0 For vulnerable Google Pixel phones, we can extract the

Sequence SENSORID from both an Android app and a website running
on an Android browser. In the case of Google Pixel 4 and
Axis x y z 4 XL, the SENSORID includes both the ACCID and GYROID.
For other Pixel models excluding Pixel 1, the SENSORID only
Fig. 4: Comparison between Pixel 3 and 4 XL (Accelerometer) includes the ACCID. In summary, Table III lists all device
models whose SENSORID includes the ACCID, GYROID, and
MAGID, respectively.

F. Fingerprinting Android devices IV. EVALUATION

To study whether Android devices are susceptible to similar A. Fingerprinting iOS Devices
fingerprinting attacks, we used four automated testing plat-
forms to collect data from 146 Android device models from We developed both a website and an iOS app to collect
11 vendors: BQ, Google, HTC, Huawei, LG, Motorola, Nokia, sensor data. The iOS app collects raw data from the motion
OnePlus, Samsung, Sony, and Xiaomi (IV-B). Among all the sensors (accelerometer, gyroscope, and magnetometer) at 200
Android devices we have tested, we found that all Google Hz and does not ask users to put the device in any particular
Pixel phones, other than the Pixel 1/1 XL, can be fingerprinted position. The app also embeds a WebView; the embedded
by our approach; we did not observe per-device calibration WebView and the separate website both collect fused ac-
behaviour on the Pixel C tablet. In addition, we noticed that celerometer and gyroscope data via JavaScript.
the calibration process applied to motion sensors varies across
device models. In particular, we found the full gain matrix For both the app and the website, we use the Finger-
of both the accelerometer and gyroscope in Google Pixel 4 printjs2 [12] library in the default configuration to generate
and 4 XL are per-device calibrated, while only the leading a browser fingerprint for evaluation purposes. In addition to
diagonal of the gain matrix for the accelerometer is calibrated volunteers, we recruited participants from Amazon Mechanical
in other Pixel devices. Turk2 and Prolific3 to download the app and contribute sensor
data. The public data collection exercise has been approved by
Fig. 4 shows the consecutive difference between 2 000 ac- the ethics committee of the Department of Computer Science
celerometer outputs collected from a Pixel 3 and a Pixel 4 XL and Technology at the University of Cambridge.
when they were at rest on a desk. The quantisation in the
accelerometer outputs is clear in both cases. In addition, the To date, the SENSORID app has collected data from 795
figure suggests that only the scale matrix of the accelerometer unique iOS devices; 761 of them contain an M-series motion
is calibrated in Pixel 3 (i.e., only main-diagonal elements in the coprocessor. In addition, the website has collected fused data
gain matrix are calibrated); the same pattern is also observed from another 75 devices. Some users chose to participate in
in Pixel 2/2 XL/3 XL/3a/3a XL. Fig. 4 also suggests that all this study multiple times. Thus, there might be more than
9 values in the gain matrix are calibrated in the Pixel 4 XL; one record for each unique device. On both the app and the
the same pattern is also observed in the Pixel 4. Apart from website, we ask users to tell us whether they have submitted
the accelerometer, the gyroscope in Google Pixel 4 and 4 XL the data from this device before.
is also per-device calibrated.
Using the raw gyroscope data collected from the 761 iOS
In addition to Pixel devices, we have noticed that the devices with an M-series coprocessor, we are able to recover
accelerometer in Huawei Honor 20 Lite, MediaPad M3 Lite the exact GYROID. For the other 34 devices that do not contain
10, and MediaPad T3 10 and the gyroscope in BQ Aquaris an M-series coprocessor, we use the rounding option in III-D
X2 have different sensitivity in each axis. However, we only to generate the GYROID due to the small sample size. Based
have one device for each of these models and thus cannot on the GYROID, we successfully identify multiple records that
confirm whether they are per-device calibrated. So far we are submitted by the same device. This is confirmed by user-
have tested 321 unique devices (146 unique device models); supplied data about whether they have submitted samples from
we did not observe per-device calibration behaviour on any this device before and the device IP address when they submit.
other Android device models we tested. We therefore focus The GYROID of each device is distinct.
on Google Pixel devices in the rest of the paper. The choice
2https://www.mturk.com
3https://prolific.ac
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 7

TABLE IV: Comparison of iOS device fingerprints TABLE V: Comparison of Pixel device fingerprints

Devices Fingerprint Group Size # Groups Device Model Fingerprint Group Size # Groups

870 GYROID ACCID
1 870 Pixel 2/2 XL 1 46
795 Fingerprintjs2 1 391 Fingerprintjs2 1 17
10 236 96 Pixel 3/3 XL 2 4
MAGID 45 1 & ACCID 4 1
1 775 Fingerprintjs2 5 2
Fingerprintjs2 2 10 Pixel 3a/3a XL 7 1
ACCID 1 308 ACCID 1 61
236 97 Pixel 4/4 XL GYROID 1 25
Fingerprintjs2 45 1 2 8
1 10 Fingerprintjs2 3 5
1 8 5 1
2 1 1 45
1 45
Since the website only collects fused gyroscope data, we 1 10
choose the rounding option in III-D to generate the GYROID. 2 1
Then, we compare it with the GYROID of the 795 devices 9 1
that we recovered from the raw data. As a result, we identify 10 1
3 devices submitted through both the website and the app. 14 1
The app also collects fused sensor data from the built-in
WebView. For this data, we use the clustering approach to device in our dataset, 45 out of 135 iPhone 7 devices have
generate a group of gain matrix estimates. Then, we apply the same Fingerprintjs2 fingerprint; these 45 devices are all
the Multivariate ANalysis Of VAriance (MANOVA) technique from the UK. In the case of ACCID, it identifies all 10 unique
to analyse these estimates and successfully identify all 795 devices, while Fingerprintjs2 generates the same fingerprint
unique devices in the dataset. In particular, we also identify for two iPhone 4S devices; both devices are from Germany.
6 devices that submitted multiple times through the app. The The results indicate that the Fingerprintjs2 fingerprint may be
results are the same as we obtained from the raw data. correlated with a particular handset configuration.

In addition, we apply the improved approach to fingerprint We have also developed a proof of concept app for iOS
the magnetometer with the rounding option. After generating devices with an M-series motion coprocessor. The app imple-
the MAGID, we group devices by their MAGID and present ments our attack to generate the GYROID of the test device.
the results in Table IV. In the table, the group size records The code is written in Swift 4.1 with XCode 9.4.1. The app
the number of different devices sharing the same MAGID. collects 100 raw gyroscope samples and attempts to generate
Therefore, a group of size 1 means the device has a unique the GYROID. If it fails (due to intense shaking of the phone)
MAGID in our dataset. We find that the 10 groups of size the app automatically collects another 100 raw samples and
2 are all old device models with a Type I magnetometer, repeats the process. Overall, it takes about 0.5 seconds to
indicating they have a higher chance of collision on MAGID collect 100 gyroscope samples and another 0.01 seconds to
than others. The reason is that the entropy of the MAGID for generate the GYROID. Vigorous movement during extraction
Type I devices is only provided by the scale matrix (i.e., main- may require additional samples, but the task nevertheless
diagonal elements in MAGID). Nevertheless, the MAGID is completes within a few hundred samples and takes a few
orthogonal to the GYROID, and thus, they can be combined seconds. In any case, the generated GYROID always stays
together to provide additional entropy. the same. A proof-of-concept webpage and demo videos can
be found on our website: https://sensorid.cl.cam.ac.uk.
Similar to the analysis of data collected from the built-in
WebView, we use the clustering option in III-D to analyse B. Fingerprinting Google Pixel devices
the accelerometer fingerprint and apply MANOVA to identify
unique devices. As discussed in III-E, our attack only applies In general, it is difficult to find many people with a Pixel
to the older generations of iOS devices. In our dataset, that device via crowdsourcing platforms due to the relatively small
includes 9 iPhone 4S devices and an iPad 3. We apply our market share. Nevertheless, we found most online app testing
attack on these 10 devices and find that all of them have a platforms provide access to Pixel devices. Therefore, we
unique ACCID. It is likely that other iOS devices prior to developed an Android app to collect raw motion sensor data
iPhone 4S can also be attacked by our approach, but we do and send it back to our server. In a method similar to the one
not have data from these devices to confirm it. used in our iOS app, our app also embeds a WebView that
collect web sensor data via JavaScript as well as a fingerprint
Finally, we compare the GYROID, MAGID, ACCID with generated by Fingerprintjs2. In addition, the app records the
the default configuration of Fingerprintjs2, which utilises font ANDROID_ID that is unique to each combination of the app-
detection, canvas, WebGL, etc to fingerprint devices. Table IV signing key, user, and device to identify unique devices in our
presents the results and demonstrates GYROID, MAGID, dataset.
and ACCID provide more entropy than traditional browser
fingerprinting techniques. While GYROID is unique for every
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 8

During our experiment, we deployed the Android app on by both tests at the 0.05 significance level. The result suggests
AWS Device Farm4, Firebase Test Lab5, App Centre6, and that we may need a finer-grained analysis for the main-
Sauce Labs7 to collect data from various Android device diagonal elements. When we run a normality test on data from
models. Since we only found per-device calibration on Pixel each device model separately we find that the main-diagonal
phones other than the Pixel 1/1 XL, we focus our analysis on elements also show strong normality.
these devices. By the end, we have collected data from 152
unique Pixel devices. Correlation Analysis. To test for correlation, we run the
Pearson correlation test on each Dij and find that D12 and
Using the raw accelerometer data, we generate the ACCID D13 are strongly correlated with D21 and D31 at the 0.01
for each device and use clustering to determine whether two significance level, respectively. Therefore, we exclude D21 and
devices have the same ACCID. We compare the results with D31 from our entropy calculation to avoid over-estimation.
Fingerprintjs2 in Table V. For Pixel 4 and 4 XL devices,
we also calculate their GyroID and compared it with other Entropy Calculation. We first calculate the entropy of
fingerprints. As shown in the table, both ACCID and GYROID non-diagonal elements in D, excluding D21 and D31. For
uniquely identify every Pixel device while multiple devices each non-diagonal element, we estimate the parameters of
have the same fingerprint generated by Fingerprintjs2. In the normal distribution, including the mean and standard
particular, 14 out of 45 Pixel 4/4 XL devices have the same deviation , from the dataset. Technically, it is not a strict
Fingerprintjs2 fingerprint. This is likely because the embedded normal distribution since each element can only be an integer.
WebView with default configuration does not expose many Nevertheless, it is a result of rounding, and thus we can still
distinctive characteristics when two devices are running the use the normal distribution to estimate the entropy.
same Android version. The fingerprint is likely to have more
entropy if Fingerprintjs2 is running in an Android browser. In general, the entropy of a discrete random variable X,
Nevertheless, unlike SENSORID, which is a hardware iden- which is denoted as H(X), can be calculated by:
tifier, Fingerprintjs2 cannot track users as they move across
Android browsers. H(X) = - P(xi) log2 P(xi) (5)

In addition, we have tried to generate the SENSORID for xi X
each device using the web sensor data collected via JavaScript
in the embedded WebView. We then differentiate devices based where P(xi) is the probability of X being equal to xi. In
on their SENSORID, generated from the web data, using our case, we regard the element Dij as the variable X. Then,
clustering. We successfully identified all unique Pixel devices we have xi {-65535, . . . , 65535} because of the 16-bit
by their ACCID. For Pixel 4 and 4 XL phones, we were also resolution. Suppose X N (, 2) with the density function
able to identify every individual device by their GYROID.
f (x), then we can calculate P(xi) as follows:
V. DISCUSSION
xi+0.5
In this section, we discuss some possible concerns regarding
the validity of this research. f (x) dx, if xi (-65535, 65535)

A. Is SENSORID unique for iOS devices?

To study how unique is SENSORID, we first study the
GYROID of all iOS devices with an estimated nominal gain xi -0.5
of 61 mdps. Device models included in this category can be
found in Table I. We choose this category for two reasons.
First, all device models in this category are modern devices
which contain an M-series motion coprocessor and this makes -65534.5
it possible to extract their exact gain matrix. Second, devices
with different default gain may have a different GYROID
distribution, so we select the larger size group, which contains P(xi) = f (x) dx, if xi = -65535 (6)
693 devices in total. For simplicity, we denote the GYROID
as D Z33 in the following analysis. -

Normality Analysis. To test for normality, we applied
both the Kolmogorov-Smirnov test and the Shapiro-Wilk test +
of normality for each element in D. Results show that the
non-diagonal elements in D have strong normality, while
elements in the main diagonal (D11, D22, D33) are rejected
f (x) dx, if xi = 65535
4https://aws.amazon.com/device-farm
5https://firebase.google.com/docs/test-lab
6https://appcentre.ms
7https://saucelabs.com 65534.5

By this equation, we calculate the entropy of D12, D13,
D23, and D32. For main-diagonal elements (i.e., D11, D22,
and D33), we calculate their entropy on a per device type basis.
Here, we use the iPhone 6S as an example to calculate the

GYROID entropy because it is the most popular device model
in our dataset (127 devices). For these iPhone 6S devices, we
adopt a similar approach and apply both Equation 5 and 6 to

calculate the entropy. As a result, we estimate the GYROID
for iPhone 6S has about 42 bits of entropy.

By the same analysis, we estimate the entropy of the

MAGID for iPhone 6S. If adversaries launch the attack using
the rounding option (III-D), each element could have 1
uncertainty. In this case, we estimate that the MAGID contains
about 25 bits of entropy. The MAGID should have more
entropy if adversaries choose the clustering option. Since we
only have 10 old-generation iOS devices that have an ACCID,
we do not include ACCID into the SENSORID entropy calcula-
tion. We observe no evidence of strong correlation between the

MAGID and GYROID. Therefore, we estimate the SENSORID
for iPhone 6S has around 67 bits of entropy.

Uniqueness Analysis. There were 728M active iPhones
worldwide in April 2017 and the iPhone 6S devices accounted

for 18% of them [13]. Therefore, there were around 131M
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 9

iPhone 6S devices. From the birthday problem, we know that TABLE VI: SENSORID entropy estimation (Pixel devices)
the chance of two iPhone 6S devices having the same SEN-
SORID is around 0.0058%, suggesting it is a globally unique Fingerprint Device Model # Devices Entropy (bits)
device fingerprint. In addition, the SENSORID is orthogonal ACCID
to other fingerprinting techniques. Therefore, adversaries can GYROID Pixel 2/2 XL 46 ~14
combine the SENSORID with other metadata (e.g., system Pixel 3/3 XL/3a/3a XL 61 ~12
language) or other fingerprinting techniques (e.g., canvas fin- 45 ~25
gerprinting) to further increase the fingerprint entropy. Pixel 4/4 XL
45 ~45
Limitations. Results from both the Kolmogorov-Smirnov Pixel 4/4 XL
and Shapiro-Wilk normality tests suggest that values in D are
consistent with a normal distribution, but it is possible that series (Pixel 2/2 XL), Pixel 3 series (Pixel 3/3 XL/3a/3a XL),
the actual distribution is not normally distributed in the tail and Pixel 4 series (Pixel 4/4 XL). For each category, we anal-
regions. For example, manufacturers may discard sensors that yse the normality of each value and the correlation between
have an extreme value in the gain matrix; this would reduce the values in the fingerprint. For Pixel 2 and 3 series, the ACCID
available entropy. We therefore need to consider whether non- only has non-zero values in the leading diagonal (D11, D22,
normal distributions might invalidate our entropy calculations. D33), and thus it provides less entropy than the Pixel 4 series.
For Pixel 4 series, we find that some off-diagonal values in
Firstly, it is worth mentioning that this kind of rejection the ACCID/GYROID are strongly correlated with each other.
policy is unlikely in practice; one of the key benefits of factory Thus, we only keep one of the dependent variables in the
calibration is that sensors with anomalous physical gains will entropy calculation to avoid over-estimation.
still perform well when calibrated. More importantly, the
calculation of entropy is dominated by the core shape of the Using a similar method to the one used in our previous
distribution, where we have abundant data. Non-Gaussianity work on the iOS magnetometer, we estimate the entropy based
may affect the tails of the distribution, but this would have a on the assumption that adversaries choose to attack using the
negligible effect on the calculated entropy. To give a concrete rounding option, which has 1 uncertainty for each element.
example: we found all values in D fall inside the range Results are presented in Table VI. In addition, we find off-
(-4, +4). If we make the assumption that values outside diagonal elements in GYROID are strongly correlated with off-
this range are discarded, we still estimate the SENSORID diagonal elements in ACCID in Pixel 4 series devices. This
provides around 67 bits of entropy for the iPhone 6S. is likely because the accelerometer and gyroscope are inte-
grated into the same chip (LSM6DSR). Therefore, to estimate
A related concern is there could be undetected higher-order the entropy of SENSORID, the combination of ACCID and
correlations between values in D. A similar argument applies GYROID, we simply add the entropy provided by the main-
in this case: the entropy calculation is dominated by the core diagonal variables in the ACCID to the entropy provided by
of the (now multivariate) distribution, where we have abundant the GYROID. As a result, we estimate the SENSORID provides
data, and where we see no evidence of non-independence. In around 57 bits of entropy; a precise estimate of entropy is
the tail regions, non-independence might go undetected, but difficult since we only have data from 45 Pixel 4/4 XL devices
this would have little impact on the calculated entropy. whereas in our previous study with iOS we used data from
127 iPhone 6S devices. Assuming that our entropy estimate
Ultimately, the calculation of entropy cannot be done with is accurate, and analysing this as an example of the birthday
absolute rigour given a finite number of samples from an un- problem, if there are 100 million Pixel 4/4 XL devices in the
known distribution, but it is still possible to perform a thorough market, then the probability that every device has a globally
analysis, and significant errors in the estimated entropy of unique SensorID is around 97%.
SENSORID due to non-Gaussianity or non-independence are
very unlikely. C. Is SENSORID correlated with the manufacturing batch?

B. Factory calibration in Android devices To answer this question, we first study the correlation
between the SENSORID and the country of the device, which
Rooted Android handsets provide access to the gain matrix is inferred from the IP address when a user submits data.
values for the motion sensors in the local file system on boot. We do not find any evidence of strong correction at the 0.05
We therefore confirmed that our distinct estimates for the significance level. In addition, we collected gyroscope data
ACCID on two Pixel 3 devices were correct as well as our from 25 iOS devices in an Apple Store. Some of these devices
estimated ACCID and GYROID values for a Pixel 4 device. have similar serial numbers, which suggests they may come
While the magnetometer in the Pixel 3/4 also has a full gain from the same manufacturing batch. However, the GYROID
matrix, its values appear to be the same for all devices of of these devices differs significantly. Furthermore, there is no
the same model and thus does not provide any entropy. The significant difference in the GYROID distribution for devices
motion sensors in other Android devices may also be factory from the Apple Store and for devices that we collect otherwise.
calibrated. If the calibration is restricted to offsets (i.e., bias
compensation) then our approach is ineffective since it targets D. Consistency of SENSORID
the gain matrix and cannot recover bias compensation.
We have not observed any change in the SENSORID of
To estimate the entropy of SENSORID for vulnerable Pixel our test devices in the past 16 months. Our dataset includes
devices, we group these devices into three categories: Pixel 2 iOS devices running iOS 9/10/11/12 and Pixel devices running
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 10

Android 8/9/10. We have tested compass calibration, factory

reset, and updating operating system; the SENSORID always 30

stays the same. We have also tried measuring the sensor data iOS 11.4.1
20

at different locations and under different temperatures; we

confirm that these factors do not change the SENSORID either. 10

Count 0

E. Impact and responsible disclosure 10

We followed a responsible disclosure procedure and re- 5 iOS 12.3.1
ported this vulnerability to Apple on 3rd August 2018 and
Google on 10th December 2018. In particular, we suggested 0
two possible countermeasures. The first is to add a random
noise R31, from the uniform distribution in the range -40000 -30000 -20000 -10000 0
[-0.5, 0.5], to each ADC output. The added noise obfuscates
the effect of quantisation making the attack much harder. Gyroscope Output in y axis (2-16 dps)
The second approach we proposed is to round the calibrated
sensor output to the nearest multiple of the nominal gain. This Fig. 5: Histogram of raw gyroscope data of an iPhone X
approach is more practical to apply since it does not require
access to the ADC values. A. Analysis of Apple's Fix

In iOS 12.2, Apple adopted our suggestion and added Fig. 5 presents the histogram of the raw gyroscope data in
random noise to sensor outputs (CVE-2019-8541). In addition, the y axis collected from the same iPhone X with two different
Apple removed access to motion sensors from Mobile Safari iOS versions. In both cases, the device is at rest on a desk.
by default and in later versions removed motion sensor access When the device is running iOS 11.4.1, the quantisation in the
from WebKit as well. Recently, Google pushed a fix in histogram is clear and we can recover the exact gain matrix
Android 11 that rounds the motion sensor outputs to the (III-B). To mitigate our attack, Apple added random noise to
nearest multiple of the nominal gain. the gyroscope outputs in iOS 12.2, concealing the quantisation
information. Fig. 5 suggests that the added noise follows a
When running an iOS version prior to iOS 12.2, all iOS uniform distribution, which is one of the countermeasures
devices that have motion sensors can be fingerprinted by this we proposed to Apple. However, we notice there are some
approach, including the iPhone XS and iPhone XS Max. A peculiarities in the noise added.
SENSORID can be generated by both apps and mobile web-
sites and requires no user interaction. Both mainstream iOS To figure out the range of the uniform noise applied, we
browsers (Safari, Chrome, Firefox, and Opera) and privacy- first obtain the gyroscope gain matrix of an iOS device when
enhanced browsers (Brave and Firefox Focus) were vulnerable it is running an iOS version before iOS 12.2. Then, we update
to this calibration-based fingerprinting attack, even with the the device to the latest iOS version and take 20K gyroscope
fingerprinting protection mode turned on. For Google Pixel measurements from the device at 200 Hz when the device is
phones running Android 10, we notice that some privacy- at rest on a desk. We denote the gain matrix as G and these
enhanced browsers, including Brave and Tor Browser, do block gyroscope outputs as O. Then, the underlying bias-corrected
access to motion sensors by default while others (Chrome, ADC outputs I (i.e., I = A + B) can be estimated by:
Firefox, Firefox Focus, Opera, and Duckduckgo) do not. Using
a browser that blocks motion sensor access could protect Pixel I = round(G-1O) (7)
phone users from this attack when browsing online. A recent
study shows that motion sensor data is accessed by 2 653 Although the estimated ADC values may not be accurate
of the Alexa top 100K websites, including more than 100 due to perturbation, it gives us useful insights about the added
websites exfiltrating motion sensor data to remote servers [14]. noise. Furthermore, we can get the noise estimate, N, by:
This is troublesome since it is likely that the SENSORID
can be calculated with exfiltrated data, allowing retrospective N = O - GI
device fingerprinting. The latest iOS devices which always
run iOS 12.2 or later so the attack described does not work. By way of an example, Fig. 6 presents the histogram of
Nevertheless, a dedicated attacker may still be able to extract the estimated gyroscope noise of an iPhone XS. As shown in
the fingerprint (VI). the Fig. 6, the majority of the estimated noise are distributed
uniformly in the range [-1997, 1997] 2-16 dps. The small
VI. APPLE'S FIX number of outliers are likely produced due to the inaccurate
estimation of the ADC values in Equation 7.
Apple declined to share the details of the fix deployed in iOS
12.2. Therefore we reverse-engineer Apple's fix by studying We have also tested other iOS devices and observed the
the gyroscope outputs in iPhone devices with iOS 12.2 or later; same result. This confirms that Apple did not add ran-
we show that the random noise applied does not fully conceal dom noise in the range [-0.5, 0.5] to the ADC values as
the calibration fingerprint. we proposed but instead added random noise in the range
[-1997, 1997]2-16 dps to the calibrated signal. Because the
width of the random noise is slightly narrower than the sensi-
tivity of some gyroscope axes, it leaks more information than
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 11

200 Furthermore, we define the range-related likelihood function
for each data sample as follows:
150

100 f (i)
T
50 lr (i ) = exp(- )

0

Count -2000 -1000 0 1000 2000 where exp() is the natural exponential function and T is
the temperature variable used in simulated annealing that
200 decreases over iterations.

150 Although the likelihood function lr(i) penalises data
samples with an offset beyond the added noise range, it does
100 not give us any information about the distribution of data
within the range. In general, the ADC outputs of the gyroscope
50 in every axis follow a normal distribution when the device is
resting on a platform such as a desk (as shown in Fig. 5). If
0 the device has moved during the data collection, we can use a
stationary position filter to get the segments with stationary
1980 2000 2020 measurements. Therefore, we can fit a normal distribution
N (a, a) to Ia for each axis a {x, y, z}. Then, based
Estimated Gyroscope Noise (2-16 dps) on the normal distribution, we can calculate the distribution-
related likelihood function, ld(Ii), by:
Axis x y z

Fig. 6: Histogram of estimated gyroscope noises (iPhone XS)

our original proposal. In the case of the iPhone XS in Fig. 6, ld(Ii) = pa(Iia )
the width of the perturbation, 3995, is lower than the sensitivity
of all three axes (4012, 4031, and 4016, respectively). Here, we a{x,y,z}
show that we can recover the gain matrix from the noisy data
by performing a maximum likelihood search using simulated where pa() is the probability density function of the normal
annealing. distribution N (a, a) and Iia is the output Ii in the axis a.

B. Attack of Apple's Fix Finally, we define our objective function L(O|G) as a

In this section, we first define the objective function to quan- negative log likelihood function:
tify the likelihood of observing the outputs given a gain matrix.
Then, we show that the exact gain matrix can be estimated N
from the objective function using simulated annealing.
L(O|G) = - log(lr(i)ld(Ii))
Objective Function. For a candidate gain matrix G, we
estimate the corresponding bias-corrected ADC outputs I by: i=1

I = round(G-1O) where N is the number of gyroscope outputs. Then, the true
gain matrix can be estimated by the following equation:
Here, we did not subtract sensor outputs to remove the bias as
we did in III-B because it would spread the noise (double the G = arg min L(O|G) (8)
noise range) and make the ADC value estimation less accurate.
Both the O and G are in the units of 2-16 dps so they only G
contain integer values. Nevertheless, the estimated I is not
guaranteed to be correct due to the perturbation, which is why Simulated Annealing. Simulated annealing is a probabilis-
we observed a few outliers in Fig. 6. tic technique for solving optimisation problems and is often
used in the presence of large numbers of local optima [15].
Then, we estimate the clean gyroscope outputs (i.e., without Since the objective function in Equation 8 is highly non-
added noise) by: smooth, we use simulated annealing to solve this optimisation
problem.
O = GI
First, we set the initial state of the candidate gain matrix
And the offset between the estimated outputs O and observed to the nominal value (i.e., G0 = G0) and the temperature
outputs O can be calculated by: parameter T to 10. The temperature T will decrease in each
iteration and finishes at 0.1. Then, we calculate the objective
function L(O|G0) and denote its value as L0.

In each following round t, we propose a new candidate gain
matrix by adding a random perturbation to the previous state:

=O-O Gt = Gt-1 + round(tRt) (9)

Since the added noise is uniformly distributed in the range Here, Rt is a 3-by-3 matrix that contains random floating-
[-1997, 1997] 2-16 dps, any offset beyond this range is
caused by either an incorrect gain matrix (i.e., G = G) or point values sampled from a standard uniform distribution at
incorrect ADC estimations (i.e., I = I). To quantify the error round t. We also use a step parameter t to control the step
in each data sample, we define the following error function: size at each round; its initial state is set to 5 (i.e., 0 = 5) to

f (i) = max(|| - 1997, 0) allow bigger steps in the beginning.
Then, we calculate the objective value Lt and compare it
i
with the previous objective value Lt-1. If Lt is lower than
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 12

Value 20 Variable VII. RELATED WORK
D11
0 1000 2000 3000 4000 D12 Device fingerprinting is an important technique for app
D13 developers and advertisers to track their users. The IP address
-20 D21 is one of the earliest identifiers used to fingerprint devices.
D22 However, the adoption of dynamic IP allocation and network
-40 D23 address translation, particularly for home PCs and mobile
0 D31 devices, has greatly reduced the effectiveness of this approach.
D32 Cookies are also commonly used to track users across web-
D33 sites. However, cookies are stored locally and can be changed
by users at any time. In fact, many privacy-focused browsers,
5000 such as Brave and Safari, by default block all third-party
cookies. In addition, regulations in the US and Europe require
Iteration websites to obtain user-permission before using cookies, which
also decreases the usability of this approach [16].
Fig. 7: Estimated GYROID at each iteration (iPhone XS)
A variety of IDs in the device can be used as fingerprints,
Lt-1, we always accept the proposal and keep Gt as the latest including the IMEI, UDID, and MAC address of hardware
estimate of gain matrix. Otherwise, we choose to accept Gt modules. A study in 2011 showed that these identifiers were
or keep Gt-1 probabilistically to prevent getting stuck in a widely used in mobile apps [17]. However, both Apple and
local minimum. If the proposal is accepted, we also keep the Google have adopted more stringent privacy policies to pre-
corresponding object value (i.e., Lt = Lt-1) and increase the vent developers from accessing these unique IDs. Addition-
step size slightly (e.g., t+1 = t 1.05) to allow faster ally, many information flow tracking systems, such as Taint-
exploration. Otherwise, the step size will be decreased slightly Droid [18] and Panorama [19], can capture these malicious
(e.g., t+1 = t/1.05) to help finding the minimum. We also behaviours and report them to users.
set a lower bound for t at 0.7 to prevent the step size being
too small to update the candidate gain matrix in Equation 9. Passive Device Fingerprinting Passive device fingerprint-
ing is the action of characterizing a target device by observing
Result. We test the algorithm on our iPhone XS test handset; its network traffic. It analyses the captured data to reveal
the GYROID of this iPhone XS is shown in Equation 4. In fingerprintable patterns (e.g., the software, operating system,
particular, we first collect 50K gyroscope samples from the or hardware components). Since passive fingerprinting only
device at 200 Hz when it is stationary. We run our algorithm relies on network traffic, it is compatible with more devices,
on this data for 5K iterations and present the result in Fig. 7. difficult to discover, and can track users across different
The figure shows the estimated GYROID stabilises after round browsers. In general, most passive fingerprinting techniques
3383; the stabilised GYROID is the same as the one we rely on machine learning models to differentiate devices.
estimated before noise was added. We have also tested the Uluagac et al. applied Artificial Neural Networks (ANNs)
algorithm on an iPhone X and we were also able to recover to classify devices based on the time-variant behaviour in
the exact gain matrix using the same approach and setups. their traffic [20]. Neumann et al. evaluated several features
extracted from network traffic and found that the frame inter-
Discussion. The experiments show that Apple's fix is still arrival time, which is correlated with the hardware status and
susceptible to probability-based attacks. However, we found installed applications, is the most effective feature for device
that the attacker would need at least 50K data samples. Since fingerprinting [21]. Machine learning approaches usually re-
the sample frequency of the gyroscope in recent iOS devices quire more computing resources and a large amount of data for
is 200 Hz, this means the attacker would need to collect training. Thus, passive fingerprinting techniques usually have
gyroscope output for at least 4.2 minutes when the device a longer response time than active fingerprinting techniques.
is resting on a platform. In addition, the attack we proposed
is also computation-intensive and thus it is unlikely to be Active Device Fingerprinting Active fingerprinting tech-
implemented directly inside a mobile app. These restrictions niques deploy embedded code to actively gather informa-
make the attack less practical. Since Apple has also removed tion about a device and use these characteristics to make a
access to motion sensors from Safari and Webkit such an distinction between different devices. For example, Finger-
attack can now only be conducted via an app. printjs2 [12] is a popular browser fingerprinting library that
utilises the characteristics of a browser, including the user-
Even if Apple had adopted our proposed mitigation (adding agent, version, plugins, fonts, and canvas. Apple has realised
uniform noise in the range [-0.5, 0.5] to ADC outputs) this the risk of browser fingerprinting. From macOS Mojave,
maximum likelihood estimation based attack would still work. Safari scrubs most distinctive browser data, exposing only
However, the attacker would need even more samples. A generic configuration information and default fonts [22]. The
better-designed noise scheme may enhance security further, information about the operating system (e.g., version and root
but it might be harder to implement in mobile devices and permission) and system configurations (e.g., network and flash
could degrade the user experience. configurations) can also be used to identify devices. Although
this information cannot uniquely identify a device, it can be
combined with other features from browsers and embedded
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 13

hardware to increase precision. held in hand. They also applied their approach to making a
Hardware Fingerprinting Hardware fingerprints are gen- distinction between 85 iPhone 6 devices. When devices were
held in hand, only 60% of these devices produced unique
erally consistent because it is typically difficult to replace fingerprints, which, by reference to the birthday problem, in-
the embedded hardware. Some embedded hardware, such as dicates that their approach provides around 13 bits of entropy.
motion sensors, can be accessed by both JavaScript running in Based on the motion sensor data that they collected through
a web browser and by mobile apps installed on a smartphone JavaScript, we correctly identify all iOS devices in the dataset
and does not require any permission from users. Hardware based on the calibration behaviour without knowing the device
modules that have been studied for fingerprinting purposes model in advance. Most recently, Das et al. studied the sensor
include: RF modules [23], [24], motion sensors [25], [26], API usage in popular websites [14]. They showed that 2 653 of
clocks [27], camera [28], [29], and acoustic components [30], the Alexa top 100K websites accessed motion sensor data and
[31]. In particular, a well-known hardware fingerprint in digital 63% of the scripts for accessing motion sensors also engaged
forensics is the Photo Response Non-Uniformity (PRNU) in browser fingerprinting. Although the prior art has realised
of digital cameras. The PRNU is a result of manufacturing the idiosyncrasies across different sensors, none of them, to
imperfections and inhomogeneity of silicon wafers. The classic the best of our knowledge, has exploited the factory calibration
algorithm to estimate the PRNU was presented by Luks to form a device fingerprint; this paper fills the gap.
et al. [32]. Similar to SENSORID, the PRNU itself is stable to
environmental conditions and is likely to be globally unique. VIII. CONCLUSION
Nevertheless, the exact value of the PRNU cannot be extracted
and the quality of the estimated PRNU is dependent on the In this paper we introduced the factory calibration finger-
imaging processing used in the camera. Recently, Ba et al. printing attack: a new method of fingerprinting devices with
presented a protocol named ABC to authenticate smartphones embedded motion sensors by careful analysis of the sensor
using the PRNU of their built-in camera [33]. According to output alone. We demonstrated the effectiveness of this attack
their study, the PRNU estimated from one photo alone can on iOS devices and found the lack of precision in the M-
identify the source smartphone camera with high accuracy. series coprocessor helps the generation of such a fingerprint.
However, their study only focuses on two device models with Our attack is easy to conduct by a website or an app in
a single camera. It is unclear whether the image fusion process under 1 second, requires no special permissions, does not
in multi-camera devices would degrade the performance. In require user interaction, and is computationally efficient. Our
addition, accessing the camera or photos would require explicit attack can also be applied retrospectively to an historic archive
permission from the user and thus it is less practical. In of sensor data. Using the iPhone 6S as an example, we
addition to smartphones, hardware fingerprinting also has showed that the GYROID contains about 42 bits of entropy
applications on other targets. In particular, Son et al. used and the MAGID provides an additional 25 bits of entropy.
the power-on offset calibration of the gyroscope embedded Furthermore, we demonstrated that the combination of the
in a drone to serve as its identity [34]. However, this power- MAGID and GYROID is very likely to be globally unique for
on offset calibration is not factory calibration. The calibrated iPhone 6S, does not change on factory reset or after a software
offsets are dynamically calculated every time the drone is update. For older generations of iOS devices, such as the
turned on. Thus, it changes over time and varies with tem- iPhone 4S and iPad Mini, we can further extract the ACCID
perature. By comparison, our work is the first to recover the and use it to provide extra entropy. In addition to iOS devices,
factory calibration parameters that are digital values stored in we also conducted a large study of popular Android device
persistent memory and do not change afterwards. models in the market and found that all Google Pixel phones
except for Pixel 1/1 XL can be fingerprinted by our attack.
Existing hardware fingerprinting techniques are mostly We estimate the SENSORID entropy for each vulnerable Pixel
based on machine learning approaches. Bojinov et al. demon- model and show that it provides approximately 57 bits of
strated it is possible to fingerprint both the speakerphone- entropy for Pixel 4/4 XL.
microphone system and the accelerometer using typical clus-
tering approaches [26]. However, they only correctly identified Furthermore, we analysed Apple's fix to our attack and
53% of the devices in their dataset even after integrating showed that it is still possible to extract the GYROID even after
the UA string into their model. Das et al. applied several the fix, although doing so would require significantly more
supervised machine learning models to make a distinction data and computation power. Since it is no longer possible to
between devices based on the gyroscope and accelerometer access the motion sensors in iOS browsers, the opportunity to
readings [35]. To increase accuracy, they used inaudible sound launch this attack is restricted to installed apps.
to stimulate the motion sensors. As a countermeasure, they
suggested to better calibrate the motion sensors. However, they The concept of a calibration fingerprint is widely applica-
did not realise that the calibration process could leak informa- ble. Although this paper mainly targets the motion sensors
tion if not properly implemented. More recently, they further found in mobile devices, we anticipate the factory calibration
improved its accuracy by introducing a voting scheme among information used in other embedded sensors may also be
different classifiers [36]. Nevertheless, their approach requires recovered and used as a fingerprint, and therefore we expect
a lot of computing resources, which cannot be implemented future research will successfully perform factory calibration
locally on the device. Even then, their approach achieved less fingerprinting attacks on other types of sensor.
than 60% F1 score in an open-world setting when devices were
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 14

ACKNOWLEDGEMENT [19] H. Yin, D. Song, M. Egele, C. Kruegel, and E. Kirda, "Panorama:
capturing system-wide information flow for malware detection and
Jiexin Zhang is supported by the China Scholarship Council. analysis," in Proceedings of the 14th ACM conference on Computer
and communications security (CCS). ACM, 2007, pp. 116127.
Alastair R. Beresford is partly supported by EPSRC under
[20] A. S. Uluagac, S. V. Radhakrishnan, C. Corbett, A. Baca, and R. Beyah,
Grant No.: EP/M020320/1. We would like to thank Nokia "A passive technique for fingerprinting wireless devices with wired-
side observations," in 2013 IEEE Conference on Communications and
Bell Labs for supporting this work and valuable discussions. Network Security (CNS). IEEE, 2013, pp. 305313.

The opinions, findings, and conclusions or recommendations [21] C. Neumann, O. Heen, and S. Onno, "An empirical study of passive
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[22] L. H. Newman. (2018) Apple just made safari the good
A. Kollmann, Diana A. Vasile, Ricardo Mendes, Andrew Rice, privacy browser. [Online]. Available: https://www.wired.com/story/
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