What3Words Geo Encryption: An Alternative Approach to Location

based Encryption

Julian Dreyer and Ralf T

onjes

Faculty of Engineering and Computer Science, University of Applied Sciences Osnabr

uck, Osnabr

uck, Germany

Keywords:

Identity based Encryption, Location Based Encryption, What3Words, GPS.

Abstract:

Identity Based Encryption (IBE) is a steadily emerging ﬁeld of research in the cryptographical domain. A

special ﬂavor of IBE called Location Based Encryption (LBE) includes a given location attribute to add ad-

ditional access control to the encrypted entity. The main goal is to allow an entity to decrypt the ciphertext

only and only if the correct location information is provided. This allows to control the access based on the

position of the data user. Existing solutions for LBE make use of the conventional Global Positioning System

(GPS). Though, conventional GPS solutions are known to be inﬂuenced by an artiﬁcially added error, result-

ing in inaccuracy of the location data. This will consequently require the LBE scheme to include a level of

tolerance, as the GPS coordinates may slightly diverge between different points in time. In order to mitigate

this problem by design, an alternative approach to LBE is proposed to add additional tolerance. The approach

presented in this paper makes use of the What3Words location system, which offers the required tolerance for

the decryption and thereby mitigating the problem of GPS inaccuracy. A following study then evaluates the

real-world performance of the new encryption algorithm.

1 INTRODUCTION

This paper proposes a new method of implementing

a Location Based Encryption (LBE) scheme, which

represents a special variation of Identity Based En-

cryption (IBE). In general, IBE can be used to add an

additional layer of access control, onto a previously

encrypted plaintext. With the introduction of LBE,

the access control is implemented by using the loca-

tion of a receiver. The main goal is to restrict the abil-

ity to decrypt a ciphertext only to receivers at a des-

ignated position. Existing proposals make use of the

Global Positioning System (GPS) and use the mech-

anism within a Digital Rights Management (DRM)

Engine. A ﬁlm production studio for instance, could

make use of LBE to protect the digital versions of

the produced ﬁlms, thus enabling only mobile users

to consume the content only at a speciﬁc location.

Other forms of access control, e.g. in the domain of

the Internet of Things (IoT) are possible.One inherent

problem of the GPS is the artiﬁcial inaccuracy of the

signal. Therefore, approaches are need to cope with

the varying coordinates by introducing a method to

tolerate inaccurate coordinates. This work is propos-

ing a novel way of approaching the previously de-

scribed problem by utilizing the What3Words local-

ization service.

The rest of the paper is organised as follows: sec-

tion 2 introduces various existing approaches of mit-

igating the inaccuracy of the GPS and implementing

a LBE scheme. It also shows a study, which indicates

the accuracy of modern GPS receivers in order to later

evaluate the real-world usage potential of the newly

proposed LBE scheme. Said scheme is brieﬂy de-

scribed as well as the What3Words service in section

3. In section 4, an experimental study is conducted

to evaluate the real-world tolerance of the newly pro-

posed LBE scheme. Afterwards, the results are eval-

uated in section 5 and compared to the results of the

GPS receiver accuracy study, mentioned in section 2,

thus indicating the real-world application potential of

the encryption scheme.

2 RELATED WORK

The Location Based Encryption (LBE) is a widely re-

searched ﬁeld within the Identity Based Encryption

domain. Thus, there are already proposals for ef-

ﬁcient algorithms for encryption like the Location-

Dependent Data Encryption Algorithm (LDEA), ﬁrst

proposed by Liao and Chao (Liao and Chao, 2008).

Dreyer, J. and Tönjes, R.

What3Words Geo Encryption: An Alternative Approach to Location based Encryption.

DOI: 10.5220/0009791904450452

In Proceedings of the 5th International Conference on Internet of Things, Big Data and Security (IoTBDS 2020), pages 445-452

ISBN: 978-989-758-426-8

445

The algorithm makes use of a GPS coordinate, con-

sisting of the latitude and longitude of the receiver.

It ensures conﬁdentiality by including well known

and tested symmetric encryption algorithms like the

Data Encryption Standard (DES), the Advanced En-

cryption Standard (AES) or the triple-DES and hash-

ing algorithms like the Message Digest Algorithm 5

(MD5). Though, due to advanced security research

by Xie et.al. (Xie et al., 2013), the MD5 hash al-

gorithm is considered as not reliable anymore and

more sophisticated ones like the Secure Hashing Al-

gorithm (SHA) should be used. Additionally, the DES

algorithm in its plain form is vulnerable to known-

ciphertext attacks. Due to its key size of only 56 Bits

(NIST, 1999), an attacker is able to perform a brute

force attack on the encryption keys with at most 2

tries (Biham and Shamir, 1991). With further inves-

tigative cryptanalysis methods described by Matsui

(Matsui, 1993), the conventional DES cipher can be

broken in up to 2

tries. With modern and specialized

hardware at hand, an attacker is able to decrypt a DES

encrypted ciphertext within a feasible amount of time.

Thus, the proposed usage of DES in its plain form

is not recommended for modern encryption schemes.

Liao and Chao also showed potential future research

on their algorithm, including the replacement of the

aforementioned cipher suites and concepts, thereby

stressing the modularity of the LDEA algorithm itself

(Liao and Chao, 2008).

Another approach to Location Based Encryption

is given by Scott and Denning (Scott and Denning,

2003), which is focusing on the application of Geo

Encryption on digital ﬁlm licensing and DRM pro-

tection. The main goal is to mitigate the problem of

unauthorized users being able to capture a ﬁlm signal,

duplicating it and sharing it illegally. Geo Encryption

would allow ﬁlm producers to lock their ﬁlms with

a GeoLock Key, which they would only distribute to

cinemas or authorized users in general. Only these

key holders will then be able to decrypt the ﬁlm in this

scenario. The distribution of the key would not be re-

quired, because the location of the cinema requesting

access might be known to the ﬁlm producer. The ﬁlm

can then be encrypted for only the cinema’s coordi-

nates. Thus, a preceding key exchange is not neces-

sary. Scott and Denning propose a new geo encryp-

tion algorithm called ”GeoCodes GeoEncryption Al-

gorithm” (Scott and Denning, 2003), which involves

the recipient’s location coordinates, as well as the ve-

locity and time of the recipient. The algorithm also

includes a Position Velocity Time (PVT) → GeoLock

Mapping Function, which attempts to accommodate

for the inherent error and inaccuracy of the GPS con-

sumer signal. The function works by establishing a

three-dimensional mapping of latitude, longitude and

time onto a hexadecimal value. The underlying ma-

trices can be scaled to accommodate for an arbitrar-

ily accurate receiver. By including more dimensions

into the mapping function, more entropy will be gen-

erated. In order to hinder potential attackers to extract

the GeoLock values from the matrices, the use of a

cryptographic hash function is recommended.

The civil consumer GPS signal is known to be in-

ﬂuenced by an artiﬁcially added inaccuracy. There-

fore, Wing et al. (Wing et al., 2005) conduced a ﬁeld

study to evaluate the positional accuracy of consumer

GPS devices. They have set up different testing en-

vironments and chose six different GPS receivers by

well-known manufacturers, which were then be ex-

amined regarding their accuracy. The devices them-

selves make use of the differential GPS algorithm

(Van Sickle, 2015), that involves the difference be-

tween two positions, to further decrease the error of

the GPS Signal. The study shows that the average er-

ror of the GPS receivers lies within a 4.1m range with

a standard deviation of 1.47m, thus concluding that

even on modern consumer GPS receivers an error of

four to ﬁve meters is to be expected.

3 CONCEPT AND METHODS

The intention of this paper is to propose an ex-

tended form of the LDEA algorithm (Liao and Chao,

2008), which not only involves an improved crypto-

graphic cipher suite, but also makes use of a differ-

ent approach to the problem of GPS inaccuracy. The

”What3Words” service provided by the what3words

Ltd. (what3words Ltd., 2019b) offers an alternative

localization approach to the GPS. By including this

service into the LDEA algorithm (Liao and Chao,

2008), an intrinsic theoretical tolerance of nine square

meters can be achieved, thus solving the GPS inaccu-

racy problem of the LDEA algorithm in its plain vari-

ant. The given theoretical tolerance lies below the av-

erage error of consumer GPS receivers of 4.1m (Wing

et al., 2005). Therefore, an experimental study will

evaluate the real-world tolerance of the newly intro-

duced What3Words mechanism. The following sub-

chapters will describe the What3Words service, intro-

duce the newly proposed LDEA* algorithm in detail

and give an evaluation of its real-world application

potential.

3.1 What3Words Service

The What3Words service works by dividing the

earth’s surface into three by three meter squares and

IoTBDS 2020 - 5th International Conference on Internet of Things, Big Data and Security

446

Figure 1: The LDEA* algorithm.

giving each of these squares a unique three word ad-

dress. The address itself is separated by dots and

involves human readable words from a dictionary

(what3words, 2019), e.g. English. There exists a de-

veloper API capable of converting regular GPS coor-

dinates into a unique What3Words address. A exam-

plary What3Words address can look like the follow-

ing:

/// ﬁlled.count.soap

In order for the user to easily identify an address in

the What3Words format, three slashes are prepended

to the address. The service is designed to simplify

the use case of sharing a location with other people

or with a navigation system. By making use of hu-

man readable and pronounceable words, unlike reg-

ular GPS coordinates, which make use of multi digit

numbers, voice recognition systems can easily grasp

the desired address. Additionally, the addresses are

easier to remember as their structure is made easy

to read for humans. Unlike the dot-separated words

might suggest, the addresses themselves do not fol-

low a hierarchical structure (Macgregor, 2019). This

is due to the intended use case of automobile navi-

gation systems and especially voice recognition sys-

tems. If the addresses would follow a hierarchical

scheme rather than randomly assigned words like they

do now, misinterpretations by wrong voice recogni-

tion could occur, leading to a wrong location being

determined. This would impact the usability of the

whole system. For this reason the developers decided

on a random assignment of words for each address.

Additionally, they focused on words that are easily

pronounceable by humans (Day, 2019), which in-

creases the overall usability of the system even more.

When using the service, a developer can access the

freely available online API provided by what3words

or even request an ofﬂine SDK. Though, the ofﬂine

SDKs are only distributed to contractors who pay

a monthly fee. The What3Words developers claim,

that the ofﬂine SDK, which involves an ofﬂine ver-

sion of the address database in conjunction with either

a C++, Java or Mobile Library, only requires about

5 Megabytes of storage (what3words Ltd., 2019a).

Thus, an ofﬂine version of the API would even be

suitable for small IoT devices, which are not able to

communicate with the online API directly and possess

limited hardware resources.

Generally, the algorithm behind the addressing

of individual squares is not transparent to the user.

By the deﬁnition of the aforementioned concept, a

theoretical tolerance of about nine square meters

can be achieved (what3words, 2019). By introduc-

ing the What3Words service to the LDEA algorithm

and thereby exchanging the GPS coordinates with a

What3Words address, an intrinsic tolerance is estab-

lished. Thus, the problem of the GPS inaccuracy is

inherently resolved. Given an IoT device, which in-

cludes a low-cost GPS receiver and online capabili-

ties, the What3Words service would be able to cope

with the inaccuracy of the GPS receiver and offering

a LBE encryption option.

3.2 LDEA* Algorithm

The LDEA* algorithm represents an encryption

scheme, that allows arbitrary data to be symmetri-

cally encrypted and location locked at the same time.

Due to its underlying similarities with the LDEA al-

gorithm ﬁrst described in (Liao and Chao, 2008), an

asterisk has been added, indicating its new function-

ality in combination with updated crypto algorithms.

The LDEA* algorithm, the process shown in Fig-

What3Words Geo Encryption: An Alternative Approach to Location based Encryption

447

Figure 2: Split-Hash-Combine method.

ure 1 will be executed. At ﬁrst, the sender needs to

determine the location of the receiver, who is intended

be able to decrypt the message later on. Once the

sender knows the receiver coordinates (Lat

, Long

these will be sent to the What3Words API in or-

der to convert them into a What3Words address. As

there exist either the ofﬂine SDK or online API of

the What3Words service, the implementation of the

What3Words component may vary accordingly. Due

to varying lengths of the addresses, a hash function

with a deﬁned output length (e.g. 64 Bytes using the

SHA-512 hash algorithm) is being applied onto the

What3Words address. The resulting hashed address

is then XORed with a randomly generated symmet-

ric key. Following a similar scheme like the original

LDEA key generation by Liao and Chao (Liao and

Chao, 2008), the randomly generated key is of half

the size of the hashed address. In order to XOR both

parts, the hashed address is split in half. Both result-

ing halfes of the hashed address then are XORed sepa-

rately with the randomly generated key. The ﬁnal key

is then produced by combining the keys again to re-

gain the original length of the hashed address. Notice

that the length of the randomly generated key needs

to be half of the hashed address length. This whole

method is shown in Figure 2.

Once the ﬁnal key is generated, it is supplied to the

symmetric block cipher encryption algorithm. Here,

the AES-256 in Galois/Counter Mode (GCM) mode

was chosen due to its efﬁciency and it being the stan-

dard symmetric encryption algorithm standardized by

the National Institute for Standards and Technology

(NIST) (Farooq and Aslam, 2017). In its plain variant,

the AES block cipher only ensures conﬁdentiality but

no authenticity. Therefore, a modern Authenticated

Encryption with Associated Data (AEAD) mode like

GCM is used. The resulting ciphertext does not only

contain the encrypted plaintext of the sender, but also

a set of unencrypted associated data items. The asso-

ciated data ensures the authenticity of the encrypted

data, because it is being included within a Message

Authentication Code (MAC). Therefore, the integrity

and authenticity of the received data can be directly

evaluated. Thus, the overall security requirements for

a secure and authentic data exchange are satisﬁed.

The most notable disadvantage of symmetric

block ciphers is its intrinsic demand for both parties

to share the same key for both de- and encryption.

In general, the assumption of both parties knowing

each other is often not valid. Thus, an asymmetric

key exchange is needed beforehand. ”Hybrid Encryp-

tion” utilizes asymmetric encryption to share a sym-

metric block cipher key. The LDEA* algorithm rec-

ommends to share the randomly generated key either

by Difﬁe Hellman Ephemeral (DHE) or RSA key ex-

change (Rountree, 2011). It is to be noted that this

randomly generated key alone is not enough to de-

crypt the cipher-text. The receiver also needs to per-

form the key derivation process described in Figure 2.

For the decryption, the receiver needs to gener-

ate the access key with his own What3Words ad-

dress.In order to generate the ﬁnal key, the receiver

makes use of his GPS coordinates, which are deter-

mined with a tamper-proof GPS receiver. The re-

sulting coordinates (Lat

, Long

) are passed to the

What3Words API, which returns a valid What3Words

address. Then the address undergoes the Split-Hash-

Combine method (s. Figure 2) resulting in the ﬁ-

nal key for the decryption. With the AES encryption

algorithm in GCM mode, a receiver can also deter-

mine, whether a ciphertext was correctly deciphered

by checking the hash of the resulting plaintext with

the associated data. Thus, the receiver can immedi-

ately determine, whether the message was intended to

be decrypted at his position, assuming the symmetric

key was correctly shared beforehand. This allows a

sender to broadcast data to multiple receivers, while

only one of them being able to decrypt the data, as-

suming the all receivers hold the same symmetric key.

The overall method of mapping the GPS coordinates

into a predeﬁned rectangle has also been described

by Scott and Denning (Scott and Denning, 2003).

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448

Though their method requires a more computationally

intense workﬂow in order to generate the GeoLock

Keys, making it infeasible for small scale devices with

restricted hardware resources. This problem is miti-

gated by the unique mapping of the What3Words ser-

vice intrinsically. Considering the results of Wing et

al. (Wing et al., 2005), a tolerance level of three me-

ters, which is theoretically given by the LDEA* algo-

rithm, is below the expected accuracy range of con-

sumer GPS equipment, making it suitable for small

scale devices. As stated by What3Words, the size of

the ofﬂine SDK version of the What3Words service

only packs 5 Megabytes in size, thus making it feasi-

ble to store it on the local memory of the device. Even

with limited hardware resources, this approach can be

implemented efﬁciently.

3.3 Potential Issues

The LDEA* algorithm offers a theoretical tolerance

of ±1.5m for a consumer GPS receiver with ex-

pectable inaccuracies. This theoretical tolerance level

is only ﬁtting for the best-case assumption, which

would resemble a GPS point, that is located in the

center of the square on the What3Words world map.

The GPS coordinates may shift arbitrarily in any di-

rection with the same amount of tolerance. This can

be seen in the ﬁrst square of Figure 3.

Figure 3: Varying tolerances due to different point loca-

tions.

In general, it cannot be assumed that the point

lies within the center but rather at a uniformly dis-

tributed location within the square. Thus, different

locations of the point within a given square are pos-

sible and most likely. In a real-world scenario, a po-

tential receiver, who’s location lies on the edge of a

square, might be unable to decrypt the message due to

a square change, if the GPS receiver has inaccuracies.

Considering Figure 3 again, this would be the case if

the receiver is on the marked point within the second

square and owns a GPS receiver with an inaccuracy

rating of up to one meter. If a sender would encrypt

a message for the address ”///dips.pipeline.motivate”

and the receiver would determine his location with

one meter inaccuracy to the left, the What3Words API

could return the address ”///waitress.asleep.pouting”,

thus leading to the receiver being unable to decrypt

the message. Though, the distribution of tolerances

within a given square is always three meters, consid-

ering the designed dimensions of the squares within

the What3Words world map. Regarding these as-

sumptions, an experimental study will be conducted

to identify the real-world tolerance of the LDEA* al-

gorithm. With the design principles at hand, one can

hypothesize that the LDEA* algorithm will not ex-

ceed the tolerance level of three meters.

3.4 Proof of Concept

In order to leverage an experimental study to evalu-

ate the capabilities and the tolerances, the LDEA* al-

gorithm is implemented in a high level programming

language. The fundamental use case for the experi-

mental study involves two parties. The sender pro-

duces arbitrary data which gets encrypted using the

LDEA* algorithm. Consequently, the receiver’s GPS

coordinates are needed by the sender, to successfully

encrypt the data for the desired receiver. These get

provided on runtime. The data itself is being sent

via MQTT as the underlying communication proto-

col. The receiver then attempts to decrypt the data,

using the LDEA* algorithm with the employment of

his own GPS coordinates. If the access key, as well

as the location of the receiver are correct, the data is

decrypted successfully by the receiver.

In order to facilitate the asymmetric key exchange

between the two parties over MQTT, which itself does

not encrypt any data (Singh et al., 2015), RSA was

chosen. The receiver and the sender both own a pri-

vate and public key pair. The sender generates a new,

random symmetric key which will then be encrypted

with RSA and the previously broadcasted public key

of the receiver. The sender then transmits the en-

crypted symmetric key over the insecure network to

the receiver who will be able to decrypt the symmetric

key with his own private RSA key. The key exchange

process is then ﬁnalized and the LDEA* algorithm it-

self can be executed.

4 EXPERIMENTAL STUDY

This chapter examines the real-world performance of

the LDEA* algorithm. The hypothesized outcome of

a tolerance level of three meters will therefore be val-

idated.

What3Words Geo Encryption: An Alternative Approach to Location based Encryption

449

Figure 4: The resulting tolerance in latitude and longitude.

4.1 Methodology

In order to get a measurement for the tolerance level

of a given point, a custom testing method has been im-

plemented. The tolerance in this case is deﬁned as the

distance between the opposite edges within a square,

either in vertical or horizontal direction. Therefore,

randomly chosen points on the world map undergo a

custom testing methodology. Each point P

possesses

a unique GPS coordinate pair (Lat

, Long

). For most

consumer GPS receivers, the accuracy of the ﬂoating

point numbers do not exceed 1.0 ∗ 10

−7

(Wing et al.,

2005). Therefore, this scale can be set as the step size

for the following algorithm:

1. A new random point P

at (Lat

, Long

) is being

generated from a uniform distribution.

2. The point is shared amongst sender and receiver.

Both set the point as their own location for de-

cryption and encryption.

3. The sender encrypts the points latitude and lon-

gitude with the LDEA* algorithm and sends them

to the receiver. A decryption should be successful,

as the receiver knows the position of the point.

4. The sender subtracts an amount of 1.0 ∗10

−7

from

the coordinate and encrypts the new data for the

resulting coordinate. He then sends the message

to the receiver for decryption.

5. The sender repeats the previous step for each

direction until a min

Lat

, min

Long

, max

Lat

and

max

Long

value are reached. At some point, the

receiver will not be able to decrypt the cipher-

text anymore, thus marking the minimum or max-

imum value of the respective coordinate.

6. The distance in meters between the minimum and

maximum coordinates of the latitude and longi-

tude represent the tolerance and can be deter-

mined by utilizing the following formula (Shep-

pard and Soule, 1922):

∆Lat = Lat

− Lat

∆Long = L ong

− Long

tmp

lat

(Lat

+ Lat

)

∗

180

dx = 111.3 ∗ cos(tmp

lat

) ∗ (∆Long)

dy = 111.3 ∗ (∆Lat)

distance =

+ dy

∗ 1000[m]

(1)

This testing algorithm yields a deﬁnitive metric

for the tolerance within a given square in meters.

Thus, this algorithm assigns any given random point

a tolerance value which can be evaluated afterwards.

The value itself represents the mean tolerance within

the square surrounding the given point. Given the pre-

vious hypothesis, the expected value is approximately

three meters.

For this particular evaluation, a dataset of 2000

sample points was generated with lat

∈] − 90, 90]

and long

∈]−180, 180] using a uniform distribution.

Thus, a large scale of the earth surface is evaluated.

The resulting latitude and longitude tolerances are

shown in Figure 4.

4.2 Results

The study yields results which exceed the previously

hypothesized tolerance of three meters by about a me-

ter difference. The resulting mean tolerance of the

study is 3.9302m. To further investigate the results of

the study, the relation between the change in latitude

and longitude of the examined point is of particular

interest. The ﬁrst diagram of Figure 4 assumes a ﬁxed

latitude and a changing longitude value. A change in

IoTBDS 2020 - 5th International Conference on Internet of Things, Big Data and Security

450

longitude will, apart from error noise, tend to a mean

longitude difference value of 3∗10

−4

. No regular pat-

tern can be extracted from the the ﬁrst Diagram of 4.

Though, the difference in latitude remains steadily at

2.6 ∗ 10

−4

Regarding the second diagram of Figure 4, a sig-

niﬁcant parabola shaped pattern results. When alter-

ing the latitude of the random points and ﬁxing the

longitude, the resulting longitude difference describes

a parabola pattern, while the latitude difference stays

at 2.6 ∗ 10

−4

. This relation can be shown in a three-

dimensional plot to further interpret the results. By

utilizing formula 1, which gives a distance between

two points, the effective tolerance in meters can be

visualized.

Figure 5: A 3D plot of the tolerance.

The trapezoid shaped ﬁgure in Figure 5 shows the

relation between the change in the point’s coordinates

and the resulting tolerance in meters. A signiﬁcant

decrease in tolerance for latitude values with an in-

creasing absolute value exists within the data. For

longitude values ∈ [−71, 71] degrees, the tolerance is

tending towards the previously mentioned mean value

of 3.9302m and even exceeding it. This behavior is

contradictory to the statement of the What3Words ser-

vice, which ensures a tolerance of theoretically three

meters. As for latitude values 6∈ [−71, 71], the tol-

erance falls below three meters, thus contradicting

the statement. The expected behavior for the out-

come in regards to the hypothesis would have been a

steady plane in the 3D space on the three meter level.

Though the three-dimensional trapezoid hints towards

a different aspect, which has not been considered yet.

On the one hand, the upper and lower latitudes

of the earth are signiﬁcantly smaller concentric cir-

cles than the latitudes further towards the equator,

thus resulting in different circumferences. On the

other hand, the longitudes all possess the same length,

reaching from the north to the south pole of the earth.

In order to ﬁll the surface of the globe with

squares, like the What3Words service does, a uniform

distribution of the squares is required. The claims

of the service, in regards to the three-by-three meter

squares are thereby not feasible. A grid of equally

sized squares cannot be ﬁtted onto a spherical surface

like the earth. So, in order to keep the organized grid

form, the shape of the squares needs to be morphed.

Thus, the upper and lower lengths or the square get

shrunk down to adapt to the shrinking circumference

of the latitudes. Therefore, the ”squares” should not

be considered as squares at that point but rather as

trapezoids. Therefore, the results of Figure 5 are plau-

sible. With rising absolute value of the latitudes to-

wards the poles, the side lengths of the trapezoid con-

sequently shrink. The tolerances behave accordingly,

as there are lower tolerance bounds for the trapezoid

itself. When lowering the absolute value of the lati-

tude, thereby moving towards the equator, the toler-

ances get bigger as the trapezoid’s side lengths and

consequently its area increase.

Within the interval of [-71,71] degrees of latitude,

no signiﬁcant increase in circumference is appearing

as the curvature of the sphere within this range is not

as steep in comparison to the outer range of the in-

terval. Thus, the tolerance almost stagnates within

this interval, as can be seen in Figure 4. Never-

theless, the average value amongst all the measured

tolerances is well above the hypothesized three me-

ters, thereby contradicting the previously mentioned

hypothesis. The LDEA* algorithm therefore allows

a larger tolerance of 3.9302m. With more samples

at hand, the mean value may tend towards four me-

ters, as the interval of ∈ [−71, 71] degrees includes

more values above four meters than the outer inter-

vals which mainly consist of tolerance values in the

interval ]2.7, 3.5] m.

4.3 Security Considerations

Regarding the security of the LDEA* algorithm, a

potential attacker only needs to gather information

about the location of the receiver with a tolerance of

1.9651m. Due to the XOR operation of the symmetric

access key and the What3Words hash (s. Figure 2), an

attacker might be able to get hold of the secret access

key. When conducting a ciphertext only attack on the

algorithm, the computational effort would be analo-

gous to the effort of breaking the AES-256 algorithm,

thus making it infeasible.

If an attacker would get hold of the randomly gen-

erated key, either by intercepting the key exchange

or rather by extracting the key from a legitimate sen-

sor node within the network, he would only need to

break the What3Words hash. Theoretically, the at-

tacker needs to hash all 57 ∗ 10

possible addresses

What3Words Geo Encryption: An Alternative Approach to Location based Encryption

451

and XOR them with the symmetric key. Though, the

search space can be reduced by a large factor with ad-

ditional knowledge about the location of the receiver,

e.g. the country or state. Also, an attacker might

know even more about the node, e.g. if it is located

within a building thereby excluding rural areas. So,

by educated guessing, a large scale of irrelevant ad-

dresses can be extracted from the set of potential ad-

dresses. This is all assuming that the attacker already

knows the randomly generated key. To hinder an at-

tacker from getting the symmetric key for all the par-

ticipants in the network, it is recommended that every

partner in the network exchanges a unique key with

the sender. This leads to a more complex communi-

cation scheme but beneﬁts the overall security of the

algorithm.

5 CONCLUSION

The experiments conducted in this paper showed, that

the overall mean tolerance of the LDEA* algorithm

lies well above the hypothesized three meters of tol-

erance. This is due to the underlying grid structure of

the What3Words world map. The varying sizes of the

”squares” lead to a divergence of tolerance within the

most northern or southern regions of the earth.

With regards to the LDEA* algorithm, the toler-

ance leads to a larger area of decryption. A poten-

tial sender may very well assume, that a receiver will

be able to decrypt the ciphertext, if encrypted with

the LDEA* algorithm. This assumption only holds,

when the GPS measurement equipment on the re-

ceiver side is accurate enough to fall within the region

3.9302m

= 1.9651m, as the tolerance applies to the

whole ”square”. Modern GPS receivers are well capa-

ble of achieving this level of accuracy by utilizing the

differential GPS technology, described in (Van Sickle,

2015). This allows a GPS receiver to calculate its po-

sition in difference to another ﬁxed point, thus elim-

inating some of the artiﬁcial inaccuracies of the re-

ceivers.

With the LDEA* algorithm at hand, e.g. an IoT

sensor network is able to efﬁciently encrypt the data

shared between the communication partners, who op-

erate in a publish-subscribe scheme. Future work may

focus on the concrete implementation of a tamper-

proof GPS receiver, since this aspect is assumed as

given in this paper. Existing proposals by Pozzobon

et al.(Pozzobon et al., 2011) already give a theoretical

approach but lack an implementation of the system

itself.

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