Wireless Sensor Networks IKE Phase One Negotiation Approach
based on Multivariate Quadratic Quasi-groups
Yassine Essadraoui and Mohamed Dafir Ech-cherif El Kettani
Information Security Research Team ISeRT, Mohammed V University in Rabat, Rabat, Morocco
Keywords: Internet Key Exchange, Wireless Sensor Network, Multivariate Quadratic Quasigroups, Internet of Things.
Abstract: Key management is one of the biggest problems in IoT security. The Internet Key Exchange (IKE) protocol
is well known as a secure key exchange protocol to establish secure channels between two hosts. However,
IKE uses RSA as public key cryptography algorithm that is based on Diffie-Hellman (DH) key exchange
which is very heavy, in term of arithmetic operations, for very constrained resources devices such as the
case for WSNs. In this paper, we propose to use Multivariate Quadratic Quasigroups (MQQ) to negotiate
and share a secret key between two sensors. Phase 1 of the IKE protocol is supposed, by the proposal in this
paper, to use MQQ instead of Diffie-Hellman (DH) key exchange.
1 INTRODUCTION
Internet is the biggest network used for different
goals and offers different services. Each service
requires some level of security (integrity,
authorization, confidentiality, ...) and to achieve this
goal different algorithms and protocols have been
proposed and used. The most used protocol is IPsec.
IPsec uses two protocols to provide traffic security
services, Authentication Header (AH) and
Encapsulating Security Payload (ESP)(R.~Atkinson,
1995). The Internet Key Exchange (IKE) protocol
belongs to IPsec protocol suite and is used to
establish secure channels between hosts
implementing IPsec. IKE prepares what’s called
security associations (SA) that will be used, by IPsec
protocol, for transmitting data securely between
nodes involved in a communication (Hallqvist and
Keromytis, 2000). In symmetric cryptography, two
peers share a secret key and use it for encryption and
decryption. This kind of cryptography is secure as
well as the secret key is protected and kept secret
between the two parties involved in the
communication. As we can see peers need to
exchange the secret key securely, with big systems
where many communications should be established
it’s not easy to keep and exchange securely all
shared keys. The Internet Key Exchange (IKE)
protocol is used to produce, independently and
dynamically, the same key in each communicating
peer. IKE proceeds by authenticating both sides and
negotiating encryption algorithms. The result of an
IKE negotiation is a Security Association.
Internet Key Exchange relies on Diffie-Hellman
(DH) algorithm to exchange the shared secret key
between hosts. DH builds the shared secret key on
each side without having to exchange the secret key
between peers. In our context of wireless sensor
networks (WSN) using IKE without modification
won’t be practical viewing WSN’s constraints
(limited calculation power, memory, energy, ...) also
the Diffie-Hellman algorithm is a little heavy, in
term of arithmetic operations needed to share the
secret key between peers in communication, to be
used in a sensor. Our approach is to use Multivariate
Quadratic Quasi-groups to exchange the shared key
and to do mutual authentication of communicating
nodes. Our work will be based on a previous work
(Essadraoui and Dafir Ech-cherif El Kettani, 2015)
which proposed an authentication approach based on
Multivariate Quadratic Quasi-groups (MQQ). In the
proposed approach nodes do mutual authentication
and share a secret key that could be used for
symmetric encryption and decryption.
MQQ has emerged as an alternative to classical
cryptography schemes and was seen that MQQ is
faster in encryption and decryption. In (El-Hadedy et
al., 2008) authors have done an implementation that
is 10,000 times faster in decryption and 17,000 times
faster in encryption than RSA. In (Quirino and
Moreno, 2013) authors have found that in ARM
224
Essadraoui, Y. and Kettani, M.
Wireless Sensor Networks IKE Phase One Negotiation Approach based on Multivariate Quadratic Quasi-groups.
DOI: 10.5220/0006241902240231
In Proceedings of the 2nd International Conference on Internet of Things, Big Data and Security (IoTBDS 2017), pages 224-231
ISBN: 978-989-758-245-5
Copyright © 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

platform MQQ is faster and uses less amount of
memory compared to ECC (Zhu et al., 2008) and
RSA(Breu et al., 2008).
The remaining of this paper will be organized as
follow, section 2 gives an overview of Internet
exchange protocol, in section 3 we introduce
multivariate quadratic quasi-groups, in section 4 an
overview of wireless sensor networks is given, in
section 5 we present the proposed lightweight
version of IKE for WSNs, in section 6 we give a
security analysis of the proposed protocol and in
section 7 we give a conclusion.
2 OVERVIEW OF INTERNET
KEY EXCHANGE (IKE)
Internet Key Exchange protocol (IKE) (Kivinen and
Snyder, 2015) is used in conjunction with IPsec to
dynamically and automatically create security
associations (SA), especially for a large scale
deployment IKE becomes very useful. IKE is based
on the Internet Security Association and Key
Management Protocol (ISAKMP), Oakley key
management protocol and SKEME key management
protocol. The IKE is two phases protocol. Phase One
starts the process to establish SA between two peers
by authenticating all peers, then creating a Diffie-
Hellman key and agreeing on methods for phase two
of IKE. The creation of Diffie-Hellman key means
that peers will have a shared secret key. All
exchanges and agreements preformed during phase
one must be done securely. Figure 1 depicts IKE
phase one process.
Phase Two consists of using all algorithms,
methods and keys that have been chosen by
agreements performed in phase one. During phase
two a new security association is going to be built
and prepared for IPsec, in fact IPsec security
association is an agreement on methods and keys
that will be used by IPsec. Figure 2 depicts IKE
phase two process.
At the end we can say that IKE phase one
prepares methods and keys for IKE phase two which
itself prepares methods and keys for IPsec.
3 OVERVIEW OF
MULTIVARIATE QUADRATIC
QUASI-GROUPS (MQQ)
Multivariate Quadratic Quasi-groups (MQQ) is a
system of m multivariate quadratic equations with n
Figure 1: IKE phase one process.
Figure 2: IKE phase two process.
variables over a finite field F. This system of
multivariate quadratic equations is easy to evaluate
for some given values from F but it’s very difficult
to find its inverse and if a brute force attack is
launched against this system the time needed will be
exponential depending on the number of variables.
A MQQ system is considered secure because it
doesn't rely on the difficulty of calculation of the
problem of factorization and the discrete logarithms.
STS (Shamir, 1994), TTM (Moh, 1999), HFE
(Patarin, 1996), UOV (Kipnis et al., 1999) are
examples of systems that have been proposed based
on multivariate quadratic (MQ) problem but most of
these schemes have been broken. In 2008 a new
approach called Multivariate Quadratic Quasi-
groups (MQQ)(Gligoroski et al., 2008a)(Gligoroski
et al., 2008b) have been proposed by Gligoroski et al
based on the theory of quasi-groups.
Multivariate Quadratic cryptography consists of
solving systems of multivariate quadratic equations
Wireless Sensor Networks IKE Phase One Negotiation Approach based on Multivariate Quadratic Quasi-groups
225

over a finite field.
Let’s consider a system P of m multivariate
quadratic polynomial equations with n variables
over a finite field F.
(1)
where y
i
belongs to F. Each p
k
is a polynomial of
degree two over F of the form:
(2)
where a
ij
(k)
, b
i
(k)
, c
(k)
belong to F and 1 ≤ k ≤ m. The
coefficients a
k
, b
k
and c
k
are called the quadratic,
linear and constant parts of the polynomial p
k
,
respectively. The challenge is to find a solution x to
the system P. The MQ-problem is a NP-complete
problem (Patarin et al., 1997).
The m multivariate quadratic equations of P
system are composing the public key, as we
mentioned before the MQ problem is NP-complete
so we need an easily invertible (Ding and Yang,
2009) trapdoor function to be defined into
polynomial equations.
The construction of P, the public key, is done
through a composition of three functions S, P’ and T
such as P = T○P’○S where S: F
n
→ F
n
and T: F
m
→
F
m
are linear or affine transformations and are easily
invertible and they are used to hide the function P’
which is a quadratic function such as P’: F
n
→ F
m
.
P’ should be easily invertible. The private key is the
triple (S, P’, T). Figure 3 illustrates how to use the
MQ public and private key in cryptography.
In this paper we are interested in MQ-schemes
that are based on quasi-groups which means that the
central map P’ will be constructed using quasi-
groups. Any multiplication group is a quasi-group.
In particular, an abelian group is where
multiplication is commutative and associative.
However, quasi-group multiplications are not
required to be associative. It is in this sense that
quasi-groups are considered to be “non associative
groups”. Finite quasi-groups are characterized as
having bordered Latin squares for their
multiplication tables. (Smith, 2007)
Figure 3: Public key encryption based on MQ system.
As an example of Quasi-groups we mention
Latin squares. A Latin square is an n × n square
filled with n different symbols, in such a way that
each symbol occurs exactly once in each column and
in each row. Each Latin square is a multiplication
table of a quasi-group. Tables in Figure 4 list a Latin
square and a corresponding finite quasi-group.
Figure 4: A Latin square and its corresponding Quasi-
group.
A quasigroup (Q, *) of order 2
d
is called
Multivariate Quadratic Quasigroup (MQQ) of type
Quad
d-k
Lin
k
if exactly d - k of the polynomials f
i
are
of degree 2 (i.e., are quadratic) and k of them are of
degree 1 (i.e., are linear), where 0 ≤ k < d.
(Gligoroski et al., 2008b)
Q is a quasi-group such that a1,a2, a3,... an
belong to it, then the encryption operation, which is
defined over the defined elements, maps those
elements to another vector b
1
, b
2
, b
3
,...b
n
such that
the elements of the resultant vector also belong to
the same quasi-group. Markovski and Dimitrova
(Dimitrova and Markovski, 2004) show that
mapping of an incoming stream of data depends on
the initial multiplier element. The mathematical
equation used for encryption (Dimitrova and
Markovski, 2004) is defined by:
IoTBDS 2017 - 2nd International Conference on Internet of Things, Big Data and Security
226

E
a
(a
1
, a
2
, a
3
, ..., a
n
) = b
1
, b
2
, b
3
,..., b
n
(3)
where the output sequence is defined by:
b
1
=a * a
1
(4)
where i increments from 2 to the number of elements
that have to be encrypted, and a is the hidden key.
A MQQ system looks like the following system:
y
1
= x
12
+ x
1
x
3
+ x
2
x
3
+ x
2
x
4
+ x
32
+ x
3
x
4
+ 1
y
2
= x
12
+ x
1
x
2
+ x
1
x
3
+ x
22
+ x
2
x
4
+ x
32
+ x
42
+ 1
y
3
= x
1
x
2
+ x
1
x
4
+ x
2
x
3
+ x
2
x
4
+ x
32
+ x
3
x
4
+ x
42
y
4
= x
1
x
2
+ x
1
x
3
+ x
22
+ x
2
x
3
+ x
3
x
4
(5)
with x, y belong to (F
q
)
n
and F is a finite field.
Solving this system is NP-complete over any field.
The system of equations must include a hidden
trapdoor function P' and two other functions S and
T. P' is a quadratic form, that is easily invertible
[12]. T and S are affine forms that are very hard to
guess or calculate. The public key P is the
composition of T, P' and S, we hide the trapdoor
function P' by composition with T and S as follows:
P = T○P'○S
(6)
Public key must be a one-way function. The
private key is the secret matrices T, P', S.
4 OVERVIEW OF WIRELESS
SENSOR NETWORKS (WSN)
A Wireless Sensor Network (WSN) is a network of
nodes called sensors. Sensors are resource
constrained devices which have as main role sensing
data and send it to other sensors or a more powerful
Base Station (BS). The BS will gather all sent data
from sensors and process it. All sensors in a WSN
communicate through a wireless connectivity, these
sensors have, in general, as mission to sense data
and send it to a Base Station (BS), which is, in
general, a static node see Figure 5.
Sensor nodes wait for a specific event (smoke,
fire, sound …) to happen. Once the event of interest
occurs, the sensor node (one or many) that have
detected the event gathers all relevant data to the
event and sends it to the Base Station. The sensor
node can send data directly to the BS (if it was near
to it) or by hope-by-hope until the BS. It may
happen that the BS receives multiple reports on the
same event by the event's surrounding nodes.
Figure 5: Wireless sensor network architecture.
Surrounding nodes may collaborate to send one
single report to the BS. The BS after receiving the
report can process it and decide whether to send
orders to concerned nodes in view to have more
details or to express its need of a specific
information or to forward the result of its processing
to the external world. As you can see the BS is
acting as a gateway between the WSN and the
external world.
WSN permit observing places that were
unobservable or were difficult to observe and give a
way to monitor specific event for long duration.
WSN also offers a variety of potential applications
to industry, science, transportation, security, ...
Flexibility of deployment that offers WSN has,
Conversely, many challenges such as
Responsiveness, Self-Configuration and Adaptation,
Scalability, Privacy and Security, Energy Efficiency,
Heterogeneity, ...
Before starting the conception of a security
protocol that satisfy requirements above, we should
emphasize that sensor nodes are resource
constrained devices which is a limiting factor for
designing efficient security procedures. We focus
on two main constraints: Memory and Energy.
Memory: Sensor nodes are not designed to store
a huge amount of data, this is because the very little
amount of available memory. Little memory size is a
limiting factor for designing sophisticated security
algorithms or using existing security algorithms
(RSA, ...). In order to build an efficient security
scheme, the code size of the security algorithm must
be small. A typical sensor node processor is of 4-8
MHz, having 4KB of RAM, 128KB flash and
ideally 916 MHz of radio frequency (Kavitha and
Sridharan, 2010). For example, TelosB has a 16-bit,
8 MHz RISC CPU with only 10K RAM, 48K
program memory, and 1024K flash storage.
Wireless Sensor Networks IKE Phase One Negotiation Approach based on Multivariate Quadratic Quasi-groups
227

Energy: Sensor nodes, besides having small
amount of memory, have also limited amount of
energy, in fact each sensor node has a small battery
power. Sensor nodes haven't to do complicated
processing that consumes energy. Energy is a very
constraining factor for wireless sensor nodes. Once a
sensor node has been deployed in WSN it’s difficult
or very expensive to try to recharge it or to replace
it. Hence, sensor node’s battery life must be
extended as longer as possible and for any
conception or implementation of a security
algorithm in a sensor node the energy consumption
must be well studied and measured. Adding a
security protocol to a sensor node without
considering the energy factor is not a wise strategy
and this will affect and make troubles for the whole
network as well as for the sensor node itself. When
we talk about energy consumed by a security
algorithm, mainly we talk about the processing
needed for security procedures like encryption,
decryption, signing and verifying data. Several
WSN’s Operating systems provide features to save
and economize energy (Healy et al., 2007)
Sensor nodes are widely used in many fields like
health, military, environmental conditions, …
viewing their critical mission sensor nodes need to
be secured and viewing their limited memory and
energy need efficient and optimized security
algorithms. Wireless communication between sensor
nodes facilitates intruders mission where the need to
guarantee integrity and confidentiality of exchanged
data and authenticity of all sensor nodes in a way
that only legal nodes that will participate in
communications. (Shi and Perrig, 2004)
5 PROPOSED LIGHTWEIGHT
IKE FOR WSN
A wireless sensor network is a set of sensors.
Sensors are resource constrained devices (small
amount of memory, low computational power, ...) so
for any protocol conception those constraints should
be taken into account. In this work we propose a
light version of IKE protocol suitable for sensors,
more precisely we suggest an approach of
authentication and common secret key sharing
between peers and using IKE. Peers authentication
and sharing secret key are performed during IKE
phase one. We consider the scheme in Figure 5.
At first the Base Station (BS) generates its Public
(BS
PK
= T
BS
○P’
BS
○S
BS
) and Private (T
BS
, P’
BS
, S
BS
)
MQQ-based keys and publishes the public key to all
nodes. Any node who desires to join the network
should first be registered by the BS. At the end of
registration phase, the joining sensor’s MQQ-based
public key could be published as a registered sensor
node. The BS serves as a certification authority, it
guarantees that a specific public key belongs to the
node who claims it belongs to.
In the registration phase, a Sensor Node (SN)
who desires to join the network sends its ID to the
BS. The SN generates its MQQ-based Public/Private
keys and uses BS public key (BS
PK
=T
BS
○P’
BS
○S
BS
)
to resend its public key (SN
PK
= T
SN
○P’
SN
○S
SN
) plus
the signature of its MAC address encrypted using
the known BS public key (BS
PK
): T
BS
○P’
BS
○S
BS
(Sig(ID) + Sig(MAC) + SN
PK
). BS is the only node
able to decrypt the message. The BS gets the SN’s
public key then declares the SN as a registered node
and publishes SN’s MQQ-based public key.
After registration, SNs, in view to communicate,
must authenticate each other and share a secret key.
The Initiator sends its list of cryptographic proposals
(SA
prop
) to the receiver. The receiver selects from the
proposals and responds by sending its selected list of
cryptographic algorithms (SA
select
). At this point we
have started the IKE phase one process and all
exchanged messages have the ISAKMP (Maughan
D, Schertler M, Schneider M, 1998) header (HDR).
HDR contains:
Initiator’s Cookie (8 octets)
Receiver’s Cookie (8 octets)
Next Payload (1 octet)
Major Version (4 bits)
Minor Version (4 bits)
Exchange Type (1 octet)
Flags (1 octet)
Message ID (4 octets)
Length (4 octets)
In view to share a secret key and do mutual
authentication peers do as follows:
1) The Initiator generates its cookie C
I
, prepares its
proposals list SA
prop
and sends them to the
receiver with signature of its ID
I
plus timestamp
T
I
using its MQQ-based private key (T
SNI
, P’
SNI
,
S
SNI
). The Initiator encrypts the signature of its
ID
I
and T
I
using the receiver’s published public
key (SN
PKR
= T
SNR
○P’
SNR
○S
SNR
) to be sure that
only the Receiver that could decrypt the
message.
2) The receiver responds with its selected proposal
SA
select
, its generated cookie C
R
and the
signature of its ID
R
plus a timestamp T
R
using
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228

its MQQ-based private key (T
SNR
, P’
SNR
, S
SNR
).
The receiver encrypts the signature of its ID
R
and T
R
using the Initiator’s MQQ-based public
key (SN
PKI
= T
SNI
○P’
SNI
○S
SNI
) to be sure that
only the Initiator that could decrypt the
message.
The Initiator decrypts the received message from
the receiver, then gets the Receiver’s ID
R
, the
timestamp T
R
.
The receiver decrypts the received message from
the Initiator, then gets the Initiator’s ID
I
, the
timestamp T
I
.
3) At this stage both peers have exchanged their
IDs and identified each other’s public keys, then
the Initiator calculates a hash of a generated
nonce N
I
HASH(N
I
) and encrypts the hash with
the Receiver’s public key then sends it to the
Receiver.
4) The receiver extracts the nonce N
I
and also do
the same by calculating a hash of a generated
nonce N
R
HASH(N
R
) and encrypts the hash
with the initiator’s public key and sends it to the
Initiator.
Now both peers have succeeded to exchange
their generated nonce and they could construct their
shared secret key by doing a composition of both
nonces N
I
*N
R
. We summarize this process of mutual
authentication and sharing secret key in Figure 6.
6 SECURITY CONSIDERATIONS
 Man-in-the-middle Attack
Man-in-the-middle attack is where two peers believe
that they are communicating directly to each other,
but in reality they are communicating through an
intruder node that have succeeded to impersonate
both peers and have gained access to their
information and their exchanged messages.
Let’s consider this situation where 2 sensor
nodes SNA and SNB are initiating an IKE session
and a malicious node SNC tries to enter in between
SNA and SNB to do a Man-in-the-middle attack.
Figure 6: Authentication and share of secret nonce.
Our proposal is free from this attack viewing that
any joining sensor node is first registered by the
Base Station (BS) that stores each sensor node’s
MQQ-based public key, ID and MAC address. In the
process of exchanging nonces sensor nodes
exchange their mutual IDs encrypted using the
public key, which have been already published by
the BS, of the other sensor node. A malicious node
can’t do a man-in-the-middle attack because all
public keys are published by the BS and sensor
nodes have exchanged their IDs encrypted using
each other’s public key.
 Replay Attack
A replay attack is where a malicious node
intercepts a message and tries later to reuse it by
resending the intercepted message to a receiver in
view to trick it or to gain some privileges illegally.
Our proposal is free from this attack viewing that
any exchanged message between 2 sensor nodes
contains the cookie (ISAKMP header) of the
Initiator or the Receiver and among information
included in a peer’s cookie is the timestamp that the
sender estimated for the moment when the message
was sent. Any sensor node compares any received
message’s timestamp with the last received
timestamp and it cancels the communication if there
was any inconsistency between timestamps.
 Denial-of-service (DoS) Attack
Wireless Sensor Networks IKE Phase One Negotiation Approach based on Multivariate Quadratic Quasi-groups
229

A denial-of-service happens when a network or a
node is targeted in view to make it unavailable or
unresponsive temporally or permanently.
Our proposal is free from this attack viewing that
every exchanged message contains ISAKMP header
which contains Initiator’s and Receiver’s cookie (C
I
,
C
R
)
 Impersonation Attack
An impersonation attack is where a malicious
node presents itself to other network nodes by
impersonating a legitimate node in view to exchange
messages on behalf the legitimate node.
Our proposal is free from this attack viewing that
an attacker couldn’t read a message encrypted by the
legitimate node’s MQQ-based public key (which has
been already published by the BS).
7 CONCLUSION
A lightweight version of the IKE protocol based on
Multivariate Quadratic Quasi-groups (MQQ) is
discussed in this paper. MQQ is not based, like RSA
or ECC, on the difficulty of solving factorization
problem or discrete logarithm and is for this reason
MQQ is considered as a
post-quantum algorithm.
MQQ has emerged as an alternative to classical
cryptography schemes and was seen, as mentioned
before, that MQQ is faster, than RSA and ECC, in
encryption and decryption so it’s a promising public
key cryptography alternative, especially to adapt
existing protocols, like IKE in this paper, to wireless
sensor network’s context. A security analysis of the
proposed protocol against some known attacks is
done and is shown that the proposed protocol is
secure. We are in preparation of some
implementation for this approach to endorse it with
experimental results.
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