Rethinking Self-organized Public-key Management for
Mobile Ad-Hoc Networks
Candelaria Hern
, Pino Caballero-Gil
and Amparo F
Dept. Statistics, O.R. and Computing, University of La Laguna
38206 La Laguna (Tenerife), Spain
Institute of Applied Physics, C.S.I.C., 28006 Madrid, Spain
Abstract. In this paper, the self-organized public-key management scheme pro-
posed for MANETs is considered in order to guarantee that all nodes play identi-
cal roles in the network. Our approach involves that the responsibility for creating,
storing, distributing and revoking nodes’ public-keys is on the nodes themselves.
In particular, the methods here described and evaluated are aimed at improving
the process of building the local certificate repositories associated to each node
in the self-organised model. In order to do it, we face the problem by combin-
ing known authentication elements such as the web-of-trust concept, together
with common ideas of routing protocols, such as the MultiPoint Relay technique
used in the Optimized Link State Routing protocol. Our proposal leads to a sig-
nificant improvement in the efficiency of the whole model and implies a good
trade-off among security, overhead and flexibility. Results of experiments show
an important reduction in resource consumption while undertaking the certificate
verification process associated to the authentication.
1 Introduction
Lack of fixed infrastructure, highly dynamic topology, heavy constraints in node’s ca-
pabilities jointly with they spontaneous nature are some of the characteristics of Mo-
bile Ad-hoc Networks (MANETs) that hinder to provide them with security services.
A particular example of this situation is the deployment of Public Key Infrastructure
(PKI). The proposals in the bibliography related to the previous issue adopt two main
approaches: using a distributed certification model or a self-organized scheme.
In the first case, the certification process is underpinned by distributed Certification
Authorities (CAs), which use a threshold digital signature scheme and are in charge of
issuing and renewing certificates associated to the members of the network. One of the
first proposals under this approach was put forward in [1]. There, a group of special
nodes, acting as a coalition, were responsible for certification tasks. The main draw-
backs of this model are the computational intensive operations required by the threshold
application when signing a certificate, and the definition of additional procedures such
Research supported by the Spanish Ministerio de Ciencia e Innovaci
on and FEDER funds
under grant TIN2008-02236/TSI
Hernández-Goya C., Caballero Gil P. and Fúster-Sabater A. (2009).
Rethinking Self-organized Public-key Management for Mobile Ad-Hoc Networks.
In Proceedings of the 7th International Workshop on Security in Information Systems, pages 103-110
DOI: 10.5220/0002175401030110
as share refreshing [2]. Also, when dealing with certificate validation, nodes should lo-
cate a correct coalition but, depending on the actual network topology and conditions,
it might result infeasible.
Consequently, the scalability of the proposal cannot be considered adequate since
as network size increases, computational and communication overload increases too.
Later on, in [3] and [4], nodes playing special roles are not considered since the CAs
secret key used for signing certificates is distributed among all the nodes in the network.
In this paper the self-organised method for public-key management is chosen as
base in order to guarantee identical roles for all the network nodes. This approach in-
volves the relocation of the responsibility for creating, storing, distributing, and revok-
ing their public keys to the members of the network.
The method here described and evaluated is aimed at improving the process of build-
ing the local certificate repository associated to each node in the self-organised model.
This will lead to significant improvements in the efficiency of the whole model. Partic-
ularly, as it will be appreciated from the experiments, a reduction in resource consump-
tion while undertaking the verification process associated to authentication is obtained.
In order to achieve this aim, we face the problem by combining typical authentication
elements with common ideas used in routing protocols in MANETs. In particular, the
Optimised Link State Routing (OLSR) protocol from which some ideas regarding the
use of the Multi-Point Relay (MP R) technique have been borrowed in order to design
the algorithm for updating repositories.
The structure of this paper is as follows. Section 2 is devoted to the description
of the M P R technique. Since our proposal is specifically designed to be deployed
in the self-organised key management model, section 3 deals with the details of that
approach, including the description of the method originally proposed to built such
repositories called Maximum Degree Algorithm (MDA). Both the M P R technique
described in section 2 together with the graph-based public-key certification protocol
described in section 3 constitute the keystones of the proposal. A complete algorithmic
description of the method is also provided here. Section 4 describes the results of several
computational experiments carried out with the objective of comparing the M P R and
MDA approaches. Some questions that deserve more research and the final conclusions
are included in last section.
2 Preliminaries
In order to improve the construction of certificate repositories defined in the key man-
agement scheme when adopting the web of trust model and the self-organised approach
to implement a Public-Key Infrastructure (PKI) we use certain elements of the proac-
tive routing protocol known as OLSR protocol, one of the four basic protocols adopted
for MANETs. This section contains an introductory description of this protocol, paying
particular attention to the MP R technique embedded in such protocol.
OLSR belongs to the proactive set of protocols. In networks with high mobility
these routing protocols have a good behaviour since the paths are re-calculated as soon
as a link state change is detected. Building an accurated topological map of the network
requires exchange of information among nodes on a regular basis, which can lead to
certain network overloading on the network, unless network traffic is sporadic. On the
other hand, when dealing with delay-sensitive networks (such as VANETs) the OLSR
protocol outperfoms better [5].
Most proactive protocols consider techniques aimed at controlling overhead. In
OLSR the technique used is MPR. An example of the important improvements ob-
tained when introducing these procedures is the reduction on redundant packets. It may
reach the 60% under some conditions [6].
It can be said that this technique allows determining the minimum number of nodes
needed for reaching the whole network when it is recursively applied. This procedure
is named as the MultiPoint Relay (MPR) technique. The way we will utilise the basics
of this technique in the key management proposal as well as its relationship with Graph
Theory problems are included below.
The MPR technique was originally deployed for reducing the duplicity of messages
at local level when broadcasting information in a proactive MANET. In general, the
number of redundant packets received by a node may be equal to the number of neigh-
bours a node has. In the OLSR protocol, only a subset of nodes will be in charge of
retransmitting the received packets. In this way, every node u must define among its
direct neighbours a set of transmitters (here denoted by MP R(u)) that will be the only
ones in charge of retransmitting the messages emitted by the initial node.
According to this method, the choice of the set M P R should guarantee that all the
nodes in a two-hop distance of the initial node receive the messages. In order to fulfil
this requirement every node in a two-hop distance of u must have a neighbour belonging
to MP R(u).
In routing models the network is usually represented with a graph whose vertex
set V = {u
, u
, . . . , u
} symbolizes the set of nodes of the network. In this way,
for any node u, N
(u) denotes the set of us neighbours in a i-hop distance from u.
Consequently, N
(u) stands for us direct neighbours. These sets are defined by using
the shortest path and in such a way that N
(u) and N
(u) are disjoint sets.
With the notation previously introduced the M P R set for a vertex u may be defined
as MP R(u) N
(u)|∀w N
(u)v MP R(u)|w N
The MPR heuristic defined in the OLSR routing procedure uses a greedy approach
handling the vertex degree as parameter. The idea is to select the neighbours of the
original vertex u which cover the highest number of vertices in us two-hop vicinity
that have not been previously covered.
The greedy heuristic is composed by two main stages stages. In the first one those
vertices w in N
(u) which have an only neighbour v in N
(u) are examined, in order
two include in M P R(u) the vertex v to which is connected. In case there are remaining
nodes without covering in N
(u) those vertices in N
(u) which cover more vertices in
that situation are also included in MP R(u) in the second stage.
Analyzing the description of the problem from the Graph Theory point of view, it
can be concluded that the node being examined and its M P R set must form a dominant
set in its level 2 vicinity. A dominant set in a graph is a vertex subset such that any node
in the corresponding graph has and edge linking it to a vertex in the dominant set.
3 Key Management in MANETs: Self-organized Model
In the bibliography we may find two main alternatives for the deployment of PKI in
MANETs: distributed certification authorities, and self-organized public-key manage-
ment model.
In this work we decided to follow the self-organized key management model based
on the web of trust approach. Several are the reasons that justify the choice of this
option. First, this model demands less maintenance overhead. Secondly, it is well worth
remarking that on the one hand the self-organized approach eases the use of a simple
bootstrap mechanism and on the other hand all the nodes perform equal roles.
The self-organized model in MANETs was initially described in [7]. Its authors put
forward the substitution of the centralized certification authority by a self-organized
scenario where certification is carried out through chains of certificates which are issued
by the nodes themselves. Such a scheme is based on the information stored by each node
and the trust relationship among neighbour nodes.
In this model public keys and certificates are represented as a directed graph G =
(V, A), known as certificate graph. Each vertex u in this graph defines a public key
linked to a node, and each arc (u, v) symbolizes a certificate associated to vs public
key, signed by using us private key. Each node u has a public key, a private key, and
two certificate repositories, the updated (G
) and the non-updated repositories (G
Initially the updated certificate repository will contain the list of certificates on which
each node trusts (out-bound list) and the list of certificates of all the nodes that trust on
u (in-bound list).
When a certificate for a node u is issued by a node v the edge (v, u) is added to
the certificate graph and each node u and v stores it in its in-bound and out-bound list,
In the original proposal two ways of building the updated certificate repository G
of a node u were described:
1. Node u communicates with its neighbours in the certificate graph.
2. Node u applies over G
an appropriate algorithm in order to generate G
checking the validity of every single certificate.
The selection of the certificates stored by each node in its repository should be done
carefully in order to satisfy at the same time two requirements: limitation in storing
requirements, and usefulness of the repository in terms of ability to find chains for the
largest possible number of nodes.
The algorithm used in the construction of the updated repositories will influence in
the efficiency of the scheme, so it should be carefully designed. The simplest algorithm
for that construction is the so-called Maximum Degree Algorithm (MDA), where the
criterion followed in the selection of certificates is the degree of the vertices in the
certificate graph.
When using the MDA, every node u builds two subgraphs, the out-bound subgraph
and the in-bound subgraph, which when joined generate the updated certificate repos-
itory G
. The out-bound subgraph is formed by several disjoint paths with the same
origin vertex u while in the in-bound subgraph u is the final vertex. The starting node
is u and deg
(u), deg
(u) stands for the out-degree and the in-degree respectively of
node u. The number of chains to be found is represented by c.
Note that the process to build the in-bound subgraph is equivalent to it except for
the fact that in this case the edges to be chosen are always incoming edges.
In this paper it is proposed to substitute the MDA algorithm proposed for the up-
dated repository construction by a new algorithm that uses the M P R. In this way, for
each vertex in the certificate graph we have to define a re-transmitter set. Hence, the
smallest number of vertices required for reaching the whole certificate graph will be
In order to extend the notation used in 2, which is required to be used in the certifi-
cate graph, we denote by N
(u) the set of predecessors of node u that may be found in
an i-hop distance.
The algorithm proposed is an iterative scheme and it can be summarized as folllows.
First, node u starts by calculating M P R(u) = {v
, v
, . . . , k}. Then, these vertices are
included in G
together with the edges (u, v
), i = 1, 2, . . . , k. Henceforth, nodes
in M P R(u) apply recursively the same procedure of retransmitting backwards the
result MP R(v
The certificate chains required in the authentication are built by using the arcs
(u, M P R(u)). After that, v M P R(u) and w MP R(v) the arcs (v, w) are
also added after having checked that they have not been added in previous updates.
Note that the procedure every node u G has to develop in order to build MP R(u)
takes 1 + ln(N
(u)) steps when no bound is defined on the length of the chains to be
built. Otherwise, the number of iterations to be carried out is given by the number of
hops to explore in the certificate graph. As for the definition of the aforementioned
bound, it has to be remarked that such a parameter may be dynamically adjusted in
function of the changes experienced by the certificate graph. This may be justified by
the fact that as the network evolves, the information contained in each node’s repository
is more complete.
Thanks to this substitution the generated procedure is easier and more efficient,
guaranteeing in this way that each node has a set of neighbours that allows it to reach
the biggest number of public keys. One of the main advantages of the proposal is that
all the information gathered for the construction of the chains is locally obtained by
each node.
After obtaining the in-bound (MP R
) and out-bound (M P R
) sub-
graphs, both are merged and the initial repository (G
) is generated. When a node u
needs to check the validity of the public key of another node v, it has to find a certifi-
cate chain from itself to v in the graph that results from combining its own repository
with vs repository. If this chain is not found there, the search is extended to G
what implies the inclusion of us non-updated repository in the search. If this second
exploration is successful, u should request the update of those certificates that belong
exclusively to G
. When no path is found, the authentication fails.
4 Experimental Results
This work proposes the application of the MPR technique in the computation of cer-
tificate repositories included in the self-organized public-key management model pro-
posed by [7]. Our proposal is supported by the good results obtained when using the
MP R procedure in the OLSR routing algorithm in MANETs as well as computa-
tional experiments. A detailed description of the implementation and the results pro-
vided by it is presented in the current section. The main goal of the experiments was
showing that applying the MPR technique when building certificate repositories in the
self-organized approach instead of using the MDA heuristic provides the public-key
management scheme with simplicity and efficiency.
4.1 Implementation Characteristics
The implementation has been carried out using Java and the open source library JUNG
2.0 (Java Universal Network/Graph Framework) which provides the basic tools for rep-
resenting and dealing with graphs. One of the reasons why JUNG was selected was
having the possibility of working with random graphs with the small-world property.
When a graph follows the small-world model, it is assumed that its paths have a small
average length and a high Clustering Coefficient (CC). The CC corresponds with the av-
erage of the fraction of pairs of us neighbors (taken over all the network nodes u |V |)
which are at the same time direct neighbors of each other.
This characteristic is supported by certificate graphs as it was shown in [8]. When
a graph holds this feature, most nodes may be reached by a small number of hops from
any source node. This kind of graphs has received special attention in several scientific
disciplines. The particular small-world model used in the simulation developed was
proposed by Kleingberg [9]. When generating a graph with |V | = n
vertices according
to this model, the first step is to create an nxn toroidal lattice. Then each node u is
connected to four local neighbours, and in addition one long range connection to some
node v, where v is chosen randomly, according to a probability proportional to d
d denotes the lattice distance between u and v and α stands for the CC. Generating
the graphs following this model guarantees that the shortest paths may be determined
using local information, what makes them particularly interesting for the networks we
are dealing with.
4.2 Computational Results
The computational experience consisted of generating random graphs according to the
Kleingberg’s model where the size of the graphs |V | ranges in the interval [9, 441], the
CC takes values between [0, 30]. For this parameters, the Certificate Rate obtained by
) jointly with time consumption (t
) expressed in seconds were
For analyzing the M DA alternative, it is applied over the same input graphs using
as specific parameters the maximum number of chains to built (n
) and their max-
imum length (C
) is bounded by 7. In this case, the Certificate Rate in the repository
) and time consumption (t
) were also obtained.
(a) |V | (b) CC
Fig. 1. Comparing certificate rates.
Fig. 2. Certificate Rate Difference.
From this experience, there are some general conclusions that may be remarked.
The certificate rate CR
finally contained in the local repository increases as the
size of the graph increases. However the behavior of the certificate rate is not affected by
the growth of the CC (). This phenomena may be better appreciated in figures 2(a) and
2(b), respectively. Additionally, the maximum length in the chains obtained by M P R
are kept at reasonable values, what makes the chain verification process lighter.
Probably the most important fact when comparing the certificate rates CR
is that only in the 3.95% of the executions the MDA algorithm outperforms
MP R, and it only occurs when the input certificate graph is small (see figure 2.(a)). Al-
though, in the previous figure it seems that the difference between both certificates rates
is reduced as the size of the graph increases, it should be taken in mind that MANETs
have a limited number of nodes. Furthermore, in the the 45.83% percent of the prob-
lems the difference between the certificate rates CR
and CR
is in the interval
[50%, 75%].
Hence, it may be conclude that the repository built by MPR provides further infor-
mation to facilitate the authentication process. Another result that illustrates the positive
characteristics of M P R to solve the problem of updating the certificate repository is
that in the 82.45% of the executions the repository built by MP R contains more than
the 75% of the whole certificate set.
5 Conclusions
The application of the Multipoint Relay Technique in the process of building the up-
dated certificate repository has been evaluated in the present work. For the assessment
of this alternative several experiments over an implementation developed in JAVA have
been carried out. According to these experiments the alternative presented outperforms
the original one in several aspects. Probably the more relevant are the significantly
higher certificate rate included in the repository when applying the MP R-based method
as well as the generation of shorter chains. This first characteristic results in less inter-
action among nodes at the time of building an authentication chain. The second fact
leads to a more efficient verification procedure.
Our immediate goal is to adapt the implementation developed to the network simu-
lator NS2 in order evaluate the behaviour of the method with different mobility models.
1. Zhou, L., Haas, Z.: Securing ad hoc networks. IEEE Networks, 13 (1999) 24–30
2. Narasimha, M., Tsudik, G., Yi, J.: On the utility of distributed cryptography in P2P and
MANETs: The case of membership control. In: Proceedings of the 11th IEEE International
Conference on Network Protocols (ICNP’03), IEEE (2003) 336–345
3. Luo, H., Lu, S.: Ubiquitous and robust authentication services for ad hoc wireless networks.
Technical Report TR-200030, Dept. of Computer Science, UCLA (2000)
4. Kong, J., Zerfos, P., Luo, H., Lu, S., Zhang, L.: Providing robust and ubiquitous security sup-
port for mobile ad-hoc networks. In: International Conference on Network Protocols (ICNP).
(2001) 251–260
5. Haerri, J., Filali, F., Bonne, C.: Performance comparison of AODV and OLSR in VANETs ur-
ban environments under realistic mobility patterns. In: Med-Hoc-Net 2006, 5th IFIP Mediter-
ranean Ad-Hoc Networking Workshop, Lipari, Italy (2006)
6. Ni, S.Y., Tseng, Y.C., Chen, Y.S., Sheu, J.P.: The broadcast storm problem in a mobile ad
hoc network. In: MobiCom ’99: Proceedings of the 5th annual ACM/IEEE international
conference on Mobile computing and networking, New York, NY, USA, ACM (1999) 151–
7. Capkun, S., Buttyan, L., Hubaux, J.P.: Self-organized public key management for mobile ad
hoc networks. Mobile Computting and Communication Review, 6 (2002)
8. Capkun, S., Buttyan, L., Hubaux, J.P.: Small worlds in security systems: an analysis of the
PGP certificate graph. In: Proceedings of The ACM New Security Paradigms Workshop 2002,
Norfolk, Virginia Beach, USA (2002) 8
9. Kleinberg, J.: The small-world phenomenon: An algorithmic perspective. In: Proceedings of
the 32nd ACM Symposium on Theory of Computing. (2000)