2 SELF-ORGANIZED PUBLIC
KEY MANAGEMENT SYSTEM
The Self-OrganizedPublic Key Management System,
called PGP-Like, is a public key management scheme
which uses certificate chains (
ˇ
Capkun et al., 2003;
Hubaux et al., 2001). Private and public keys of
nodes are created by the nodes themselves following
the PGP concepts (Zimmermann, 1995). In addition,
each node issues public key certificates to other nodes
in which it trusts. In PGP-Like, if a node u believes
that a public key K
v
belongs to node v, it issues a cer-
tificate binding K
v
to the node v, (v, K
v
)
prK
u
, in which
prK
u
is the private key of node u. This certificate is
stored in both nodes local certificate repositories. Fur-
thermore, each node periodically exchanges its own
repository with its neighbors.
Public keys and certificates are represented by a
directed graph G(V, A), in which V represents the
public keys and A represents the certificates. A di-
rected edge between two vertexes K
u
and K
v
, (K
u
→
K
v
), denotes a certificate, signed by node u, binding
K
v
to node v. Each node u maintains an updated local
certificate repository,G
u
, and a non-updated local cer-
tificate repository, G
N
u
, which contains the certificates
that have expired.
When node u wants to authenticate the public key
K
v
of node v, it must find a path connecting K
u
and K
v
,
represented by (K
u
K
v
). It firstly tries to find (K
u
K
v
) ∈ G
u
. If ¬∃(K
u
K
v
) ∈ G
u
, node u merges G
u
with G
v
, G
′
= G
u
∪G
v
, and it tries to find (K
u
K
v
) ∈
G
′
. If a path exists, the authentication succeeds.
The use of certificate chains makes PGP-Like
highly vulnerable to impersonation attacks, as shown
in (Silva et al., 2008). An attacker, node x, can create
a false identity m and issues a certificate binding k
m
to
m. Thus, if node x maintains a correct behavior dur-
ing a considerable time, several units will, probably,
trust it and the false identity will be spread over the
network due to the certificate exchange mechanism.
3 VIRTUAL KEY MANAGEMENT
SYSTEM
The Virtual Key Management System (VKM) uses a
virtual structure to indicate the trust between nodes
and the certificate chains formation. The virtual struc-
ture is represented by a directed graph L(N, E), which
is unrelated to the actual network topology. Set N
represents the nodes and set E represents the virtual
links. A virtual link (i, j) ∈ E indicates that node i is-
sues a certificate binding K
j
to node j. Note that node
i must do this for each node to which it has a direct
connection in the virtual structure. For example, the
virtual structure can be a RoR, a hypercube, a CCC
or a torus, though results reported in this paper were
obtained using the Rings of Rings (RoR) structure.
The Rings of Rings (RoR) structure is based on the
following: assume that there are two integers, x and
y, such that, x ∗ y = n, and let s be an integer such
that 1 < s ≤ y. Set N is partitioned into x rings, called
N
0
, N
1
, ..., N
x−1
, in which, for each a ∈ [0, x), N
a
=
{i : a∗y ≤ i < (a+ 1)∗y}. Link (i, j) belongs to E iff
either j mod y = (i+ d) mod y for some 1 ≤ d < s or
j = (i+ y) mod n. A notable feature of RoR structure
is the redundancy of virtual paths, whose degree is
determined by parameters x, y, and s. In VKM s is
the number of certificates that a node issues. Figure 1
exemplifies the Ring of Rings (RoR) structure.
5
a
V
a+1
V
a−1
1
2
3
4
5
w’
w’
w’
w’
1
2
3
4
V
s−1 s−1
w
w
w
w
w’
w
w
Figure 1: RoR Virtual Structure.
In VKM each node i creates its own pair of public
and private keys, K
i
and prK
i
. Afterwards, it must
issue certificates following the virtual structure. A
pair of nodes in the virtual structure must exchange
its keys through a secure channel. When a certificate
is issued, its issuer stores it in a local repository and
sends it to the correspondent node. All certificates are
issued with a limited lifetime T
v
.
VKM can behave in a restrict way, being able to
tolerate impersonation attacks to a certain level, or it
can behave similarly to the PGP-Like, just by chang-
ing a simple parameter. The main difference between
these behaviors is the way nodes authenticate public-
keys. Both forms will be presented next.
In VKM with reactive authentication (VKM-RA),
each node maintains only its initial certificates, the
certificates issued by it and the ones issued to it, thus
reducing the memory needed by the local certificate
repositories. When node i wants to authenticate the
public-key of node j, it must find a virtual path from i
to j, a certificate chain, in the virtual structure. After
choosing a virtual path, thesource must gather all cer-
tificates to validate the entire virtual path as follows:
(i) the first certificate is directly verified by node i us-
ing its own public key, as it is the issuer; (ii) each
remaining certificate can be verified using the public
key contained in the previous certificate; (iii) the last
certificate contains the public key of node j.
SECRYPT 2009 - International Conference on Security and Cryptography
156