Criptography approach using magnets

A Cryptographic approach for MANET’s
MrJ.C.Lokanath1
, Mr. M. Shiva Kumar2
, Dr. K. Krishnamoorthy3
, Ms.R.Subalakshmi4
1
III/I Sem/Dept of IT/Kuppam Engineering College,/Kuppam/A.P
2
Resarch Scholar/Dept of CSE/Karpagam University/Coimbatore/T.N,
3
Professor/cse/sona college of technology/salem/T.N.
4
Asst. Prof/IT/Kuppam Engineering College/Kuppam/A.P
Email-id : mca_hod@kec.ac.in, Phone: +91-9449611552
Abstract
Security of mobile ad hoc networks is
built upon a reliable key management system to
generate and distribute symmetric
encryption/decryption keys for communicating
parties. While central servers generate and
distribute the keys in traditional wired networks,
Distributive key management systems are used in
mobile ad hoc networks where central approaches
will fail in such dynamic, high mobility networks.
Threshold cryptography1 has been proposed to
provide a reliable, distributive key management for
networks. In an (n, t+1) threshold system, there are
n servers to provide key generation and
distribution when needed for the whole network.
From these n servers, any x servers (t<x≤n) can
co-operate and generate a key for any node. Until
now, threshold cryptography has remained only a
theory. No practical key management system has
been proposed to use threshold cryptography that
mentioned what kind of shares servers will have in
common and the practical way of creating the key
from these shares. In this paper, we will construct
a practical (n, t+1)-threshold key management
system using maximum distance separable codes
(MDS). Index Terms—ad hoc networks, MDS code,
mobile security, symmetric key, threshold
cryptography.
Keywords : MANET, Kerberos, MDS,
TTP, SKGS, Reed Solmon code.
1. Introduction
Mobile ad hoc networks
(MANETs) are new paradigms in wireless
communication. A MANET is an
autonomous system of mobile nodes
connected by wireless links. Each node
operates not only as an end system, but
also as a router to forward packets on
behalf of others. The nodes are free to
move and organize themselves into a
dynamic network. A MANET does not
require any fixed infrastructure such as
base stations, and therefore, it is an
attractive networking 1We will use the
term threshold cryptography and (n, t+1) -
threshold cryptography interchangeably.
Option for connecting mobile devices
quickly and spontaneously to
environments such as military battle fields
and rescue operations. Networks security
is an important factor in constructing any
network. In traditional wired networks,
central servers are available to provide
security services for the users inside the
network system. In Kerberos, a central
server will generate the keys and distribute

them securely to the nodes in the network.
In MANETs, absence of fixed
infrastructure creates new challenges in
security measurements. Secure mobile
network necessities like privacy,
authentication, integrity and non-
repudiation rely on secure key
management framework. For MANETs,
the existence of a secure key management
protocol is a prerequisite for network
establishment. Central key management
protocols based on trusted third party
(TTP) technology works well for
traditional wired networks, because all the
nodes can access the TTP to retrieve the
key needed for communication with any
other node. In contrast, due to mobility and
topology changes, mobile networks cannot
rely on central approaches: only
distributive key management protocols
(e.g., threshold key management
protocols) can operate in such mobile
networks efficiently. The threshold
approach for key Management assigns
number of nodes to be servers. Any
number of these servers greater than the
threshold value can co-operate to generate
keys for any node in the network. Bloom
[1] proposed a distributed symmetric key
generation system (SKGS) based on the
key redistribution scheme. In SKGS, a
central server is responsible for the
creation and distribution of nodal key
chains. Nodes can derive any future key
from the key chain they received from the
main server. SKGS provides security
against cooperative malicious attacks: to
retrieve the key of the node the attacker
has to compromise a minimum number of
nodes (t+1), and with any number less than
t+1, the attacker can not retrieve the key
chain for the attacked node. The main
problem in the SKGS approach is the
single point of failure of the central server:
if an attacker compromises the central
node, all the keys it has can be retrieved,
and the security of the network is exposed.
Threshold cryptography [2] is a proposed
cryptography scheme suited for mobile
networks to provide robustness and
defense against single point of failure in
the central server. In threshold
cryptography, the central server unction is
distributed among a group of servers.
When one of these servers is compromised
or fails, the rest of the group can take place
of this single server. This distribution
provides a co-operative security model and
robustness against the single point of
failure. The main drawback in threshold
cryptography is the difficulty in applying
the distributive function. Until now, there
has been no practical security model that
could use threshold cryptography
efficiently. In this paper we will propose a
distributed co-operative key management
system to generate and deliver the keys
based on SKGS and threshold

cryptography. This paper is organized as
follows. Section 2 gives an overview of
the MDS code that will be used
extensively in this paper. Threshold
cryptography will be defined in section 3.
Section 4 summarizes the previous work.
Section 4 proposes our approach.
Conclusion and future work will come in
section 6.
2. Maximum Distance Separable
(Mds) Codes
Coding theory and its applications have
long been used extensively in the
communication field to provide parity
checking and an error detection
mechanism. In coding theory, we define
“code” as a group of code words with
known length, such that the mapping
between the data we are going to transmit
and the code words is a one-to-one
function [8]. If we have data mi of length
k, by using codes, we can convert it to a
code word ci with length n, where n > k
using some defined encoding scheme. The
code word ci will have n − k redundant
elements. Those elements are used for
parity checking and error detection
purposes on the decoding side. We define
the distance d of the code C [n, k] as the
number of different elements between any
two code words. Singleton [3] found that
the minimum distance for code C [n, k]
must satisfy d(C) ≤ n−k +1. When
Singleton bound is at maximum (i.e., d(C)
= n−k+1), the code C [n, k] will be an
MDS code. MDS codes are a class of error
control codes created to deal with the
problem of communication over a noisy
channel, where some of the bits of the
message may be corrupted on route. Such
codes are used in cryptography and coding
theory applications [6] [7]. The MDS code
satisfies the Singleton Bound [3]
requirement. The value of distance d
determines the maximum error t that can
be corrected using this code (d ≥ 2t+1).
We can view MDS codes as a linear
independent set of vectors that form a
subspace in the vector space GF (qk). The
basis of these vectors can form the
generator matrix (G) for that MDS code.
All MDS code words (i.e., the key chains
for the nodes) can be generated using a
carefully chosen special matrix called a
generator matrix G, a [n, k] - MDS code
with k rows and n columns. The relation
between G and code words C can be
expressed as
C = v.G
where v is the message represented as a
vector and C is the code word generated
for that message v.Let C be a [n, k] linear
code in GF (qk) with minimum distance d.
We can assume C to be MDS if the
following properties were satisfied [3]:
1) Generator matrix G for this code is an
MDS code.

2) The code G_| dual to C is an MDS
code.
3) Any k columns of a generator matrix for
G are Linearly independent.
4) If a generator matrix for C is in standard
form [I, A], then every square sub matrix
of A is Nonsingular.
5) Given any d (G) coordinate positions,
there is A minimum weight code word
whose non-zero Entries are in precisely
these positions. Using matrix
transformation on MDS code to generate
code C from a secret symmetric matrix D,
each node does not need large amounts of
memory space to save all its keys. The
security of MDS codes relies on the idea
that all the columns of C are linearly
independent and any coalition of less than
k nodes can not retrieve the secret. Reed
and Solomon [4] have found an equation
to generate G matrix for any MDS-[n, k, d]
in GF (qk) by using the value α which is a
primitive root of GF (q). Reed-Solomon
codes are very common MDS codes in the
communication world. They are famous
for their optimized generator matrix G in
GF (q). Using α, which is a primitive root
of q (i.e., ax ≡ 1 mod q, the least value of
x is q-1), we define the generator matrix
for Reed-Solomon codes as
Gi,j = α(i−1)(j−1) mod q.
3. Threshold Cryptography
The basic idea of threshold cryptography
is to protect encryption keys by making a
group of nodes (servers) to co-operate to
provide fault-tolerant distribution of keys
within the security model. Threshold
cryptography allows one to distribute a
piece of secret information (keys) among
several servers in a way that meets the
following two requirements:
1) No group of compromised servers
(smaller than a given threshold) can figure
out what the secret is, even if they
cooperate.
2) When it becomes necessary that the
secret information be reconstructed, any
large enough Number of servers (a number
larger than the Above threshold) can
always do it. The primary objective of
sharing of a key by multiple servers
(shareholders) in threshold cryptography
system is to have distributed architecture
in a hostile Environment. Other than
sharing keys or working in a distributed
manner, threshold cryptography can be
implemented to redundantly split the
message into n pieces s much that with t or
more pieces the original message can be
recovered. This ensures secure message
transmission between two nodes over n
multiple paths. An (n, t + 1)-threshold
cryptography scheme allows n parties to
share the ability to perform a

cryptographic operation (e.g., creating a
digital signature), so that any t + 1 parties
can perform this operation jointly, while it
is infeasible for at most t parties to do the
same operation even by collusion. In our
proposed key management scheme, the n
servers of the key management service
share the ability to create the key chain for
the node. For the service to tolerate t
compromised servers, we employ an (n,
t+1) threshold cryptography scheme and
divide the secret symmetric matrix D. The
matrix is used in conjunction of the
generator matrix of the MDS code to
generate the key chains for the participant
nodes in the network into n shares (s1, s2,
……, sn), assigning one share to each
server. We call (s1, s2, ……., sn) shares of
the secret matrix D. In order for a node to
have its key chain, it will ask t+1 on n
shareholder to generate a partial share of
the key chain. Each one of those k servers
generates a partial sum for this key chain
and sends it to the sender, who will in turn
perform the operation of complete key
chain retrieval from these partial sums.
4. Previous Work
Bloom proposed a symmetric key
generation system (SKGS) [1] based on
secret sharing systems. In SKGS, nodes
are supplied with a relatively small amount
of secret data that is used to derive all the
node’s keys. A central server (trusted
authority) generates a global matrix G of
size k x n that is known to all the nodes in
the network, and a symmetric secret matrix
D of size k x n. The central node calculates
the key atrix for the network as K = (D .
G) T. G. Because D is symmetric, K will
be also symmetric, for rows i and j in K,
we have Ki,j = Kj,i. So, Ki,j is common
between the rows i, j. If row i is the key
chain for node i, and row j is the key chain
for node j, the element Ki,j will be the
symmetric key between
Them. Because G is known by all the
participant in the networks, while external
nodes (malicious nodes) do not know this
matrix G, the central server delivers the ith
row of (D. G)T to node i. Upon reception,
node I will calculates its key chain ki = ith
row of (D.G)T .G. This division of key
generation into more than one step adds
more secrecy to their key chains, and
makes it harder for the intruder to retrieve
any information about other nodes. Bloom
showed in his paper that by using SKGS
scheme, at least k users have to co-operate
to get any information about keys they do
not have. Thus, any coalition of less than k
nodes can not reveal any information
about the key chain of any other node. The
problem of this approach is that it relies on
a central point to do all the work, making
it vulnerable as a single point of failure.
Another problem arising from key request

and delivery is that some nodes may not be
able to reach the central server due to
existence of broken links or untrustworthy
routing information.
5.Proposed Approach
The assumptions we made and the
notation we will use are as follows: •
Symmetric matrix D is of size k x k. •
MDS code generator matrix G is of size k
x n with k < n.
• Number of servers is equal to n.
• All the keys value is in GF (q).
• Any node is able to reach k server when
it requests a key.
• K denotes key matrix.
In order to construct a practical key
management system for MANETs, we
used Blom’s SKGS in conjunction with
theory of threshold cryptographic systems.
In addition, we also used coding theory to
overcome the shortcomings of central
approaches in SKGS, and to provide a
practical threshold cryptographic system
capable of operating in a dynamic
environment. In our proposed approach,
each node will be provided with a group of
keys (key chain) when it joins the network.
This key chain will be used to derive all
the future keys for this node such that any
two nodes can calculate symmetric keys
between them based on these key chains.
Key authority servers are distributed
among the network in a threshold way.
There are n key authority servers with k
threshold value. Generator matrix (G) for
the MDS code used in our distributive key
management system (with code distance
d=n-k+1) will be distributed among the n
key authority servers. Recall from MDS
code properties that every set of k columns
in G are linearly independent. Thus, it is
enough to know k columns of G to
construct it [5]. Now, any k servers chosen
from the n authority servers
Are capable of reconstructing G. Each of
the n servers in the network will be
initialized with a column r of G during the
network setup, such that any k nodes can
collaborate with each other and reconstruct
G, while any number less than this
threshold value k will not be able to
reconstruct G. On the other hand, since
matrix D is known only to the authority
servers, regular nodes do not know any
information about D except what they
receive from the servers during the key
generation’s phase. Now, each of the n
servers knows what is the secret matrix D,
but knows only a part of G. When a node
demands a key, it will initialize the key
generation system, and k servers will be
asked to communicate with. One server
will be elected as a collector, and every
selected server (within the k group) will
send its share of G to the collector, who in
turn will construct G and then calculate K

which contains shares from the other
servers. Since the key chain of node i will
be row i, the collector will send the key
chain to node i.
6. Conclusion and Future Work
In this paper, we proposed a
distributive key management system
suitable for ad hoc networks. Based on
threshold cryptography and MDS codes
with SKGS, the proposed system is
applicable and practical. The future work
will include the simulation of the proposed
approach in addition to the study of the
effect of dishonest nodes on the security of
the proposed system.
Biography
The Paper Entitled “A
Cryptographic approach for MANET’s”
is a research paper prepared by Mr.J.C.
Lokanath, III/I Sem Dept. of IT, Kuppam
Engineering College, Kuppam, A.P, under
the guidance of Mr. M .Shiva Kumar
,HOD/Asst. Prof .Dept of MCA, Kuppam
Engineering College, Kuppam, A.P, Dr. K.
Krishnamoorthy, Professor, Dept of CSE,
Sona College of Technology, Salem, T.N
and Ms.R.Subalakshmi, Assistant
Professor ,Dept of MCA, Kuppam
Engineering College, Kuppam, A.P.
References
[1] R. Blom, “Optimal class of symmetric
key generation systems”, Proc. of the
EUROCRYPT 84 workshop on Advances
in cryptology: theory and application of
cryptographic techniques, p.335-338,
December 1985, Paris, France.
[2] L. Zhou, Z. Haas “Securing ad hoc
networks ” , IEEE Network Magazine, vol.
13, no.6, 1999.
[3] S. Yamiolkoski,“The Road to
Maximum Distance Separable Codes ”,
Lecture notes in projective geometry.
[4] I.S. Reed, G. Solomon, “Polynomial
codes over certain finite fields”, Journal of
the Society for Industrial and Applied
Mathematics (SIAM), vol. 8, no. 2, pp.
300-304, 1960.
[5] A. Jeffrey, “Advanced Engineering
Mathematics” , ISBN 012382592X,
Academic Press Publisher, London, 2001.
[6] L. Xu, “A general encryption scheme
based on MDS code”,Proceedings of IEEE
International Symposium on Information
Theory, 2003.
[7] T. Matsumoto, H. Imai, “On the Key
Predistribution System: A Practical
Solution to the Key Distribution Problem”,
A Conference on the Theory and
Applications of Cryptographic Techniques
on Advances in Cryptology, vol. 293, pp.
185-193, 1987.

[8] H. K. Kim, V. Lebedev, “On optimal
superimposed codes” , Journal of
Combinatorial Designs, Vol. 12, Issue 2 ,
pp. 79 91, 2003. 536

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