_____________________________________________________________SCIENCE WORLD JOURNAL VOL 3 (NO4) 2008

www.sciecnceworldjournal.org
ISSN 1597-6343
Bibu &Angai (SWJ ):19-22 Application Of Elliptic Curve





















Network security refers to all hardware and software functions,
characteristics, features, operational procedures, accountability
measures, access controls, and administrative and management
policy required to provide an acceptable level of protection for
hardware, software, and information in a network (Shaffer et al.,
1994). The need to ensure data security on University campuses
all over Nigeria is necessary as very important documents and
sensitive information are transmitted from one point to another, like
examination questions, students results, very important circulars,
and even financial transactions of the university. Most networks
today, especially in Nigeria and particularly in the University of Jos,
do not have a comprehensive way of securely transmitting data
over their networks. The most common means of providing data
security over these networks is the use of passwords, which over
time has proven to be quite unreliable as they can easily be
breached. Encryption algorithms applied on these networks are
based on symmetric or private key cryptography which do not
provide a high level of security. So the need to provide a highly
efficient method of securely transmitting data over a network
cannot be over emphasized.

Elliptic curve cryptography (ECC) is an approach to public-key
cryptography based on the algebraic structure of elliptic curves
over finite fields. The use of elliptic curves in cryptography was
suggested independently by Neal Koblitz and Victor Miller in 1985.
Their security is based on the hardness of the elliptic curve discrete
logarithm problem (ECDLP) (Hankerson et al., 2004). Elliptic curve
cryptography is an effective tool for ensuring data security that
could be applied to a network to enhance secure data transfer over
the network. This is due to the fact that elliptic curve cryptography
provides security based on the hardness of the elliptic curve
discrete logarithm problem. Also, elliptic curve encryption has a
high implementation rate, and it does not require a lot of bandwidth
like other public cryptosystem. It is also very robust making it a
viable encryption tool to be used on networks that desire to achieve
maximum security (Robshaw & Yin 1997).

In this work, elliptic curve cryptography was used to provide a
much shorter key length, with the same level of security as other
public key cryptosystems such as Rivest-Shamir-Adleman (RSA).
Thus it is an ideal method for securely transmitting data over a
network to achieve the following:

- Provide high confidentiality by ensuring that messages sent from
a source to a destination would not be readable by a third party.

-

-

- Detect any modifications that might have been made on the data
during transmission over the network.

The destination should be able to authenticate the origin of the
data, and verify indeed that the data originated from the claimed
source.

The destination should be convinced of the identity of the other
communicating entities. When the destination receives a message
from the source, not only is the destination convinced that the
message originated from the source, but the destination can
convince a neutral third party of this; thus the source cannot deny
having sent the message to the destination.

THE PROPOSED SYSTEM
The proposed network security system is graphically described by
the following data flow diagram:

The cryptosystem distributes public and private keys to each user,
these keys are used by the user to encrypt and decrypt plain texts
and files. The server generates addition points using an elliptic
curve over a specified field. The public key (encryption key) is
usually a point on the elliptic curve while the private key (decryption
key) is us used to decrypt data in elliptic curve cryptography. The
private and public keys used by each user at any instance are
stored in the database to avoid public and private key conflicts.

OPERATION OF THE PROPOSEDSYSTEM
Elliptic Curve Cryptography schemes use an elliptic curve E over a
finite field such as p Z , where p is a very large prime, and
involves both encryption and decryption operation. This project
uses the ElGamel public-key cryptosystem based on the Discrete
Logarithm problem in p Z , the set of integers1,2,..., 1 p , under
the multiplication modulo p

The scheme will be demonstrated using Alice and Bob as sender
and receiver of a secret message respectively. The coordinates of
the points on the elliptic curve itself serves as a pool of numbers to
choose from.

The Encryption Operation
To encrypt plaintext messages M, into cipher text, the plaintext
message is encoded into a point M P from the finite set of points
in the elliptic group ( , ) p E a b .

SHORT COMMUNICATION
APPLICATIONOF ELLIPTIC CURVE CRYPTOGRAPHY
ON DATA ENCRYPTIONOVER A NETWORK

*
BIBU, G. D. & ANGAI, S.

Department of Mathematics
University of J os, Nigeria
*(Corresponding author)
gidadik@yahoo.com

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Bibu &Angai (SWJ ):19-22 Application Of Elliptic Curve

_____________________________________________________________SCIENCE WORLD JOURNAL VOL 3 (NO4) 2008
www.sciecnceworldjournal.org
ISSN 1597-6343














































FIG. 1. THE CRYPTOSYSTEMDATA FLOWDIAGRAM


The first step consists of choosing a generator point
( , ) G Ep a b e such that the smallest value of n for which
0 nG = is a very large prime number. The elliptic group
( , ) p E a b and the generator point G are made public.

Each user selects a private key A n n < and computes the public
key A P as: A A P n G = . To encrypt the message point M P for
Bob (B), Alice (A) chooses a random integer k and computes the
cipher text pair of points C P using Bobs public key B P :
( ) ( ) , C M B P kG P kP = + (


The Decryption Operation
After receiving the cipher text pair of points, C P , Bob multiplies the
first point, ( ) kG with his private key B n , and then adds the
result to the second point in the cipher text pair of points,
( M B P kP + ):
| | ( ) | | ( ) ( ) ( ) M B B M B B
M
P kP n kG P kn G n kG
P
+ = +
=


Which is the plain text corresponding to the plain text message M,
only Bob knowing the private key B n can remove ( ) B n kG from
Public/ private
keys
Chat
text/ files
Generates
Public/ private
keys
DATABASE
Systems update

SERVER
ADDITION
TABLE
Public/ private
keys
CRYPTO-
SYSTEM
Encrypted data
File location/
Client IP

CHAT
STYSTEM
Public/ private
keys
USERS
Public/ private
keys
USER
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Bibu &Angai (SWJ ):19-22 Application Of Elliptic Curve

_____________________________________________________________SCIENCE WORLD JOURNAL VOL 3 (NO4) 2008
www.sciecnceworldjournal.org
ISSN 1597-6343

the second point of the cipher text pair of points, that is
( M B P kP + ), and hence retrieve the plain text information M P .

IMPLEMENTATION OF NEWSYSTEM
The system was implemented and tested using a simple chat
scenario. The messenger server (Fig. 2) coordinates all users that
login to the messenger and most importantly, it generates
quadratic residues, which is used to compute an elliptic group, and
performs addition and multiplication of points over the elliptic
group. These points are used by the cryptosystem which generates
the public and privates keys for each logged on user to encrypt (at
the source) and decrypt (when it arrives at the destination) data as
they travel over the network.




FIG 2. SERVER INTERFACE

Each user is required to provide an E-mail address and a password
in order to gain access to the messenger.

After login, the messenger interface pops-up as shown in Fig. 3,
this interface enables users to send plain text and files which get
encrypted as they are being transmitted over the network.

















FIG 3. MESSENGER INTERFACE

Figs. 4 and 5 show two users chatting in real time over a network.
This system only permits real time communication. Although each
user sees their message in plain texts, the message is actually
enciphered at the source as it travels through the network and
deciphered at the destination as it is displayed on the two chat
interfaces below. This therefore makes it difficult for any third party
that may want to listen in on any conversation between users to
make any sense out of the messages while on transit between the
users.



FIG 4. CHAT




FIG 5. CHAT

The system not only permits transmission of plain texts, but also
allows transmission of files over a network. However, the user at
the source who wishes to send a file must receive
acknowledgement from the user at the destination (the receiver)
before the transmission can be affected. The receiver therefore has
the choice to accept or reject. These files are also encrypted using
elliptic key cryptography as they make their transit across the
network. This method of encryption ensures that the source cannot
deny that the file(s) originated from it and also ensures that no
modifications can be made on the file as it moves through the
network. It is imperative to mention that when encrypting data over
a network, the cipher texts are not visible or can not be seen with
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Bibu &Angai (SWJ ):19-22 Application Of Elliptic Curve

_____________________________________________________________SCIENCE WORLD JOURNAL VOL 3 (NO4) 2008
www.sciecnceworldjournal.org
ISSN 1597-6343

the human eye, this is because data is encrypted only while in
transit, existing as plaintext on the originating and receiving hosts.

CONCLUSION
The climax of the work is the design and implementation of data
security over a network through the use of elliptic curve
cryptography, which is a very strong tool that can be implored to
achieve high level of security over a network.




















































REFERENCES
Hankerson D., Menezes A., Vanstone S. (2004). Guide to Elliptic
Curve Cryptography, Springer-Verlag Inc, New York.

Robshaw, M.J.B. & Yin, Y.L. (2008). Overview of elliptic curve
crptosystems. Technical reports. RSA Laboratories.

Shaffer, S. L. & Simon A. (1994). Network security. Academic
press.


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