This document summarizes a research paper on using elliptic curve cryptography for message authentication. It begins with an introduction to elliptic curve cryptography and how it can provide equivalent security to other public key encryption methods but with smaller key sizes. It then describes the proposed methodology which includes generating an ECC key pair, encrypting a message with the public key, transmitting the encrypted message, and decrypting it with the private key. The results show a message being encrypted and decrypted correctly using this ECC process. It concludes that ECC can provide an efficient method for authentication in systems like vehicular networks due to its lower computation and communication overhead compared to other encryption methods.

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Pairing Based Elliptic Curve Cryptosystem for
Message Authentication
T.Punitha1
1
Sethu Institute of technology,
Computer Science & Engineering,
tpunitha.cse@gmail.com
M.Sindhu2
2
Sethu Institute of Technology,
Computer Science & Engineering,
Sindhucse18@gmail.com
Abstract— Elliptical curve cryptography (ECC) is a public key encryption technique based on elliptic curve theory that
can be used to create faster, smaller, and more efficient cryptographic keys. ECC generates keys through the properties of
the elliptic curve equation instead of the traditional method of generation as the product of very large prime numbers.
Because ECC helps to establish equivalent security with lower computing power and battery resource usage, it is
becoming widely used for mobile applications. Recently the bilinear pairing such as Weil Pairing or Tate Pairing on
elliptic curves and hyper elliptic curves has been found various applications in cryptography. Several identity-based
cryptosystems using bilinear pairings of elliptic curves or hyper elliptic curves were presented. Blind signature and ring
signature are very useful to provide the user’s anonymity and the signer’s privacy. The proposed method focuses an ID-
based ring signature scheme which is based on the pairings with elliptic curve cryptography. The proposed method is used
to reduce the number of computation of the pairing for the verification of the id based signature and also decoding of the
id based public key cryptosystems with authentication by factor of 2.
Index Terms— Asymmetric Cryptography, Bilinear pairing, Elliptic Curve, Elliptic Curve CryptoSystem(ECC), Secure ID
based signature.
.
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1 INTRODUCTION
ECC is a public key encryption technique based on the theory
of elliptic curves [1]. It can be used to create faster, smaller and more
efficient cryptographic keys. And also it generates keys through the
properties of the elliptic curve equation rather than the traditional
method of generation, as the product of very large prime numbers
[2]. This technology can be used in conjunction with most of the
public key encryption methods such as RSA and Diffie-Hellman.
ECC can yield a level of security with a 224-bit keys compared with
other systems that require a 2,048-bit keys. ECC provides features
such as security and computational efficiency [3]. The security of
ECC depends on the difficulty of solving the elliptic curve logarithm
problem.
Cryptography was used to assure only secrecy. Wax seals,
signatures, and other physical mechanisms were typically used to
assure integrity of the media and authenticity of the sender. With the
advent of electronic funds transfer, the applications of cryptography
for integrity began to surpass its use for secrecy [4]. The problem
with proving properties of protocols under other schemes is that the
mathematics is extremely complex for the RSA, and there is no
sound mathematical basis for the DES [5].
Public key cryptosystems are constructed by relying on the
hardness of mathematical problem. RSA based on Integer
Factorization Problem and DH based on the Discrete Logarithm
Problem [6]. The main problem of conventional Public key
Cryptosystems is that the Key size has to be sufficiently large in
order to meet the high level security requirement, resulting in lower
speed and consumption of more bandwidth [7].
The basic concept of cryptography is very simple. In a typical
cryptographic exchange, information that is meant to be hidden for
whatever reason is encrypted, or ciphered into a difficult-to-interpret
form. This is called conversion, encryption because it involves the
change of clear text, or understandable data, into cipher text, or
difficult-to-interpret data. The encryption process is one-half of the
entire cryptographic exchange [8].
At the other end of the process is decryption, or the
conversion of cipher text into clear text. Decryption is not always a
part of encryption, however – some algorithms are called ―hashes‖ as
they only apply encryption (that is, from clear to cipher text) and
have no means of deciphering the information. However, most
cryptographic algorithms can theoretically be cracked, but require
extraordinary amounts of computational power to do so.
A safety message authentication scheme networks using an
ID-based signature and verification mechanism. An ID-based
technique offers a certificate-less public key verification, while a
proxy signature provides flexibilities in message authentication and
trust management [1]. Message authentication, to ensure the
receiving message is true and coming from the claimed source, the
traditional PKI security schemes are not suitable for VANET [9].
Aiding of roadside unit (RSU) make message authentication in
VANET easily, but it is still embedded some problems: how to
authenticate the message transmitted from different RSU range, and
to process the vehicle's message hand-off among the different RSU
communication range. A comprehensive message authentication

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scheme which enables the message authentication in intra and inter
RSU range, and the hand-off within the different RSUs. The
proposed scheme makes the balance in the overhead of computations
and communication, and the security against the attacking. The
results of efficiency analysis and comparison with the related works
show the proposed scheme is a superior message authentication
method in VANET [10].
The most important research challenge is the authentication of
VANET messages with less communication as well as storage
overhead. So, Elliptic Curve Cryptography has chosen.
2 PROPOSED METHODOLOGY
The overall concept is explained through the flow diagram
as shown in the figure.1.
Fig. 1. Flow diagram of the proposed Methodology
Elliptical curve cryptography (ECC) is a public key
encryption technique based on elliptic curve theory that can be used
to create faster, smaller, and more efficient cryptographic keys. ECC
generates keys through the properties of the elliptic curve equation
instead of the traditional method of generation as the product of very
large prime numbers [13]. Because ECC helps to establish equivalent
security with lower computing power and battery resource usage, it
is becoming widely used for mobile applications.
A. Elliptic Curve
An Elliptic Curve can be described as the set of
solutions of an equation of the form Y2
= x3
+ ax + b over some
field[4]. The importance of elliptic curves is its rich structure
B. Elliptic Curve Cryptosystem
The system based on the elliptic curve is called Elliptic curve
cryptosystem. To form a cryptosystem, generally a set of three
algorithms is required:
1. Key-generation: An algorithm for generating an
encryption/decryption key.
2. Encryption: An algorithm for encrypting plain texts.
3. Decryption: An algorithm for decrypting cipher texts.
In traditional symmetric or private-key cryptography, the
generated key is used for both encryption and decryption, with the
consequence that anybody that possesses the key is able to en- and
decrypt messages. To ensure confidentiality, the key has to be kept
secret between communication partners [17].
C. Elliptic Curve Parameters
The most important thing defines all the elements in the
elliptic curve before used by all the parties. That is called as the
domain parameters of the scheme. Let p be the field in the prime
case and the pair (m, f) in the binary case. The elliptic curve is
defined by the constants a and b use in elliptic curve equation. And
the order of G, be the smallest non-negative number n such that
nG=∞, it is prime. Since is the size of a subgroup of E (FP) follows
from Lagrange's theorem that the number H=│E (FP) │is an integer.
In cryptographic applications h, called the cofactor, must be small
(H ≤) and, preferably h=1. The prime case the domain parameters are
(p, a, b, N, g, h) and in the binary case they are (M, P, a, b, n, G,h)
[11].
Several classes of curves are weak and should be avoided:
Curves over F2M
non-prime m are vulnerable to Weil descent attacks.
Curves such that n divides PB
=1(where p is the characteristic of the
field – q for a prime field, or 2 for a binary field) for sufficiently
small B are vulnerable to Menezes-Okamoto-Vanstone (MOV)
attack which applies usual Discrete Logarithm Problem (DLP) on a
small degree extension field of FB to solve ECDLP [12]. Curves such
that E (Fq) =Q are vulnerable to the attack that maps the points on the
curve o the additive group of FQ.
D. Key Sizes
ECC achieves the security level with smaller keys. Key
length is most important feature in Elliptic Curve Cryptography. For
example, for 80-bit security one needs a curve over FQ
, where
Q=2160
. This can be contrasted with finite-field cryptography (e.g.,
DSA) which requires 3072-bit public keys and 160-bit private keys,
and integer factorization cryptography (e.g., RSA) which requires a
1024-bit value of n, where the private key should be just as large.
E. Asymmetric Data Encryption
Group manager distributes and efficiently allocates the
public keys and authenticate by using the ECC authentication
mechanism. The Group owner's file has been applied security. The
confidentiality of this transformation is data in theory secure; we will
simply give the safety via the cryptography formula named as ECC
[15]. Since client files are stored in the server, they have lesser
security options. For crypto process we use the ECC algorithm for
the encryption and decryption process.
F. Asymmetric Data Decryption
Using the ECC algorithm file is converted as crypto files.
In order to get view the original content of the files, the encrypted
files should be decrypted. Each and every encrypted file should be
decrypted. Using Respective Private keys, files are decrypted using
the ECC Key Generator Decryption process is done by ECC
Algorithm, Since ECC has 166 key lengths it executes faster and
Plain Text
Message
Encryption
Logic
Encrypted
Message
ECC Key Pair
Generation
Decryption
Logic
RSU
Sender
Private Key
Receiver
Public
Key

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more secured algorithm than RSA [16].Our methodology gives the
results using ECC based algorithm, such as public key encryption for
sending the keys to co-distributors and secret key encryption for
further distribution of key.
G. Pairing
Pairing-based cryptography is used to pair two
cryptographic groups to a third group to construct cryptographic
systems [17]. If the same group is used for the first two groups, the
pairing is called symmetric and is a mapping from two elements of
one group to an element from a second group [3]. In this way,
pairings can be used to reduce a hard problem in one group to a
different, usually an easier problem in another group.
3 RESULTS AND DISCUSSION
The NetBeans IDE is a reusable framework that is
used to simplify the Java desktop applications developments.
NetBeans visual libraries are used. The additional SDK is required.
Installation of modules can be performed dynamically. It
also includes the features such as memory management, user setting
management, storage management.
The result shown in figure 2 and 3 describes message creation and
its corresponding Key pair generated by using Elliptic Curve
Cryptosystem.
Fig 2: Message Creation
Fig 3 : ECC Key Pair Generation
Fig 4: ECC Encryption
Fig 5: ECC Decryption
Fig.4. Shown the encrypted message of the given
message. Fig.5. Shown the decrypted message of the given
encrypted format of the message and finally we got an original
message. From the result, Message authentication be achieved by
Elliptic Curve Cryptosystem.
4 CONCLUSION
The developed method has to provide an efficient method
for a class of ID based cryptosystem using Elliptic Curve
Cryptography (ECC). The proposed method focuses an ID-based
ring signature scheme which is based on the pairings with elliptic
curve cryptography. Also, we analyze their security and efficiency.
The pairing on elliptic curves is applied for secure id based
cryptography. The proposed method is used to reduce the number of
computations of the pairing for the verification of the id based
signature and also decoding of the id based public key cryptosystems
with authentication by factor of 2.
Elliptic Curve Cryptography (ECC) will be applied in the
Vehicular Ad hoc Network (VANET).Hash function is going to use
to verify the messages exchanged with the VANET environment.
This will be helpful to achieve message authentication.

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ACKNOWLEDGMENT
I would like to express my special thanks of gratitude to my
college management. In addition, I would also like to thank my parents
who helped me a lot in finalizing this project within the limited time
frame.
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