Data Security Using Elliptic Curve Cryptography

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International Journal of Computer Engineering In Research Trends
Volume 3, Issue 5, May-2016, pp. 222-225 ISSN (O): 2349-7084
Data Security Using Elliptic Curve
Cryptography
Karishma Bhirud, Dipashree Kulkarni, Renuka Pawar, Prachi Patil.
Abstract:- Cryptography technique is used to provide data security. In existing cryptography technique the key
generation takes place randomly. Key generation require shared key. If shared key is access by unauthorized user then
security becomes disoriented. Hence existing problems are alleviated to give more security to data. In proposed system a
algorithm called as Elliptic Curve Cryptography is used. The ECC generates the key by using the point on the curve. The
ECC is used for generating the key by using point on the curve and encryption and decryption operation takes place
through curve. In the proposed system the encryption and key generation process takes place rapidly.
Keywords – Curve Cryptography, shared key, encryption, decryption.
——————————  ——————————
1. INTRODUCTION
The Cryptography is a technique which provides
security to data. In cryptography all the data is
presented in the encrypted form and only authorized
user can decrypt information.The main goals of
cryptography are to maintain data confidentiality,
integrity, availability, centralized data collection to
provide data authenticity in the digital world that
provide high security to database. Plaintext is a term
used in cryptography that refers to a message before
encryption or after decryption. That is, it is a dispatch
in a form that is easily readable by humans. Cipher text
is also known as encrypted or encoded data because it
contains a form of the unique plaintext that is
unreadable by a human or computer without the
proper cipher to decrypt it. A cryptographic key is a
string of bits used by a cryptographic algorithm to
transform plain text into cipher text or vice versa.
In cryptography Elliptic Curve Cryptography
(ECC) is one of the effective cryptography algorithm
which was discovered in 1985 by Neil Koblitz and
Victor Miller. Elliptic Curve Cryptographic (ECC) are
Public-key mechanisms that provide the same
functionality as Rivest-Shamir-Adlemon algorithm.
Most of the standards that use public-key
cryptography for encryption based on RSA algorithm.
Their security is based on the hardness of a different
problems. The competing algorithm to RSA [1] is
elliptic curve cryptography over finite fields.
2. RELATED WORK
In last twenty years, elliptic curve cryptography has
been thoroughly researched. The actual application of
elliptic curve cryptography and the practical execution
of cryptosystem primitives in the real world constitute
interdisciplinary research in computer science as well
as in electrical engineering. Elliptic curve
cryptography has moved to a cutting edge technology
adopted by an increasing number of organizations.
There are two reasons for this new development. One
is that ECC has survived a generation of attacks.
Second, in the growing industries, its advantages over
RSA have made it an attractive security alternative.
Elliptic curve cryptography is not only emerged as an
attractive public key cryptosystem for mobile or
wireless environments but also provides bandwidth
savings. ECC has a high level of security which can be
achieved with high considerably shorter keys than
other conventional public key cryptography. ECC has
a advantage that it helps to establish equivalent
security with lower calculating power and battery
resource usage for mobile applications. The strength of
encryption depends on its key and the alphabetical
table. As much as the key size is affecting the execution
time, it should be preserved to be as short as possible
Available online at: www.ijcert.org

Karishma Bhirud et al., International Journal of Computer Engineering In Research Trends
Volume 3, Issue 5, 2016, pp. 222-225
for an acceptable security requirement. There will be
no impact on strength and runtime performance. ECC
provides an excellent solution of data and secure
transfer of keys between two communicating parties
[2]. An elliptic curve cryptography based
communication system, where the various characters
can be symbolized as the co-ordinates of the elliptic
curves, can also be generated [3]. ECC structure is a
group structure based on non-singular curve having
finite number of integer points with each of this point
having a finite order. A novel idea of ECC encryption
and decryption based on Knapsack also shows on how
the elliptic curves technology can be used for
encryption and decryption [4].
Fig.6 System architecture
3. PROPOSED SYSTEM
A general Elliptic Curve equation takes the general
form:
y² = x³+ ax + b…………………… (1)
(x, y) = co-ordinates on the Elliptic curve
a, b = coefficients.
Though ,for fixed fields a improved equation is used
[5]:
y² mod q = (x³ +ax + b) mod q……….. (2)
Where q = prime number for which the Elliptic curve
be defined a, b satisfy the equation [2]
(4a³ + 27b³ ) mod q ≠ 0 mod q……….. (3)
An elliptic curve E over GF (q) consist of the answers
(x, y) distinct by (1) and (2), along with an
supplementary element called 0, which is the point of
EC at perpetuity. The set of points (x, y) are said to be
affine synchronize point demonstration. The basic
actions on elliptic curves are calculation and
replication. A scalar reproduction with a point can be
denoted as a combination of calculation operations.
Say, given a point P ( x, y) is to be multiplied k times,
say k = 37.
Thus we have to compute 37P.
In terms of addition it can be represented as
37P = P + P + P +… + P (37 times)
For addition of two points P(x1, y1) & Q(x2,
y2) where P≠Q.
3.1. SYSTEM ARCHITECTURE
Fig 1 shows the architecture of the system. System
architecture describes the various modules present in
paper which are interrelated to each other. The
previously implemented some algorithm like RSA,
Diffie Hellman has drawbacks which could slow down
the key generation and encryption process. So elliptic
curve cryptography algorithm is effective to increase
the speed of key generation and encryption process.
Encryption is done by the administrator by using
public key of user. Then decryption takes place by user
by using private key. As each user has its separate
private key so no other user can access the information.
If Administrator and user want to encrypt and decrypt
the messages then they agree upon to use an elliptic
curve Ep (a,b) where p is a prime number and a
random point C on the elliptic curve. User selects a
random number and a point A on the elliptic curve.
User computes A1 = a (C +A) and A2 = a A. User keeps
the random number a and the point A as her private
keys and distributes A1 and A 2 as her general public
keys.
Following keys are required for ECC:
Step 1.
User’s private key 1 = a, a random number less
than the order of the generator.
Step 2.

Volume 3, Issue 5, 2016, pp. 222-225
User’s private key 2 = a point A on the elliptic
curve Ep (a,b).
Step 3.
User’s general public key 1 = a point A1 on the
elliptic curve Ep (a,b).
Step 4.
User’s general public key 2 = a point A2 on the
elliptic curve Ep (a,b).
Step 5.
User’s specific public key for administrator = a
point AB on the elliptic curve Ep(a,b).
If administrator wants to encrypt the message M
then all the characters of the dispatch are coded to
the points on the elliptic curve using the code table
which is agreed upon by the administrator and
student. Then each message point is encrypted to a
pair of cipher points E1,E2 .[6]
Administrator uses a random
number r.
E1 = r C
E2 = M + (b + r) A 1 – r A 2 + AB
After encrypting all the characters of the message
administrator converts the pair of points of each
message point into the text characters using the
code table. Then administrator encrypts the plain
text.
After encrypting the cipher text, User
converts the cipher text into the points on the
elliptic curve and identifies the points E1 and E2 of
each character. Then decrypts the message as
follows.
M = E2 – ( a E1 + a B 1 + B A)
Hence, User can view this decrypted data as he wants.
3.2. ALGORITHM OF ECC:
1. Start
2: user perform the registration
3. User enter private key1 and private
key2(x,y).
4. User calculate the public key,
Calculates s
s=(3(x)^2+a)/2y x2=s^2-2x y2=s(x-x2)-y
5. User broadcast public key
(X2,Y2)
6. Admin performs encryption
6.1. Calculate 1G to 5G for each character
6.2. Retrieve matched G from generated
table
6.3. Calculate G of that character which
admin wants to encrypt and store cipher
text.
7. User performs decryption
7.1. Calculate 1G to 5G of each character.
7.2. Retrieve matched G from generated
table and stores the plain text.
8. Stop.
4. RESULT:
RSA key generation is expressively slower than ECC
key generation for RSA key of sizes 1024 bits which is
greater than key size of ECC. RSA has more
computational overheads than ECC because in RSA
algorithm, users have to choose particular prime
number for calculation of key generation. As the key
size of ECC is smaller than the key size of RSA so,
encryption of Elliptic curve cryptography is much
faster than RSA. ECC is more efficient for small
devices. If ECC algorithm is used for communication
purpose then it offers good bandwidth than RSA.
Table 1. Comparison of ECC and RSA

Volume 3, Issue 5, 2016, pp. 222-225
Parameters ECC RSA
Computational Roughly 10 More than
overheads times than that ECC.
of RSA can be
Saved.
Key sizes System System
parameters and parameters and
key pairs are key pairs are
shorter for the longer for the
ECC RSA
Key generation Faster Slower
Encryption Much faster Have good
Than RSA. speed but
slower than
ECC.
Small devices Much more Less efficient
efficiency Efficient. Than ECC.
5. CONCLUSION
In this paper, Data security is important issue in day
to day life. The elliptic curve cryptography is one of
the useful techniques to hide the data or information
so that data must be access by authorized user. In this
technique all the calculations are takes place by
considering the points on the elliptic curve. The
encryption and key generation process is faster.
Wireless devices are speedily becoming more reliant
on safety features such as the ability to do secure
email, confident Web browsing, and cybernetic
private networking to commercial networks and ECC
allows more efficient implementation of all of these
features. ECC make available better security and
more efficient performance than the first generation
public key techniques.
REFERENCES
[1]. J.Edge, An introduction to elliptic curve
cryptography, http://lwn.net/Articles/174127/,
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[2]. Ch. Suneetha, D. Sravana Kumar and A.
Chandrasekhar, “Secure key transport in symmetric
cryptographic protocols using elliptic curves over finite
fields”, International Journal of Computer.
[3]. R. Rajaram Ramasamy, M. Amutha Prabakar, M.
Indra Devi and M.Suguna, ―Knapsack based ECC
encryption and decryption‖, International Journal of
Network Security, Vol. 9, No. 3, PP. 218-226,Nov.
2009.
[4]. D.Sravana Kumar, CH. Suneetha and A.
Chandrasekhar, Encryption of data using Elliptic
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[5]. Nautiyal et al., International Journal of Advanced
Research in Computer Science and Software
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[6]. Alfred J. Menezes and Scott A. Vanstone, “Elliptic
Curve Cryptosystems and their implementations”,
Journal of Cryptology, 1993, Volume-6, Number-4,
pages 209-224.
[7]. Krithika K Annapoorna Shetty, Shravya Shetty K.
A review on asymmetric cryptography RSA and
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[8]. Richard Helm Erich Gamma. Design patterns:
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Data Security Using Elliptic Curve Cryptography

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Data Security Using Elliptic Curve Cryptography