IJPAM: Volume 89, No. 4 (2013)

AN ELLIPTIC CURVE METRIC ON
THE FUNDAMENTAL GROUP OVER $GF(2^5)$

A.R. Rishivarman$^1$, B. Parthasarathy$^2$
$^1$SASTRA University
Tanjavur, Tamilnadu, INDIA
$^1$Department of Mathematics
Dr. Pauls Engineering College
Tamilnadu, INDIA
$^2$Department of Mathematics
Mailam Engineering College
Tamilnadu, INDIA


Abstract. Since the introduction of public-key cryptography by Diffe and Hellman in 1976, the potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized. Although the discrete logarithm problem as first employed by Diffe and Hellman was defined explicitly as the problem of finding logarithms with respect to a generator in the multiplicative group of the integers module a prime, this idea can be extended to arbitrary groups and in particular, to elliptic curve groups. The resulting public - key systems provide relatively small block size, high speed, and high security. In the present paper we define a metric on the fundamental group of elliptic curve over the Galois field $GF (2^5).$ The fact that defining a new metric among the elliptic curves has potential application in the theory of cryptography; especially to thwart fixed table attack.

Received: August 17, 2013

AMS Subject Classification:

Key Words and Phrases: galois field, elliptic curve, finite field, metric, fundamental group, isomorphism class of curves

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DOI: 10.12732/ijpam.v89i4.8 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 4