AN ELLIPTIC CURVE METRIC ON
THE FUNDAMENTAL GROUP OVER

A.R. Rishivarman, B. Parthasarathy
SASTRA University
Tanjavur, Tamilnadu, INDIA
Department of Mathematics
Dr. Pauls Engineering College
Tamilnadu, INDIA
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 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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