AN ELLIPTIC CURVE METRIC ON THE FUNDAMENTAL GROUP OVER $GF(2^5)$
A. R. Rishivarman, B. Parthasarathy · International Journal of Pure and Apllied Mathematics · 2013
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.