Affiliation:
1. Institute of Science and Engineering, Academic Assembly, Shimane University, Matsue, Shimane, Japan
Abstract
We consider metrics on the set of elliptic curves in short Weierstrass form
over a finite field of characteristic greater than three. The metrics have
been first found by Mishra and Gupta (2008). Vetro (2011) constructs other
metrics which are independent on the choice of a generator of the
multiplicative group of the underlying finite field, whereas the metrics
found by Mishra and Gupta, are dependent on the choice of a generator of the
multiplicative group of the underlying finite field. Hakuta (2015, 2018)
constructs metrics on the set of non-supersingular elliptic curves in
shortWeierstrass form over a finite field of characteristic two and three,
respectively. The aim of this paper is to point out that the metric found by
Mishra and Gupta is in fact not a metric. We also construct new metrics
which are slightly modified versions of the metric found by Mishra and
Gupta.
Publisher
National Library of Serbia