Open AccessConstruction of metrics on the set of elliptic curves over a finite field
Author(s) -
Keisuke Hakuta
Publication year - 2021
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim2123125h
Subject(s) - metric (unit) , mathematics , multiplicative function , finite field , generator (circuit theory) , multiplicative group , field (mathematics) , set (abstract data type) , supersingular elliptic curve , pure mathematics , schoof's algorithm , discrete mathematics , elliptic curve , mathematical analysis , computer science , quarter period , physics , power (physics) , operations management , quantum mechanics , economics , programming language
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.