IJPAM: Volume 108, No. 4 (2016)

SOME REMARKS ON A DISTANCE BETWEEN TWO
ORDINARY ELLIPTIC CURVES OVER
THE FINITE FIELD $\mathbb{F}_{2^5}$

Keisuke Hakuta
Interdisciplinary Graduate School of Science and Engineering
Shimane University
1060 Nishikawatsu-cho, Matsue-shi, Shimane 690-8504, JAPAN


Abstract. Rishivarman and Parthasarathy (2013) have constructed a map from the direct product of two copies of the set of ordinary elliptic curves with short Weierstrass equation over $\mathbb{F}_{2^5}$ to non-negative real numbers (plus infinity), and they have claimed that the map is a metric. In this paper we point out that the proof of the claim contains several flaws. Even worse, we shall show that the map is not a metric.

Received: January 27, 2016

AMS Subject Classification: 14H52, 11G20

Key Words and Phrases: elliptic curves, metric, isomorphism

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DOI: 10.12732/ijpam.v108i4.6 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: 2016
Volume: 108
Issue: 4
Pages: 801 - 807


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