Generation of two ''independent'' points on an elliptic curve of $j$-invariant $\neq 0, 1728$

ePrint Report: Generation of two ''independent'' points on an elliptic curve of $j$-invariant $\neq 0, 1728$

Dmitrii Koshelev

This article is dedicated to a new generation method of two ``independent'' $\mathbb{F}_{\!q}$-points $P_0$, $P_1$ on almost any ordinary elliptic curve $E$ over a finite field $\mathbb{F}_{\!q}$ of large characteristic. In particular, the method is relevant for all standardized and real-world elliptic curves of $j$-invariants different from $0$, $1728$. The points $P_0$, $P_1$ are characterized by the fact that nobody (even a …

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