DLP-based cryptosystems with Pell cubics
Simone Dutto · Banach Center Publications · 2023
The classical Pell equation $x^2 - \mathrm{D}y^2 = 1$ can be extended to the cubic case considering the points $(x, y, z) \in \mathbb{F}^3$ such that, for fixed $\mathrm{R}\in \mathbb{F}$, $$ x^3 + \mathrm{R}y^3 + \mathrm{R}^2 z^3 - 3 \mathrm{R}x y z = 1