Post-quantum cryptography is rapidly evolving to counter threats posed by quantum computing, and elliptic curves combined with isogeny methodologies offer a promising avenue. This approach leverages ...

We use a connection between the arithmetic of elliptic curves of the form y² = x³ + k and the arithmetic of the quadratic number fields Q(√k) and Q(√-3k) to look for quadratic fields with high ...

In August, a pair of mathematicians discovered an exotic, record-breaking curve. In doing so, they tapped into a major open question about one of the oldest and most fundamental kinds of equations in ...

Editor's note: See the original article on PurpleAlientPlanet. Some of my research is focused on the implementation issues of elliptic curve cryptography on embedded systems. Since I often have to ...

R. P. Conceic˜ao, C. Hall & D. Ulmer, “Explicit points on the Legendre curve II”, Math. Res. Lett. 21 (2014), no. 2, p. 261-280. C. Davis & T. Occhipinti ...