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 all know the usual jokes about the ‘S’ in ‘IoT’ standing for ‘Security’. It’s hardly a secret that security in embedded, networked devices (‘IoT devices’) is all too often a last-minute task that ...

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 ...

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 ...

If you and I were to meet with no possibility of being overheard, we could agree upon the secret encryption key we would use in our public communications. One of the NIST-recognized encryption schemes ...

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves. Elliptic curves seem to admit infinite variety, but they really only come in two flavors. That ...

The Myhill Lecture Series 2019, "Complex dynamics and arithmetic geometry", will be delivered by Dr. Laura DeMarco, Henry S. Noyes Professor of Mathematics at Northwestern University. She earned her ...