Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...

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 ...

Manjul Bhargava was warned long ago never to think about math while driving. "I find doing mathematical research requires very deep concentration," said Bhargava, the Brandon Fradd, Class of 1983, ...

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 ...

Author Nick Sullivan worked for six years at Apple on many of its most important cryptography efforts before recently joining CloudFlare, where he is a systems engineer. He has a degree in mathematics ...

At a prime of ordinary reduction, the Iwasawa "main conjecture" for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is ...

The elliptic curve discrete logarithm problem (ECDLP) lies at the heart of modern public-key cryptography. It concerns the challenge of determining an unknown scalar multiplier given two points on an ...

A public key cryptography method that provides fast decryption and digital signature processing. Elliptic curve cryptography (ECC) uses points on an elliptic curve to derive a 163-bit public key that ...