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, ...
We determine equations of the modular curves $X_1(N)$ for $N = 11, 13, 14, 15, 16, 17$ and 18. Except for $N = 17$, these are the only existing elliptic or ...
Elliptic curve cryptography (ECC) has emerged as a cornerstone of modern public‐key systems, offering high levels of security with relatively small key sizes. Central to many advanced cryptographic ...
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 ...
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 ...
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