Dr Jarvis works in the area of algebraic number theory, an area which uses techniques from algebra, algebraic geometry and classical number theory, amongst others. In particular, he studies the ...

Elliptic curves arise naturally in many parts of mathematics, and can be described by a simple cubic equation. They form the basis of cryptographic protocols used by most of the major internet ...

Elliptic curves are among the more beguiling objects in modern mathematics. They don’t seem complicated, but they form an expressway between the math that many people learn in high school and research ...

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 ...

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 ...

When it comes to public key cryptography, most systems today are still stuck in the 1970s. On December 14, 1977, two events occurred that would change the world: Paramount Pictures released Saturday ...