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 ...

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 ...

Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics. According to one version of the story, Hippasus made this discovery at sea, ...

Elliptic curves — actually plane curves that are very different from ellipses — have been used in key realms of number theory, such as the proof of Fermat's last theorem. In the mid-1980s, ...