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Arithmetic geometry of elliptic curves combines algebraic geometry and number theory to investigate cubic curves of genus one endowed with a distinguished rational point. Such curves admit a group law ...

Iwasawa theory investigates the variation of arithmetic invariants—such as class groups and Selmer groups—along infinite towers of number fields, most classically the cyclotomic Z p-extension of the ...

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 ...

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 ...