This chapter excerpted from Hardware Implementation of Finite-Field Arithmetic, gives an example of finite-field application—namely, the implementation of the scalar product (point multiplication) ...

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 ...

The mathematicians who toiled on the famous enigma also devised powerful forms of end-to-end encryption. By William J. Broad Defenses against digital snoopers keep getting stronger. Encryption is what ...

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 ...

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 ...