In this paper we determine the quadratic points on the modular curves 𝑋₀(𝑁), where the curve is non-hyperelliptic, the genus is 3, 4, or 5, and the Mordell–Weil group of 𝐽₀(𝑁) is finite. The ...

We all know the usual jokes about the ‘S’ in ‘IoT’ standing for ‘Security’. It’s hardly a secret that security in embedded, networked devices (‘IoT devices’) is all too often a last-minute task that ...

Elliptic Curve Cryptography (ECC) has emerged as a vital component in modern secure communication systems, offering enhanced security with smaller key sizes compared to traditional methods. Hardware ...

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 ...

“Elliptic curve cryptography (ECC), as one of the public key cryptography systems, has been widely applied to many security applications. It is challenging to implement a scalar multiplication (SM) ...

Imagine a world where the most widely-used cryptographic methods turn out to be broken: quantum computers allow encrypted Internet data transactions to become readable by anyone who happened to be ...

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 ...