A public key cryptography method that provides fast decryption and digital signature processing. Elliptic curve cryptography (ECC) uses points on an elliptic curve to derive a 163-bit public key that ...

Four researchers have recently come out with a model that upends the conventional wisdom in their field. They have used intensive computational data to suggest that for decades, if not longer, ...

As numbers go, 1729, the Hardy-Ramanujan number, is not new to math enthusiasts. But now, this number has triggered a major discovery — on Ramanujan and the theory of what are known as elliptical ...

We determine equations of the modular curves $X_1(N)$ for $N = 11, 13, 14, 15, 16, 17$ and 18. Except for $N = 17$, these are the only existing elliptic or ...

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 ...

Since ancient Greece, researchers have tried to isolate special rational points on curves. Now they have the first ever formula that applies uniformly to all curves ...

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 ...

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 ...