Si E₁ et E₂ sont deux courbes elliptiques sur un corps k, nous avons une application naturelle CH¹(E₁)₀ ⊗ CH¹(E₂)₀ → CH²(E₁ × E₂). Quand k est un corps de nombres, une conjecture due à Bloch et ...
The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...
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, ...
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 ...
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 ...
Soit E une courbe elliptique sur ℚ, soit K un corps quadratique imaginaire, et soit K∞ une ℤp-extension de K. Étant donné un ensemble ∑ de places de K contenant les places audessus de p et les places ...
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 ...
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 ...
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 ...
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