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 ...
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 ...
Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...
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 ...
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 ...
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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