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 K un corps totalement réel qui est une extension abélienne finie de ℚ non ramifiée en 3, 5 et 7. Nous prouvons que toute courbe elliptique E sur K est modulaire, en réduisant la question de ...

Elliptic Curve Cryptography (ECC) has emerged as a favoured approach in modern cryptography, notably due to its ability to deliver robust security with relatively small key sizes. Extensive hardware ...

Let K be a number field, K̄ an algebraic closure of K, GK the absolute Galois group $Gal(\bar{K}/K)$, $K_{ab}$ the maximal abelian extension of K and E/K an elliptic ...

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 ...