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 cornerstone of modern public‐key systems, offering high levels of security with relatively small key sizes. Central to many advanced cryptographic ...

We show that if E is an elliptic curve over Q with a Q-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to E is as large as allowed by the isogeny, except for ...

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 ...

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 ...

“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) ...