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 ...

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 ...

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), 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) ...

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 ...

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 ...