Elliptic Curve Cryptography (ECC) has emerged as a vital component in modern secure communication systems, offering enhanced security with smaller key sizes compared to traditional methods. Hardware ...

“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) ...

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 ...

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 ...