All Questions

Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully ...

In reading "PUBLIC-KEY CRYPTOSYSTEM BASED ON ISOGENIES" by Rostovtsev and Stolbunov, they claim on page 8 that the set $U=\{E_i(\mathbb{F}_p)\}$ of elliptic curves with a specific prime $l$ ...

Is it possible to generate an elliptic curve $E$ (randomly), together with knowing its class group $\mathrm{Cl}(\mathcal{O})$ structure? where $\mathcal{O}$ is its endomorphism rings $\mathsf{End}(E)$ ...

Elliptic Curve Digital Signature Algorithm (ECDSA) admits universal forgery (UF) if the Attacker can solve the equation $$z=\frac{f_{k-1}(x,y)f_{k+1}(x,y)}{f_{k}(x,y)^2},$$ where $k$ is unknown, $f_{k}...