Discover the implications of the Jacobian Curve vulnerability in elliptic curve cryptography, particularly its impact on the Elliptic Curve Digital Signature Algorithm (ECDSA). This article explores ...

It is known that the Jacobian J of the Klein curve is isogenous to E3 for a certain elliptic curve E. We compute explicit equations for E and prove that J is in fact isomorphic to E3. We also identify ...

Abstract: Let C(K) be the K-points of a smooth projective curve C of genus g>1 and J(K) its Jacobian. Fixing a point on the curve, one has a canonical embedding of C(K) into J(K) with the point ...

Should return 1 point, since this map is claimed to be birational, and since the curves are smooth, should be an isomorphism. The morphism returned by the phi = Jacobian(C, morphism=True) (where C is ...