Cover Attacks for Elliptic Curves over Cubic Extension Fields

We give a new approach to the elliptic curve discrete logarithm problem over cubic extension fields $${\mathbb {F}}_{q^3}$$ . It is based on transfer: First an {F}}_q$$ -rational $$(\ell ,\ell )$$ -isogeny from Weil restriction of under consideration with respect {F}}_{q^3}/{\mathbb Jacobian variety genus three applied and then solved in via index-calculus attacks. Although it uses no covering maps construction desired homomorphism, this method is, sense, kind cover attack. As result, possible solve some groups prime order time $${\tilde{O}}(q)$$