On Security of Superelliptic Curves and Ca& Curves Based Cryptosystems against GHS Weil Descent Attac

摘要

The GHS Weil descent attack by Gaudry, Hess and Smart was originally proposed to elliptic curves over finite fields of characteristic two. In this paper, we consider GHS Weil descent attacks to algebraic curves whose function fields are Galois extensions of the rational function field. Lower bounds of genera of the function fields of their Weil restrictions are obtained when the function fields of the curves are tame Galois extensions.