An Extension of GHS Weil Descent Attack

The Weil descent attack, suggested by Frey, has been implemented by Gaudry, Hess and Smart (the so-called GHS attack), on elliptic curves over finite fields of characteristic two of composite degrees. The GHS attack has been extended by Galbraith to hyperelliptic curves of characteristic two. Recently, Diem presented a general treatment of GHS attack to hyperelliptic curves over finite fields of arbitrary characteristics. This paper shows that Diem's approach can be extended to curves of which the function fields are cyclic Galois extension. In particular, existance of GHS Weil restriction, triviality of the kernel of GHS conorm-norm homomorphism, and lower/upper bounds of genera of the restricted function field are discussed.

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