An Extension of GHS Weil Descent Attack

Tsutomu IIJIMA  Mahoro SHIMURA  Jinhui CHAO  Shigeo TSUJII 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E88-A  No.1  pp.97-104
Publication Date: 2005/01/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Public Key Cryptography
Keyword: 
elliptic curves,  hyperelliptic curves,  superelliptic curves,GHS Weil descent attack,  GHS conorm-norm homomorphism,  function fields, 

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Summary: 
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 and with composite extension degrees. Recently, Diem presented a general treatment of the GHS attack to hyperelliptic curves over finite fields of arbitrary odd characteristics. This paper shows that Diem's approach can be extended to curves of which the function fields are cyclic Galois extensions. In particular, we show the existence of GHS Weil restriction, triviality of the kernel of GHS conorm-norm homomorphism, and lower/upper bounds of genera of the resulting curves.