IEICE TRANSACTIONS on Fundamentals
An Extension of GHS Weil Descent Attack
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.1 pp.97-104
- Publication Date
- 2005/01/01
- Publicized
- Online ISSN
- DOI
- 10.1093/ietfec/e88-a.1.97
- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)
- Category
- Public Key Cryptography
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Keyword
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Tsutomu IIJIMA, Mahoro SHIMURA, Jinhui CHAO, Shigeo TSUJII, "An Extension of GHS Weil Descent Attack" in IEICE TRANSACTIONS on Fundamentals,
vol. E88-A, no. 1, pp. 97-104, January 2005, doi: 10.1093/ietfec/e88-a.1.97.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.1.97/_p
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@ARTICLE{e88-a_1_97,
author={Tsutomu IIJIMA, Mahoro SHIMURA, Jinhui CHAO, Shigeo TSUJII, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Extension of GHS Weil Descent Attack},
year={2005},
volume={E88-A},
number={1},
pages={97-104},
abstract={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.},
keywords={},
doi={10.1093/ietfec/e88-a.1.97},
ISSN={},
month={January},}
Copy
TY - JOUR
TI - An Extension of GHS Weil Descent Attack
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 97
EP - 104
AU - Tsutomu IIJIMA
AU - Mahoro SHIMURA
AU - Jinhui CHAO
AU - Shigeo TSUJII
PY - 2005
DO - 10.1093/ietfec/e88-a.1.97
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2005
AB - 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.
ER -
English
