Gaudry has described a new algorithm (Gaudry's variant) for the discrete logarithm problem (DLP) in hyperelliptic curves. For a hyperelliptic curve of a small genus on a finite field GF(q), Gaudry's variant solves for the DLP in time O(q2+ε). This paper shows that Cab curves can be attacked with a modified form of Gaudry's variant and presents the timing results of such attack. However, Gaudry's variant cannot be effective in all of the Cab curve cryptosystems. This paper also provides an example of a Cab curve that is unassailable by Gaudry's variant.
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Seigo ARITA, "Gaudry's Variant against Cab Curves" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 9, pp. 1809-1814, September 2000, doi: .
Abstract: Gaudry has described a new algorithm (Gaudry's variant) for the discrete logarithm problem (DLP) in hyperelliptic curves. For a hyperelliptic curve of a small genus on a finite field GF(q), Gaudry's variant solves for the DLP in time O(q2+ε). This paper shows that Cab curves can be attacked with a modified form of Gaudry's variant and presents the timing results of such attack. However, Gaudry's variant cannot be effective in all of the Cab curve cryptosystems. This paper also provides an example of a Cab curve that is unassailable by Gaudry's variant.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_9_1809/_p
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@ARTICLE{e83-a_9_1809,
author={Seigo ARITA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Gaudry's Variant against Cab Curves},
year={2000},
volume={E83-A},
number={9},
pages={1809-1814},
abstract={Gaudry has described a new algorithm (Gaudry's variant) for the discrete logarithm problem (DLP) in hyperelliptic curves. For a hyperelliptic curve of a small genus on a finite field GF(q), Gaudry's variant solves for the DLP in time O(q2+ε). This paper shows that Cab curves can be attacked with a modified form of Gaudry's variant and presents the timing results of such attack. However, Gaudry's variant cannot be effective in all of the Cab curve cryptosystems. This paper also provides an example of a Cab curve that is unassailable by Gaudry's variant.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - Gaudry's Variant against Cab Curves
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1809
EP - 1814
AU - Seigo ARITA
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2000
AB - Gaudry has described a new algorithm (Gaudry's variant) for the discrete logarithm problem (DLP) in hyperelliptic curves. For a hyperelliptic curve of a small genus on a finite field GF(q), Gaudry's variant solves for the DLP in time O(q2+ε). This paper shows that Cab curves can be attacked with a modified form of Gaudry's variant and presents the timing results of such attack. However, Gaudry's variant cannot be effective in all of the Cab curve cryptosystems. This paper also provides an example of a Cab curve that is unassailable by Gaudry's variant.
ER -