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- W4384927249 abstract "We give a new approach to the elliptic curve discrete logarithm problem over cubic extension fields $mathbb{F}_{q^3}$. It is based on a transfer: First an $mathbb{F}_q$-rational $(ell,ell,ell)$-isogeny from the Weil restriction of the elliptic curve under consideration with respect to $mathbb{F}_{q^3}/mathbb{F}_q$ to the Jacobian variety of a genus three curve over $mathbb{F}_q$ is applied and then the problem is solved in the Jacobian via the index-calculus attacks. Although using no covering maps in the construction of the desired homomorphism, this method is, in a sense, a kind of cover attack. As a result, it is possible to solve the discrete logarithm problem in some elliptic curve groups of prime order over $mathbb{F}_{q^3}$ in a time of $tilde{O}(q)$." @default.
- W4384927249 created "2023-07-22" @default.
- W4384927249 creator A5083393341 @default.
- W4384927249 date "2023-07-20" @default.
- W4384927249 modified "2023-09-25" @default.
- W4384927249 title "Cover Attacks for Elliptic Curves over Cubic Extension Fields" @default.
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- W4384927249 doi "https://doi.org/10.1007/s00145-023-09474-2" @default.
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