Index calculus attack for hyperelliptic curves of small genus

Index calculus attack for hyperelliptic curves of small genus

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by Nicolas Thériault

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@MISC{Thériault_indexcalculus,
    author = {Nicolas Thériault},
    title = {Index calculus attack for hyperelliptic curves of small genus},
    year = {}
}

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Abstract

Citations

165	A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields, Algorithmic Number Theory - Adleman, DeMarrais, et al. - 1994
143	Solving sparse linear equations over finite fields - Wiedemann - 1986
142	Computing in the Jacobian of a hyperelliptic curve - Cantor - 1987
129	Hyperelliptic cryptosystems - Koblitz - 1989
65	An algorithm for solving the discrete log problem on hyperelliptic curves - Gaudry - 2000
57	Solving large sparse linear systems over finite fields - LaMacchia, Odlyzko
42	P.: A General Framework for Subexponential Discrete Logarithm Algorithms - Enge, Gaudry - 2002
33	Computing discrete logarithms in high-genus hyperelliptic jacobians in provably subexponential time - Enge
32	Computing discrete logarithms in real quadratic congruence function fields of large genus - Müller, Stein, et al.
20	Algorithmique des courbes hyperelliptiques et applications à la cryptologie - Gaudry - 2000
12	A generalized birthday attack - Girault, Cohen, et al. - 1988
9	Smooth ideals in hyperelliptic function fields - Enge, Stein
6	The index calculus method using non-smooth polynomials - Garefalakis, Panario - 2001