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Titlebook: Algorithmic Number Theory; 7th International Sy Florian Hess,Sebastian Pauli,Michael Pohst Conference proceedings 2006 Springer-Verlag Berl

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https://doi.org/10.1007/978-3-662-06513-6lattice reduction — for finding the small roots of multivariate polynomials modulo an integer. For our needs, we improve the lattice construction step of Coppersmith’s method: we describe a way to find a subset of a set of vectors that decreases the Minkowski theorem bound, in a rather general setup including Coppersmith-type lattices.
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On the Computation of the Coefficients of a Modular Formion of the .. torsion points of which the representation consists is found via a height estimate, obtained from Arakelov theory, combined with numerical approximation. The height estimate implies that the required precision for the approximation grows at most polynomially in ..
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LLL on the Averager to give a clearer picture of the differences/similarities between the average and worst cases. Our work is intended to clarify the practical behavior of L. and to raise theoretical questions on its average behavior.
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