• Publications
  • Influence
Interpolation of polynomials given by straight-line programs
TLDR
We give an algorithm for the interpolation of a polynomial A given by a straight-line program. Expand
  • 50
  • 14
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Sharp estimates for triangular sets
TLDR
We study the triangular representation of zero-dimensional varieties defined over the rational field and prove polynomial bounds in terms of intrinsic quantities for the height (resp. degree) of the coefficients of such triangular sets, whereas previous bounds were exponential. Expand
  • 84
  • 10
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Polynomial evaluation and interpolation on special sets of points
TLDR
We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. Expand
  • 101
  • 9
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Linear Recurrences with Polynomial Coefficients and Application to Integer Factorization and Cartier-Manin Operator
TLDR
We study the complexity of computing one or several terms (not necessarily consecutive) in a recurrence with polynomial coefficients. Expand
  • 89
  • 8
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Polar varieties and computation of one point in each connected component of a smooth real algebraic set
TLDR
We show that computing suitable sections of the polar varieties associated to generic projections of V gives at least one point in each connected component of V ∩ <b>R</b><sup>. Expand
  • 122
  • 7
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Genus 2 point counting over prime fields
TLDR
We find a method for constructing secure genus 2 curves over a large prime field that is suitable for cryptosystems. Expand
  • 78
  • 7
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Computing Parametric Geometric Resolutions
  • É. Schost
  • Mathematics, Computer Science
  • Applicable Algebra in Engineering, Communication…
  • 1 February 2003
TLDR
We define the notion of parametric geometric resolution as a means to represent some generic solutions in terms of the parameters. Expand
  • 52
  • 7
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Fast algorithms for computing isogenies between elliptic curves
TLDR
We introduce a new algorithm that computes an isogeny of degree l (l different from the characteristic) in time quasi-linear with respect to l. Expand
  • 91
  • 6
  • PDF
A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii?s Algorithm
TLDR
We present an algorithm based on the birthday paradox, which is a low-memory parallel counterpart to the algorithm of Matsuo, Chao and Tsujii, but the memory requirement drops from several GB to almost nothing. Expand
  • 33
  • 6
Complexity results for triangular sets
  • É. Schost
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 September 2003
TLDR
We study the representation of the solutions of a polynomial system by triangular sets, and concentrate on the positive-dimensional case. Expand
  • 43
  • 6
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