Simon Abelard

Papers accepted in international journals

• Broadcast Encryption using Sum-Product decomposition of Boolean functions.
  A. Dupin, S. Abelard
  To appear in Communications in Cryptology, 2024. [ePrint]
• Efficient computation of Riemann-Roch spaces for plane curves with ordinary singularities.
  S. Abelard, A. Couvreur, G. Lecerf.
  Applicable Algebra in Engineering, Communication and Computing (AAECC), 2022. [HAL, published version]
• Computing Riemann-Roch spaces via Puiseux expansions.
  S. Abelard, E. Berardini, A. Couvreur, G. Lecerf.
  Journal of Complexity, 2022, vol. 73, p. 101666. [HAL, published version]
• Counting Points on hyperelliptic curves with explicit RM in arbitrary genus.
  S. Abelard.
  Journal of Complexity, 2020, vol. 57, p. 101440. [arxiv, published version]
• Improved Complexity Bounds for Counting Points on Hyperelliptic Curves.
  S. Abelard, P. Gaudry and P.-J. Spaenlehauer.
  Foundations of Computational Mathematics, 2019, vol. 19, no 3, p. 591-621. [arxiv, published version]

Papers accepted in proceedings of international conferences

• Sub-quadratic time for Riemann-Roch spaces. The case of smooth divisors over nodal plane projective curves.
  S. Abelard, A. Couvreur and G. Lecerf.
  Proceedings of ISSAC 2020, pp 14-21. [HAL, DOI]
• On the complexity of computing integral bases of function fields.
  S. Abelard.
  Proceedings of CASC 2020, pp 42-62. [HAL, published version]
• Counting points on genus-3 hyperelliptic curves with explicit RM.
  S. Abelard, P. Gaudry and P.-J. Spaenlehauer.
  Proceedings of the Thirteenth Algorithmic Number Theory Symposium (ANTS XIII). [arxiv, published version]

Invited talks

• Counting points on hyperelliptic curves in large characteristic: the RM case, talk at a minisymposium of the SIAM conference on Applied Algebraic Geometry 2019.
• Improving Complexity Bounds for Hyperelliptic Point-counting, talk at a minisymposium of the SIAM conference on Applied Algebraic Geometry 2017.

Talks given at national events

• A faster algorithm for computing Riemann-Roch spaces, talk at the JC2 (Journées Codage et Cryptographie) in November 2020.
• Computing integral bases of algebraic function fields, talk at the JNCF 2020 (Journées Nationales de Calcul Formel). [slides]
• Point-counting on hyperelliptic curves of genus 3 and beyond, talk at the JNCF 2018 (Journées Nationales de Calcul Formel). [slides]

Seminars

• Structured algorithms for algebraic curves, talk given in February 2021 at the Polsys seminar (Paris).
• Recent progress on the computation of Riemann-Roch spaces, talk given in October 2020 at the GRACE team seminar (Palaiseau).
• Computing Riemann-Roch spaces of smooth divisors on nodal curves, talk given in July 2020 at the seminar of the MAX team (Palaiseau).
• Counting points on hyperelliptic curves over finite of large characteristic, talk given in May 2020 at the seminar of the MAX team (Palaiseau).
• Counting points on hyperelliptic curves over finite of large characteristic, talk given in March 2020 at the seminar of XLIM (Limoges).
• Counting points on hyperelliptic curves over finite of large characteristic, talk given in January 2020 at the Effective Algebra and Geometry seminar of IRMAR (Rennes).
• Counting points on hyperelliptic curves over finite of large characteristic, talk given in November 2019 at the GRACE team seminar (Palaiseau).
• Complexity Bounds for Point-counting on Hyperelliptic Curves, talk given during an invitation at the Symbolic Computation Group at the University of Waterloo in April 2017.

Thesis

• My Ph.D. dissertation can be found here (Errata: the complexity exponent in the RM case should be 9 instead of 8, see my article in the Journal of Complexity).
• The slides of the defense can be found here.