Web page of François Morain

LIX Laboratoire d'Informatique de l' École Polytechnique             Équipe Cryptologie

Member of the GRACE team.

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E-mail: morain(at)lix.polytechnique.fr

• Modular polynomials:
  • 2024/02/14: Using Fricke modular polynomials to compute isogenies
    • preprint;
    • Programs :
      • a script to check computations (in sagemath, version xxx).
      • a bundle of Magma programs corresponding to the preprints.
  • 2024/01/29: Using modular polynomials for eta products to compute isogenies.
• Using modular curves in ECM:
  • 2022/03/11: preprint + Magma data file
  • 2021/11/23: Some factors of numbers of the form b^n+/1 found using ECM with new classes of curves
• 2022/02/11: Magma files for hgcd algorithms; gcd.2022.08.31b.tgz (GMP implementation, correcting many bugs in the preceding version).
• 2018/02/23: Deterministic factoring with oracles (with G. Renault, B. Smith)
• 2017/06: Computing discrete logarithms in GF(p6) (with L. Grémy, A. Guillevic, E. Thomé)
• 2017/07/25: Breaking DLP in GF(p5) using 3-dimensional sieving (with L. Grémy et A. Guillevic)
• 2016/12/23: Discrete logarithms (with A. Guillevic)
• 2016/05/23: Solving discrete logarithms on a 170-bit MNT curve by pairing reduction (with A. Guillevic, E. Thomé)
• 2016/05/23: Computing cardinalities of Q-curve reductions over finite fields (with C. Scribot, B. Smith)
• 2015/11/16: Factoring Safe Semiprimes with a Single Quantum Query (with F. Grosshans, T. Lawson, B. Smith)
• 2015/02/03: Improving NFS for the discrete logarithm problem in non-prime finite fields (with R. Barbulescu, P. Gaudry, A. Guillevic -- EUROCRYPT 2015).
• 2015/01/08: Cryptologie, la protection par les nombres, les jeudi de l'X (in french).
• 2014/11/28: Improvements to the number field sieve for non-prime finite fields (with R. Barbulescu, P. Gaudry, A. Guillevic).
• 2012/02/21: Discrete logarithm computations over finite fields using Reed-Solomon codes (with D. Augot)
• 2010/10/15: a new record for ECPP, as announced during ECC2010 (slides).
• 2009/10/22: A remark on an article of S. Müller, FM.

Fields of Research: Computational Number Theory, Cryptography.

• HAL; older articles.
• Preprints
• Talks

My primes     The ECPP package     SEA records

Historical stuff

Manuscripts difficult to find

Some manuscripts of A.O.L. Atkin

• 19910614.txt: The Number of Points on an Elliptic Curve Modulo a Prime (I)
• 19920319.txt: The Number of Points on an Elliptic Curve Modulo a Prime (II)
• 19930303.txt: Addendum
• 19930305.txt: Partial rewriting of 19920319
• 19930312.txt: addendum on modular equation computation.

Misc

• Enumeration of rational points on Elliptic Curves over Finite Fields Leonard S. Charlap, Raymond Coley, David P. Robbins (1991).
• Random equivalence of factorization and computation of orders, D. Long, Princeton University, Depatment of Electrical Engineering and Computer Science, April 1981, Technical Report, 284.
• Problèmes et résultats en théorie des nombres (Conférence de Paul Erdos à l' Université de Limoges le 21 octobre 1986).

More links

• Number theory
  • Keith Matthews's server
  • Prime numbers server