Web page of François Morain

Version française

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

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My public key.

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Member of the GRACE team.

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

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News:

• Modular polynomials:
  • 2024年02月14日: 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年01月29日: Using modular polynomials for eta products to compute isogenies.
• Using modular curves in ECM:
  • 2022年03月11日: preprint + Magma data file
  • 2021年11月23日: Some factors of numbers of the form b^n+/1 found using ECM with new classes of curves
• 2022年02月11日: Magma files for hgcd algorithms; gcd.2022年08月31日b.tgz (GMP implementation, correcting many bugs in the preceding version).
• 2018年02月23日: 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年07月25日: Breaking DLP in GF(p5) using 3-dimensional sieving (with L. Grémy et A. Guillevic)
• 2016年12月23日: Discrete logarithms (with A. Guillevic)
• 2016年05月23日: Solving discrete logarithms on a 170-bit MNT curve by pairing reduction (with A. Guillevic, E. Thomé)
• 2016年05月23日: Computing cardinalities of Q-curve reductions over finite fields (with C. Scribot, B. Smith)
• 2015年11月16日: Factoring Safe Semiprimes with a Single Quantum Query (with F. Grosshans, T. Lawson, B. Smith)
• 2015年02月03日: Improving NFS for the discrete logarithm problem in non-prime finite fields (with R. Barbulescu, P. Gaudry, A. Guillevic -- EUROCRYPT 2015).
• 2015年01月08日: Cryptologie, la protection par les nombres, les jeudi de l'X (in french).
• 2014年11月28日: Improvements to the number field sieve for non-prime finite fields (with R. Barbulescu, P. Gaudry, A. Guillevic).
• 2012年02月21日: Discrete logarithm computations over finite fields using Reed-Solomon codes (with D. Augot)
• 2010年10月15日: a new record for ECPP, as announced during ECC2010 (slides).
• 2009年10月22日: A remark on an article of S. Müller, FM.

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Fields of Research: Computational Number Theory, Cryptography.

• HAL; older articles.
• Preprints
• Talks

My primes The ECPP package SEA records

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Historical stuff

Manuscripts difficult to find

Some manuscripts of A.O.L. Atkin

As sent via email. I think it is about time they were shared.

• 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.

More emails might follow one day.

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).

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More links

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