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News:

- 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.

- 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.

- 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).

- Number theory