François Morain

According to our database, François Morain authored at least 33 papers between 1989 and 2023.

Collaborative distances:

• Dijkstra number of four.
• Erdős number of three.

2023

Deterministic factoring with oracles.

François Morain, Guénaël Renault, Benjamin Smith

Appl. Algebra Eng. Commun. Comput., July, 2023

2022

Implementing the Thull-Yap Algorithm for Computing Euclidean Remainder Sequences.

François Morain

Proceedings of the ISSAC '22: International Symposium on Symbolic and Algebraic Computation, Villeneuve-d'Ascq, France, July 4, 2022

2017

Computing Discrete Logarithms in 𝔽_p⁶.

Laurent Grémy, Aurore Guillevic, François Morain, Emmanuel Thomé

Proceedings of the Selected Areas in Cryptography - SAC 2017, 2017

2016

Computing cardinalities of -curve reductions over finite fields.

François Morain, Charlotte Scribot, Benjamin Smith

LMS J. Comput. Math., 2016

Solving discrete logarithms on a 170-bit MNT curve by pairing reduction.

Aurore Guillevic, François Morain, Emmanuel Thomé

IACR Cryptol. ePrint Arch., 2016

Improving NFS for the discrete logarithm problem in non-prime finite fields.

Razvan Barbulescu, Pierrick Gaudry, Aurore Guillevic, François Morain

IACR Cryptol. ePrint Arch., 2016

2015

Factoring Safe Semiprimes with a Single Quantum Query.

Frédéric Grosshans, Thomas Lawson, François Morain, Benjamin Smith

CoRR, 2015

2014

Improvements to the number field sieve for non-prime finite fields.

Razvan Barbulescu, Pierrick Gaudry, Aurore Guillevic, François Morain

CoRR, 2014

2012

Discrete logarithm computations over finite fields using Reed-Solomon codes

Daniel Augot, François Morain

CoRR, 2012

2011

Elliptic Curves for Primality Proving.

François Morain

Proceedings of the Encyclopedia of Cryptography and Security, 2nd Ed., 2011

2008

Fast algorithms for computing isogenies between elliptic curves.

Alin Bostan, François Morain, Bruno Salvy, Éric Schost

Math. Comput., 2008

2007

Implementing the asymptotically fast version of the elliptic curve primality proving algorithm.

François Morain

Math. Comput., 2007

Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts.

P. Mihailescu, François Morain, Éric Schost

Proceedings of the Symbolic and Algebraic Computation, International Symposium, 2007

2006

Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm.

Pierrick Gaudry, François Morain

Proceedings of the Symbolic and Algebraic Computation, International Symposium, 2006

2005

Elliptic Curves for Primality Proving.

François Morain

Proceedings of the Encyclopedia of Cryptography and Security, 2005

Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields.

Régis Dupont, Andreas Enge, François Morain

J. Cryptol., 2005

2004

Proving the Primality of Very Large Numbers with fastECPP.

Jens Franke, Thorsten Kleinjung, François Morain, T. Wirth

Proceedings of the Algorithmic Number Theory, 6th International Symposium, 2004

2003

Fast Decomposition of Polynomials with Known Galois Group.

Andreas Enge, François Morain

Proceedings of the Applied Algebra, 2003

2002

Isogeny Volcanoes and the SEA Algorithm.

Mireille Fouquet, François Morain

Proceedings of the Algorithmic Number Theory, 5th International Symposium, 2002

Comparing Invariants for Class Fields of Imaginary Quadratic Fields.

Andreas Enge, François Morain

Proceedings of the Algorithmic Number Theory, 5th International Symposium, 2002

2001

Solvability by radicals from an algorithmic point of view.

Guillaume Hanrot, François Morain

Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, 2001

2000

Computing isogenies between elliptic curves over F_pⁿ using Couveignes's algorithm.

Reynald Lercier, François Morain

Math. Comput., 2000

Factorization of a 512-Bit RSA Modulus.

Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter M. Lioen, Peter L. Montgomery, Brian Murphy, Herman J. J. te Riele, Karen I. Aardal, Jeff Gilchrist, Gérard Guillerm, Paul C. Leyland, Joël Marchand, François Morain, Alec Muffett, Chris Putnam, Craig Putnam, Paul Zimmermann

Proceedings of the Advances in Cryptology, 2000

1999

Speeding up the Discrete Log Computation on Curves with Automorphisms.

Iwan M. Duursma, Pierrick Gaudry, François Morain

Proceedings of the Advances in Cryptology, 1999

1998

Primality Proving Using Elliptic Curves: An Update.

François Morain

Proceedings of the Algorithmic Number Theory, Third International Symposium, 1998

1996

Building pseudoprimes with a large number of prime factors.

Dominique Guillaume, François Morain

Appl. Algebra Eng. Commun. Comput., 1996

1995

Counting the Number of Points on Elliptic Curves over Finite Fields: Strategies and Performance.

Reynald Lercier, François Morain

Proceedings of the Advances in Cryptology, 1995

1994

Schoof's algorithm and isogeny cycles.

Jean Marc Couveignes, François Morain

Proceedings of the Algorithmic Number Theory, First International Symposium, 1994

1992

Easy Numbers for the Elliptic Curve Primality Proving Algorithm.

François Morain

Proceedings of the 1992 International Symposium on Symbolic and Algebraic Computation, 1992

1991

Building Elliptic Curves Modulo Large Primes.

François Morain

Proceedings of the Advances in Cryptology, 1991

1990

Speeding up the computations on an elliptic curve using addition-subtraction chains.

François Morain, J. Olivos

RAIRO Theor. Informatics Appl., 1990

Distributed Primality Proving and the Primality of (2³⁵³⁹+1)/3.

François Morain

Proceedings of the Advances in Cryptology, 1990

1989

Atkin's Test: News From the Front.

François Morain

Proceedings of the Advances in Cryptology, 1989