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## Morain, François

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 Author ID: morain.francois Published as: Morain, F.; Morain, François External Links: MGP · Wikidata · GND
 Documents Indexed: 44 Publications since 1989, including 2 Books
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#### Co-Authors

 16 single-authored 4 Enge, Andreas 3 Gaudry, Pierrick 3 Guillevic, Aurore 3 Lercier, Reynald 3 Thomé, Emmanuel 2 Atkin, Arthur Oliver Lonsdale 2 Hanrot, Guillaume 2 Schost, Éric 1 Aardal, Karen I. 1 Barbulescu, Razvan 1 Bostan, Alin 1 Cavallar, Stefania Hedwig 1 Couveignes, Jean-Marc 1 Dodsons, Bruce 1 Dupont, Régis 1 Duursma, Iwan Maynard 1 Fouquet, Mireille 1 Franke, Jens 1 Gilchrist, Jeff 1 Grémy, Laurent 1 Guillaume, Delalleau 1 Guillerm, Gérard 1 Joux, Antoine 1 Kleinjung, Thorsten 1 Lenstra, Arjen K. 1 Leprévost, Franck 1 Leyland, Paul C. 1 Lioen, Walter M. 1 Marchand, Joël 1 Mihăilescu, Preda 1 Montgomery, Peter L. 1 Muffett, Alec 1 Murphy, Brian M. 1 Olivos, Jorge 1 Putnam, Chris 1 Putnam, Craig 1 Salvy, Bruno 1 Scribot, Charlotte 1 Shallit, Jeffrey O. 1 Smith, Benjamin J. H. 1 te Riele, Herman 1 Williams, Hugh Cowie 1 Wirth, Thomas 1 Zimmermann, Paul
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#### Serials

 7 Mathematics of Computation 2 Acta Arithmetica 2 Journal of Number Theory 2 Journal de Théorie des Nombres de Bordeaux 1 The Mathematical Intelligencer 1 Utilitas Mathematica 1 Journal of Cryptology 1 RAIRO. Informatique Théorique et Applications 1 Applicable Algebra in Engineering, Communication and Computing 1 LMS Journal of Computation and Mathematics 1 Lecture Notes in Computer Science
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#### Fields

 43 Number theory (11-XX) 18 Algebraic geometry (14-XX) 13 Information and communication theory, circuits (94-XX) 5 Computer science (68-XX) 2 Field theory and polynomials (12-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX)

#### Citations contained in zbMATH

37 Publications have been cited 297 times in 197 Documents Cited by Year
Elliptic curves and primality proving. Zbl 0792.11056
Atkin, A. O. L.; Morain, F.
1993
Isogeny volcanoes and the SEA algorithm. Zbl 1058.11041
Fouquet, Mireille; Morain, François
2002
Speeding up the computations on an elliptic curve using addition- subtraction chains. Zbl 0724.11068
Morain, François; Olivos, Jorge
1990
Fast algorithms for computing isogenies between elliptic curves. Zbl 1200.11097
Bostan, A.; Morain, F.; Salvy, B.; Schost, É.
2008
Building curves with arbitrary small MOV degree over finite prime fields. Zbl 1084.94014
Dupont, Régis; Enge, Andreas; Morain, François
2005
Speeding up the discrete log computation on curves with automorphisms. Zbl 0968.14034
Duursma, I.; Gaudry, P.; Morain, F.
1999
Comparing invariants for class fields of imaginary quadratic fields. Zbl 1058.11077
Enge, Andreas; Morain, François
2002
Computing the number of points on an elliptic curve over a finite field: algorithmic aspects. Zbl 0843.11030
Morain, François
1995
Finding suitable curves for the elliptic curve method of factorization. Zbl 0815.11063
Atkin, A. O. L.; Morain, F.
1993
Improving NFS for the discrete logarithm problem in non-prime finite fields. Zbl 1365.94399
Barbulescu, Razvan; Gaudry, Pierrick; Guillevic, Aurore; Morain, François
2015
Implementing the asymptotically fast version of the elliptic curve primality proving algorithm. Zbl 1127.11084
Morain, F.
2007
Primality proving using elliptic curves: An update. Zbl 0908.11061
Morain, F.
1998
Schoof’s algorithm and isogeny cycles. Zbl 0849.14024
Couveignes, Jean-Marc; Morain, François
1994
Fast decomposition of polynomials with known Galois group. Zbl 1030.11078
Enge, Andreas; Morain, François
2003
Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums. Zbl 0874.11044
Leprévost, F.; Morain, F.
1997
Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029
Lercier, Reynald; Morain, François
1995
Factorization of a 512-bit RSA modulus. Zbl 1082.94511
Cavallar, Stefania; Dodsons, Bruce; Lenstra, Arjen K.; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Aardal, Karen; Gilchrist, Jeff; Guillerm, Gérard; Leyland, Paul; Marchand, Joël; Morain, François; Muffett, Alec; Putnam, Chris; Putnam, Craig; Zimmermann, Paul
2000
On character sums related to elliptic curves with complex multiplication. Zbl 0841.11042
Joux, A.; Morain, F.
1995
Computing the cardinality of CM elliptic curves using torsion points. Zbl 1196.11085
Morain, François
2007
Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110
Lercier, R.; Morain, F.
1998
Distributed primality proving and the primality of $$(2^{3539} +1)/3$$. Zbl 0779.11063
Morain, François
1991
Elliptic curves and primality testing. Zbl 0947.11500
Morain, François
1990
Generalised Weber functions. Zbl 1319.11039
Enge, Andreas; Morain, François
2014
Proving the primality of very large numbers with fastECPP. Zbl 1125.11359
Franke, Jens; Kleinjung, Thorsten; Morain, François; Wirth, T.
2004
Computing isogenies between elliptic curves over $$F_{p^n}$$ using Couveignes’s algorithm. Zbl 0963.11032
Lercier, R.; Morain, F.
2000
Building cyclic elliptic curves modulo large primes. Zbl 0773.14018
Morain, François
1991
Elliptic curves, primality proving, and some Titanic primes. Zbl 0760.11041
Morain, François
1991
Solving discrete logarithms on a 170-bit MNT curve by pairing reduction. Zbl 1418.11159
Guillevic, Aurore; Morain, François; Thomé, Emmanuel
2017
Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using abelian lifts. Zbl 1190.11067
Mihailescu, P.; Morain, F.; Schost, É.
2007
Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm. Zbl 1356.11091
Gaudry, P.; Morain, F.
2006
Building pseudoprimes with a large number of prime factors. Zbl 0862.11005
Guillaume, D.; Morain, F.
1996
Computing discrete logarithms in $$\mathbb F_{p^6}$$. Zbl 1384.94066
Grémy, Laurent; Guillevic, Aurore; Morain, François; Thomé, Emmanuel
2018
Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Zbl 1196.11006
Hanrot, Guillaume (ed.); Morain, François (ed.); Thomé, Emmanuel (ed.)
2010
Primality in polynomial time (following Adleman, Huang; Agrawal, Kayal, Saxena). Zbl 1097.11059
Morain, François
2004
Solvability by radicals from an algorithmic point of view. Zbl 1356.12010
Hanrot, G.; Morain, F.
2001
Isomorphism classes of supersingular elliptic curves of characteristic $$\geq 3$$. Zbl 0898.11023
Morain, F.
1997
Easy numbers for the elliptic curve primality proving algorithm. Zbl 0921.11070
Morain, F.
1992
Computing discrete logarithms in $$\mathbb F_{p^6}$$. Zbl 1384.94066
Grémy, Laurent; Guillevic, Aurore; Morain, François; Thomé, Emmanuel
2018
Solving discrete logarithms on a 170-bit MNT curve by pairing reduction. Zbl 1418.11159
Guillevic, Aurore; Morain, François; Thomé, Emmanuel
2017
Improving NFS for the discrete logarithm problem in non-prime finite fields. Zbl 1365.94399
Barbulescu, Razvan; Gaudry, Pierrick; Guillevic, Aurore; Morain, François
2015
Generalised Weber functions. Zbl 1319.11039
Enge, Andreas; Morain, François
2014
Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Zbl 1196.11006
Hanrot, Guillaume (ed.); Morain, François (ed.); Thomé, Emmanuel (ed.)
2010
Fast algorithms for computing isogenies between elliptic curves. Zbl 1200.11097
Bostan, A.; Morain, F.; Salvy, B.; Schost, É.
2008
Implementing the asymptotically fast version of the elliptic curve primality proving algorithm. Zbl 1127.11084
Morain, F.
2007
Computing the cardinality of CM elliptic curves using torsion points. Zbl 1196.11085
Morain, François
2007
Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using abelian lifts. Zbl 1190.11067
Mihailescu, P.; Morain, F.; Schost, É.
2007
Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm. Zbl 1356.11091
Gaudry, P.; Morain, F.
2006
Building curves with arbitrary small MOV degree over finite prime fields. Zbl 1084.94014
Dupont, Régis; Enge, Andreas; Morain, François
2005
Proving the primality of very large numbers with fastECPP. Zbl 1125.11359
Franke, Jens; Kleinjung, Thorsten; Morain, François; Wirth, T.
2004
Primality in polynomial time (following Adleman, Huang; Agrawal, Kayal, Saxena). Zbl 1097.11059
Morain, François
2004
Fast decomposition of polynomials with known Galois group. Zbl 1030.11078
Enge, Andreas; Morain, François
2003
Isogeny volcanoes and the SEA algorithm. Zbl 1058.11041
Fouquet, Mireille; Morain, François
2002
Comparing invariants for class fields of imaginary quadratic fields. Zbl 1058.11077
Enge, Andreas; Morain, François
2002
Solvability by radicals from an algorithmic point of view. Zbl 1356.12010
Hanrot, G.; Morain, F.
2001
Factorization of a 512-bit RSA modulus. Zbl 1082.94511
Cavallar, Stefania; Dodsons, Bruce; Lenstra, Arjen K.; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Aardal, Karen; Gilchrist, Jeff; Guillerm, Gérard; Leyland, Paul; Marchand, Joël; Morain, François; Muffett, Alec; Putnam, Chris; Putnam, Craig; Zimmermann, Paul
2000
Computing isogenies between elliptic curves over $$F_{p^n}$$ using Couveignes’s algorithm. Zbl 0963.11032
Lercier, R.; Morain, F.
2000
Speeding up the discrete log computation on curves with automorphisms. Zbl 0968.14034
Duursma, I.; Gaudry, P.; Morain, F.
1999
Primality proving using elliptic curves: An update. Zbl 0908.11061
Morain, F.
1998
Algorithms for computing isogenies between elliptic curves. Zbl 0922.11110
Lercier, R.; Morain, F.
1998
Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums. Zbl 0874.11044
Leprévost, F.; Morain, F.
1997
Isomorphism classes of supersingular elliptic curves of characteristic $$\geq 3$$. Zbl 0898.11023
Morain, F.
1997
Building pseudoprimes with a large number of prime factors. Zbl 0862.11005
Guillaume, D.; Morain, F.
1996
Computing the number of points on an elliptic curve over a finite field: algorithmic aspects. Zbl 0843.11030
Morain, François
1995
Counting the number of points on elliptic curves over finite fields: strategies and performances. Zbl 0903.11029
Lercier, Reynald; Morain, François
1995
On character sums related to elliptic curves with complex multiplication. Zbl 0841.11042
Joux, A.; Morain, F.
1995
Schoof’s algorithm and isogeny cycles. Zbl 0849.14024
Couveignes, Jean-Marc; Morain, François
1994
Elliptic curves and primality proving. Zbl 0792.11056
Atkin, A. O. L.; Morain, F.
1993
Finding suitable curves for the elliptic curve method of factorization. Zbl 0815.11063
Atkin, A. O. L.; Morain, F.
1993
Easy numbers for the elliptic curve primality proving algorithm. Zbl 0921.11070
Morain, F.
1992
Distributed primality proving and the primality of $$(2^{3539} +1)/3$$. Zbl 0779.11063
Morain, François
1991
Building cyclic elliptic curves modulo large primes. Zbl 0773.14018
Morain, François
1991
Elliptic curves, primality proving, and some Titanic primes. Zbl 0760.11041
Morain, François
1991
Speeding up the computations on an elliptic curve using addition- subtraction chains. Zbl 0724.11068
Morain, François; Olivos, Jorge
1990
Elliptic curves and primality testing. Zbl 0947.11500
Morain, François
1990
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#### Cited by 297 Authors

 11 Morain, François 8 Sutherland, Andrew V. 7 Enge, Andreas 7 Miret, Josep M. 6 Heuberger, Clemens 6 Silverberg, Alice 5 Lercier, Reynald 5 Valls, Magda 4 Galbraith, Steven D. 4 Moody, Dustin 4 Moreno, Ramiro 4 Rubin, Karl Cooper 4 Sadornil, Daniel 4 Schost, Éric 4 Thomé, Emmanuel 3 Barbulescu, Razvan 3 Bernstein, Daniel Julius 3 Bisson, Gaetan 3 Bröker, Reinier 3 De Feo, Luca 3 Joux, Antoine 3 Kleinjung, Thorsten 3 Konstantinou, Elisavet 3 Lange, Tanja 3 Lauter, Kristin Estella 3 Robert, Damien 3 Tena Ayuso, Juan Gabriel 3 Weng, Annegret 2 Atkin, Arthur Oliver Lonsdale 2 Brent, Richard Peirce 2 Cheon, Jung Hee 2 Chiesa, Alessandro 2 Couveignes, Jean-Marc 2 Dujella, Andrej 2 Dupont, Régis 2 Duquesne, Sylvain 2 Ezome, Tony 2 Gaudry, Pierrick 2 Granger, Robert A. 2 Grantham, Jon 2 Guillevic, Aurore 2 Hong, Jin 2 Ionica, Sorina 2 Kim, Minkyu 2 Kim, Taechan 2 Kontogeorgis, Aristides I. 2 Lee, Eunjeong 2 Lee, Hyangsook 2 Lenstra, Arjen K. 2 Lenstra, Hendrik W. jun. 2 Leprévost, Franck 2 Menezes, Alfred J. 2 Mihăilescu, Preda 2 Milio, Enea 2 Muir, James A. 2 Nakazawa, Naoya 2 Park, Cheol Min 2 Prodinger, Helmut 2 Rio, Anna 2 Salvy, Bruno 2 Saouter, Yannick 2 Satoh, Takakazu 2 Schertz, Reinhard 2 Scott, Michael L. 2 Streng, Marco 2 Sun, Zhihong 2 Valera, Javier 2 Yao, David D. W. 2 Zhang, Fangguo 1 Abarzúa, Rodrigo 1 Abatzoglou, Alexander 1 Abdelaziz, Y. 1 Abelard, Simon 1 Adj, Gora 1 Ahmadi, Omran 1 Alaca, Şaban 1 Baaziz, Houria 1 Balasubramaniam, Pagavathigounder 1 Bank, Efrat 1 Barreto, Paulo S. L. M. 1 Ben-Sasson, Eli 1 Bertin, Marie-Jose 1 Binegar, Skye 1 Birkner, Peter 1 Bluher, Antonia Wilson 1 Boneh, Dan 1 Bos, Joppe W. 1 Bosma, Wieb 1 Bostan, Alin 1 Brezing, Friederike 1 Brlek, Srečko 1 Brooks, Ernest Hunter 1 Bruinier, Jan Hendrik 1 Camacho-Navarro, Catalina 1 Casteran, Pierre 1 Castro, Douglas A. 1 Charles, Denis Xavier 1 Chatterji, Samaresh 1 Chen, Binglong 1 Chen, Tien-Ren ...and 197 more Authors
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#### Cited in 59 Serials

 46 Mathematics of Computation 17 Journal of Number Theory 9 Designs, Codes and Cryptography 8 Journal of Cryptology 8 Journal de Théorie des Nombres de Bordeaux 6 Applied Mathematics and Computation 6 Finite Fields and their Applications 6 LMS Journal of Computation and Mathematics 5 Theoretical Computer Science 4 Computers & Mathematics with Applications 3 Applicable Algebra in Engineering, Communication and Computing 3 Experimental Mathematics 3 International Journal of Number Theory 3 Mathematics in Computer Science 2 Bulletin of the Australian Mathematical Society 2 Discrete Applied Mathematics 2 Periodica Mathematica Hungarica 2 Journal of Symbolic Computation 2 Journal of Complexity 2 Bulletin of the American Mathematical Society. New Series 2 Computational Complexity 2 The Ramanujan Journal 2 Foundations of Computational Mathematics 2 Journal of Physics A: Mathematical and Theoretical 2 Advances in Mathematics of Communications 1 Rocky Mountain Journal of Mathematics 1 Acta Arithmetica 1 Advances in Mathematics 1 Duke Mathematical Journal 1 Information Sciences 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Pure and Applied Algebra 1 Mathematische Annalen 1 Mathematics and Computers in Simulation 1 Osaka Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Tokyo Journal of Mathematics 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Algorithmica 1 Applied Mathematics Letters 1 SIAM Journal on Discrete Mathematics 1 International Journal of Foundations of Computer Science 1 International Journal of Computer Mathematics 1 RAIRO. Informatique Théorique et Applications 1 Cybernetics and Systems Analysis 1 Journal of Mathematical Sciences (New York) 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Journal of Integer Sequences 1 Journal of High Energy Physics 1 Journal of Mathematical Cryptology 1 Involve 1 Acta Universitatis Sapientiae. Informatica 1 Afrika Matematika 1 JSIAM Letters 1 Open Mathematics 1 Research in Number Theory 1 SIAM Journal on Applied Algebra and Geometry
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#### Cited in 19 Fields

 167 Number theory (11-XX) 88 Algebraic geometry (14-XX) 65 Information and communication theory, circuits (94-XX) 26 Computer science (68-XX) 8 Combinatorics (05-XX) 5 Field theory and polynomials (12-XX) 4 Special functions (33-XX) 4 Numerical analysis (65-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Manifolds and cell complexes (57-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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